Add lean source and binary files (part 34)

lean/OAI/Analysis/PlanarPacking/Certificate/LEntries.lean

@@ -0,0 +1,692 @@
+import OAI.Analysis.PlanarPacking.MatrixIntervals
+import OAI.Analysis.PlanarPacking.Certificate.DEntries
+import OAI.Analysis.PlanarPacking.Certificate.LMoments7
+import OAI.Analysis.PlanarPacking.Certificate.LMoments9
+import OAI.Analysis.PlanarPacking.Certificate.LMoments12
+import OAI.Analysis.PlanarPacking.Certificate.LMoments13
+import OAI.Analysis.PlanarPacking.Certificate.LMoments15
+import OAI.Analysis.PlanarPacking.Certificate.LMoments16
+import OAI.Analysis.PlanarPacking.Indices
+
+namespace OAI
+
+/-!
+# Finite interval certificates for the planar Fourier construction
+
+These rational enclosures certify the numerical bounds in the sharp planar
+Fourier construction of OpenAI. All interval endpoints are exact integers.
+-/
+
+namespace SharpPlanar.Numerical
+open IntegerIntervals IntegerBasis IntegerGrid CachedData
+noncomputable def Lmat : Matrix (Fin 12) (Fin 6) ℝ := fun i j => S (columnVector (jNode j) (jDeriv j)) (lNode i,lDeriv i)
+noncomputable def lentry0_0 : RBox := ⟨386164739228853845759773052,386164739228853847338729471⟩
+lemma lentry0_0_contains : lentry0_0.Contains (Lmat 0 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) false false cm1_7_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) false true cm1_7_0_1.contains
+  have hh := S_column_value_contains (m:=node7) h0
+  change lentry0_0.Contains (S (columnVector node1 false) (node7,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry6_0 : RBox := ⟨(-428037821451401034679013730),(-428037821451401027790023895)⟩
+lemma lentry6_0_contains : lentry6_0.Contains (Lmat 6 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) false false cm1_7_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) false true cm1_7_0_1.contains
+  have hh := S_column_derivative_contains (m:=node7) h0 h1
+  change lentry6_0.Contains (S (columnVector node1 false) (node7,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry1_0 : RBox := ⟨49064967585188068869174563,49064967585188069987341210⟩
+lemma lentry1_0_contains : lentry1_0.Contains (Lmat 1 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) false false cm1_9_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) false true cm1_9_0_1.contains
+  have hh := S_column_value_contains (m:=node9) h0
+  change lentry1_0.Contains (S (columnVector node1 false) (node9,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry7_0 : RBox := ⟨(-596386320756599937937491488),(-596386320756599933047674875)⟩
+lemma lentry7_0_contains : lentry7_0.Contains (Lmat 7 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) false false cm1_9_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) false true cm1_9_0_1.contains
+  have hh := S_column_derivative_contains (m:=node9) h0 h1
+  change lentry7_0.Contains (S (columnVector node1 false) (node9,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry2_0 : RBox := ⟨349955633020704232195660108,349955633020704238293079170⟩
+lemma lentry2_0_contains : lentry2_0.Contains (Lmat 2 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) false false cm1_12_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) false true cm1_12_0_1.contains
+  have hh := S_column_value_contains (m:=node12) h0
+  change lentry2_0.Contains (S (columnVector node1 false) (node12,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry8_0 : RBox := ⟨1156450605893201085971615858,1156450605893201123879614487⟩
+lemma lentry8_0_contains : lentry8_0.Contains (Lmat 8 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) false false cm1_12_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) false true cm1_12_0_1.contains
+  have hh := S_column_derivative_contains (m:=node12) h0 h1
+  change lentry8_0.Contains (S (columnVector node1 false) (node12,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry3_0 : RBox := ⟨(-497900663495165887403278912),(-497900663495165876692203228)⟩
+lemma lentry3_0_contains : lentry3_0.Contains (Lmat 3 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) false false cm1_13_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) false true cm1_13_0_1.contains
+  have hh := S_column_value_contains (m:=node13) h0
+  change lentry3_0.Contains (S (columnVector node1 false) (node13,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry9_0 : RBox := ⟨726695844980284058022282278,726695844980284110485485687⟩
+lemma lentry9_0_contains : lentry9_0.Contains (Lmat 9 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) false false cm1_13_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) false true cm1_13_0_1.contains
+  have hh := S_column_derivative_contains (m:=node13) h0 h1
+  change lentry9_0.Contains (S (columnVector node1 false) (node13,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry4_0 : RBox := ⟨(-129722376498730229479424854),(-129722376498730219846221208)⟩
+lemma lentry4_0_contains : lentry4_0.Contains (Lmat 4 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) false false cm1_15_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) false true cm1_15_0_1.contains
+  have hh := S_column_value_contains (m:=node15) h0
+  change lentry4_0.Contains (S (columnVector node1 false) (node15,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry10_0 : RBox := ⟨735342424357373673845647416,735342424357373720939652077⟩
+lemma lentry10_0_contains : lentry10_0.Contains (Lmat 10 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) false false cm1_15_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) false true cm1_15_0_1.contains
+  have hh := S_column_derivative_contains (m:=node15) h0 h1
+  change lentry10_0.Contains (S (columnVector node1 false) (node15,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry5_0 : RBox := ⟨5192157766382216813328101,5192157766382221815251673⟩
+lemma lentry5_0_contains : lentry5_0.Contains (Lmat 5 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) false false cm1_16_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) false true cm1_16_0_1.contains
+  have hh := S_column_value_contains (m:=node16) h0
+  change lentry5_0.Contains (S (columnVector node1 false) (node16,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry11_0 : RBox := ⟨(-373604188084837902044523338),(-373604188084837871188935056)⟩
+lemma lentry11_0_contains : lentry11_0.Contains (Lmat 11 0) := by
+  have h0 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) false false cm1_16_0_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) false true cm1_16_0_1.contains
+  have hh := S_column_derivative_contains (m:=node16) h0 h1
+  change lentry11_0.Contains (S (columnVector node1 false) (node16,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry0_3 : RBox := ⟨1237841529233122015925964342,1237841529233122021272149662⟩
+lemma lentry0_3_contains : lentry0_3.Contains (Lmat 0 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) true false cm1_7_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) true true cm1_7_1_1.contains
+  have hh := S_column_value_contains (m:=node7) h0
+  change lentry0_3.Contains (S (columnVector node1 true) (node7,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry6_3 : RBox := ⟨(-10884852847347014469371491535),(-10884852847347014445864444233)⟩
+lemma lentry6_3_contains : lentry6_3.Contains (Lmat 6 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) true false cm1_7_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=7) (by decide) (by decide) true true cm1_7_1_1.contains
+  have hh := S_column_derivative_contains (m:=node7) h0 h1
+  change lentry6_3.Contains (S (columnVector node1 true) (node7,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry1_3 : RBox := ⟨(-945531822378341432500259730),(-945531822378341427352180742)⟩
+lemma lentry1_3_contains : lentry1_3.Contains (Lmat 1 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) true false cm1_9_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) true true cm1_9_1_1.contains
+  have hh := S_column_value_contains (m:=node9) h0
+  change lentry1_3.Contains (S (columnVector node1 true) (node9,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry7_3 : RBox := ⟨(-4465708184822282113792278974),(-4465708184822282091488397712)⟩
+lemma lentry7_3_contains : lentry7_3.Contains (Lmat 7 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) true false cm1_9_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=9) (by decide) (by decide) true true cm1_9_1_1.contains
+  have hh := S_column_derivative_contains (m:=node9) h0 h1
+  change lentry7_3.Contains (S (columnVector node1 true) (node9,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry2_3 : RBox := ⟨4605024524144134428523673830,4605024524144134467976903087⟩
+lemma lentry2_3_contains : lentry2_3.Contains (Lmat 2 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) true false cm1_12_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) true true cm1_12_1_1.contains
+  have hh := S_column_value_contains (m:=node12) h0
+  change lentry2_3.Contains (S (columnVector node1 true) (node12,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry8_3 : RBox := ⟨9348829383490770441808543,9348829383491012494286692⟩
+lemma lentry8_3_contains : lentry8_3.Contains (Lmat 8 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) true false cm1_12_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=12) (by decide) (by decide) true true cm1_12_1_1.contains
+  have hh := S_column_derivative_contains (m:=node12) h0 h1
+  change lentry8_3.Contains (S (columnVector node1 true) (node12,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry3_3 : RBox := ⟨(-4308649990873823136416589661),(-4308649990873823060803451595)⟩
+lemma lentry3_3_contains : lentry3_3.Contains (Lmat 3 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) true false cm1_13_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) true true cm1_13_1_1.contains
+  have hh := S_column_value_contains (m:=node13) h0
+  change lentry3_3.Contains (S (columnVector node1 true) (node13,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry9_3 : RBox := ⟨26226240502596733865099430434,26226240502596734231105827117⟩
+lemma lentry9_3_contains : lentry9_3.Contains (Lmat 9 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) true false cm1_13_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=13) (by decide) (by decide) true true cm1_13_1_1.contains
+  have hh := S_column_derivative_contains (m:=node13) h0 h1
+  change lentry9_3.Contains (S (columnVector node1 true) (node13,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry4_3 : RBox := ⟨1369022879160941407076210245,1369022879160941487324115228⟩
+lemma lentry4_3_contains : lentry4_3.Contains (Lmat 4 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) true false cm1_15_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) true true cm1_15_1_1.contains
+  have hh := S_column_value_contains (m:=node15) h0
+  change lentry4_3.Contains (S (columnVector node1 true) (node15,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry10_3 : RBox := ⟨15723242855704063078702190943,15723242855704063465727922119⟩
+lemma lentry10_3_contains : lentry10_3.Contains (Lmat 10 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) true false cm1_15_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=15) (by decide) (by decide) true true cm1_15_1_1.contains
+  have hh := S_column_derivative_contains (m:=node15) h0 h1
+  change lentry10_3.Contains (S (columnVector node1 true) (node15,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry5_3 : RBox := ⟨(-1289552013974452050024155783),(-1289552013974452005347604255)⟩
+lemma lentry5_3_contains : lentry5_3.Contains (Lmat 5 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) true false cm1_16_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) true true cm1_16_1_1.contains
+  have hh := S_column_value_contains (m:=node16) h0
+  change lentry5_3.Contains (S (columnVector node1 true) (node16,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry11_3 : RBox := ⟨(-1539994406308444939497564809),(-1539994406308444667344235719)⟩
+lemma lentry11_3_contains : lentry11_3.Contains (Lmat 11 3) := by
+  have h0 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) true false cm1_16_1_0.contains
+  have h1 := K_column_contains (n:=node1) (m:=16) (by decide) (by decide) true true cm1_16_1_1.contains
+  have hh := S_column_derivative_contains (m:=node16) h0 h1
+  change lentry11_3.Contains (S (columnVector node1 true) (node16,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry0_1 : RBox := ⟨486118439120750072856567422,486118439120750074559192952⟩
+lemma lentry0_1_contains : lentry0_1.Contains (Lmat 0 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) false false cm3_7_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) false true cm3_7_0_1.contains
+  have hh := S_column_value_contains (m:=node7) h0
+  change lentry0_1.Contains (S (columnVector node3 false) (node7,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry6_1 : RBox := ⟨257993788917541150498000107,257993788917541157888863267⟩
+lemma lentry6_1_contains : lentry6_1.Contains (Lmat 6 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) false false cm3_7_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) false true cm3_7_0_1.contains
+  have hh := S_column_derivative_contains (m:=node7) h0 h1
+  change lentry6_1.Contains (S (columnVector node3 false) (node7,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry1_1 : RBox := ⟨119087850140090609779608152,119087850140090611010500019⟩
+lemma lentry1_1_contains : lentry1_1.Contains (Lmat 1 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) false false cm3_9_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) false true cm3_9_0_1.contains
+  have hh := S_column_value_contains (m:=node9) h0
+  change lentry1_1.Contains (S (columnVector node3 false) (node9,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry7_1 : RBox := ⟨(-663777977784782234746612750),(-663777977784782229394005574)⟩
+lemma lentry7_1_contains : lentry7_1.Contains (Lmat 7 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) false false cm3_9_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) false true cm3_9_0_1.contains
+  have hh := S_column_derivative_contains (m:=node9) h0 h1
+  change lentry7_1.Contains (S (columnVector node3 false) (node9,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry2_1 : RBox := ⟨358967247032856833332163871,358967247032856840141352766⟩
+lemma lentry2_1_contains : lentry2_1.Contains (Lmat 2 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) false false cm3_12_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) false true cm3_12_0_1.contains
+  have hh := S_column_value_contains (m:=node12) h0
+  change lentry2_1.Contains (S (columnVector node3 false) (node12,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry8_1 : RBox := ⟨1619108661149769913016706898,1619108661149769955303200794⟩
+lemma lentry8_1_contains : lentry8_1.Contains (Lmat 8 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) false false cm3_12_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) false true cm3_12_0_1.contains
+  have hh := S_column_derivative_contains (m:=node12) h0 h1
+  change lentry8_1.Contains (S (columnVector node3 false) (node12,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry3_1 : RBox := ⟨(-579591941864548585450896356),(-579591941864548573447403574)⟩
+lemma lentry3_1_contains : lentry3_1.Contains (Lmat 3 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) false false cm3_13_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) false true cm3_13_0_1.contains
+  have hh := S_column_value_contains (m:=node13) h0
+  change lentry3_1.Contains (S (columnVector node3 false) (node13,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry9_1 : RBox := ⟨377184322890016097180070227,377184322890016155875518461⟩
+lemma lentry9_1_contains : lentry9_1.Contains (Lmat 9 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) false false cm3_13_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) false true cm3_13_0_1.contains
+  have hh := S_column_derivative_contains (m:=node13) h0 h1
+  change lentry9_1.Contains (S (columnVector node3 false) (node13,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry4_1 : RBox := ⟨(-195228355766339276704702654),(-195228355766339265841016551)⟩
+lemma lentry4_1_contains : lentry4_1.Contains (Lmat 4 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) false false cm3_15_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) false true cm3_15_0_1.contains
+  have hh := S_column_value_contains (m:=node15) h0
+  change lentry4_1.Contains (S (columnVector node3 false) (node15,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry10_1 : RBox := ⟨710843065811023928625760408,710843065811023981701947655⟩
+lemma lentry10_1_contains : lentry10_1.Contains (Lmat 10 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) false false cm3_15_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) false true cm3_15_0_1.contains
+  have hh := S_column_derivative_contains (m:=node15) h0 h1
+  change lentry10_1.Contains (S (columnVector node3 false) (node15,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry5_1 : RBox := ⟨25977920002013968828483999,25977920002013974478303761⟩
+lemma lentry5_1_contains : lentry5_1.Contains (Lmat 5 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) false false cm3_16_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) false true cm3_16_0_1.contains
+  have hh := S_column_value_contains (m:=node16) h0
+  change lentry5_1.Contains (S (columnVector node3 false) (node16,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry11_1 : RBox := ⟨(-467966495451986099247977206),(-467966495451986064390183177)⟩
+lemma lentry11_1_contains : lentry11_1.Contains (Lmat 11 1) := by
+  have h0 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) false false cm3_16_0_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) false true cm3_16_0_1.contains
+  have hh := S_column_derivative_contains (m:=node16) h0 h1
+  change lentry11_1.Contains (S (columnVector node3 false) (node16,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry0_4 : RBox := ⟨2125600111687210926303952134,2125600111687210932405875170⟩
+lemma lentry0_4_contains : lentry0_4.Contains (Lmat 0 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) true false cm3_7_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) true true cm3_7_1_1.contains
+  have hh := S_column_value_contains (m:=node7) h0
+  change lentry0_4.Contains (S (columnVector node3 true) (node7,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry6_4 : RBox := ⟨(-11139267443296261033356468182),(-11139267443296261006716194412)⟩
+lemma lentry6_4_contains : lentry6_4.Contains (Lmat 6 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) true false cm3_7_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=7) (by decide) (by decide) true true cm3_7_1_1.contains
+  have hh := S_column_derivative_contains (m:=node7) h0 h1
+  change lentry6_4.Contains (S (columnVector node3 true) (node7,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry1_4 : RBox := ⟨(-780891265784406832000933468),(-780891265784406826200208949)⟩
+lemma lentry1_4_contains : lentry1_4.Contains (Lmat 1 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) true false cm3_9_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) true true cm3_9_1_1.contains
+  have hh := S_column_value_contains (m:=node9) h0
+  change lentry1_4.Contains (S (columnVector node3 true) (node9,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry7_4 : RBox := ⟨(-5743618610332307669422004880),(-5743618610332307644322228913)⟩
+lemma lentry7_4_contains : lentry7_4.Contains (Lmat 7 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) true false cm3_9_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=9) (by decide) (by decide) true true cm3_9_1_1.contains
+  have hh := S_column_derivative_contains (m:=node9) h0 h1
+  change lentry7_4.Contains (S (columnVector node3 true) (node9,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry2_4 : RBox := ⟨5321012643203737848682181032,5321012643203737892803135677⟩
+lemma lentry2_4_contains : lentry2_4.Contains (Lmat 2 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) true false cm3_12_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) true true cm3_12_1_1.contains
+  have hh := S_column_value_contains (m:=node12) h0
+  change lentry2_4.Contains (S (columnVector node3 true) (node12,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry8_4 : RBox := ⟨2776571492109706045337114003,2776571492109706316069623773⟩
+lemma lentry8_4_contains : lentry8_4.Contains (Lmat 8 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) true false cm3_12_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=12) (by decide) (by decide) true true cm3_12_1_1.contains
+  have hh := S_column_derivative_contains (m:=node12) h0 h1
+  change lentry8_4.Contains (S (columnVector node3 true) (node12,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry3_4 : RBox := ⟨(-5389978260281014816719222713),(-5389978260281014732262209926)⟩
+lemma lentry3_4_contains : lentry3_4.Contains (Lmat 3 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) true false cm3_13_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) true true cm3_13_1_1.contains
+  have hh := S_column_value_contains (m:=node13) h0
+  change lentry3_4.Contains (S (columnVector node3 true) (node13,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry9_4 : RBox := ⟨27368681932658456888679605519,27368681932658457297208750387⟩
+lemma lentry9_4_contains : lentry9_4.Contains (Lmat 9 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) true false cm3_13_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=13) (by decide) (by decide) true true cm3_13_1_1.contains
+  have hh := S_column_derivative_contains (m:=node13) h0 h1
+  change lentry9_4.Contains (S (columnVector node3 true) (node13,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry4_4 : RBox := ⟨1046331030113728873277846982,1046331030113728962453513129⟩
+lemma lentry4_4_contains : lentry4_4.Contains (Lmat 4 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) true false cm3_15_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) true true cm3_15_1_1.contains
+  have hh := S_column_value_contains (m:=node15) h0
+  change lentry4_4.Contains (S (columnVector node3 true) (node15,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry10_4 : RBox := ⟨17181475429765936689474771825,17181475429765937119960748674⟩
+lemma lentry10_4_contains : lentry10_4.Contains (Lmat 10 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) true false cm3_15_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=15) (by decide) (by decide) true true cm3_15_1_1.contains
+  have hh := S_column_derivative_contains (m:=node15) h0 h1
+  change lentry10_4.Contains (S (columnVector node3 true) (node15,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry5_4 : RBox := ⟨(-1259566801050796385474280065),(-1259566801050796335904409976)⟩
+lemma lentry5_4_contains : lentry5_4.Contains (Lmat 5 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) true false cm3_16_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) true true cm3_16_1_1.contains
+  have hh := S_column_value_contains (m:=node16) h0
+  change lentry5_4.Contains (S (columnVector node3 true) (node16,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry11_4 : RBox := ⟨(-2380512632259958830256652294),(-2380512632259958528106206527)⟩
+lemma lentry11_4_contains : lentry11_4.Contains (Lmat 11 4) := by
+  have h0 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) true false cm3_16_1_0.contains
+  have h1 := K_column_contains (n:=node3) (m:=16) (by decide) (by decide) true true cm3_16_1_1.contains
+  have hh := S_column_derivative_contains (m:=node16) h0 h1
+  change lentry11_4.Contains (S (columnVector node3 true) (node16,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry0_2 : RBox := ⟨485328626881395931714985849,485328626881395932971229801⟩
+lemma lentry0_2_contains : lentry0_2.Contains (Lmat 0 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) false false cm4_7_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) false true cm4_7_0_1.contains
+  have hh := S_column_value_contains (m:=node7) h0
+  change lentry0_2.Contains (S (columnVector node4 false) (node7,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry6_2 : RBox := ⟨767399171832372983257164636,767399171832372988906161653⟩
+lemma lentry6_2_contains : lentry6_2.Contains (Lmat 6 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) false false cm4_7_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) false true cm4_7_0_1.contains
+  have hh := S_column_derivative_contains (m:=node7) h0 h1
+  change lentry6_2.Contains (S (columnVector node4 false) (node7,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry1_2 : RBox := ⟨159432915114858452138511907,159432915114858453113123532⟩
+lemma lentry1_2_contains : lentry1_2.Contains (Lmat 1 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) false false cm4_9_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) false true cm4_9_0_1.contains
+  have hh := S_column_value_contains (m:=node9) h0
+  change lentry1_2.Contains (S (columnVector node4 false) (node9,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry7_2 : RBox := ⟨(-644392944651544272181557039),(-644392944651544267855959278)⟩
+lemma lentry7_2_contains : lentry7_2.Contains (Lmat 7 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) false false cm4_9_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) false true cm4_9_0_1.contains
+  have hh := S_column_derivative_contains (m:=node9) h0 h1
+  change lentry7_2.Contains (S (columnVector node4 false) (node9,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry2_2 : RBox := ⟨344129241302690651571586296,344129241302690657533194559⟩
+lemma lentry2_2_contains : lentry2_2.Contains (Lmat 2 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) false false cm4_12_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) false true cm4_12_0_1.contains
+  have hh := S_column_value_contains (m:=node12) h0
+  change lentry2_2.Contains (S (columnVector node4 false) (node12,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry8_2 : RBox := ⟨1856497232206901564546533917,1856497232206901601841142359⟩
+lemma lentry8_2_contains : lentry8_2.Contains (Lmat 8 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) false false cm4_12_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) false true cm4_12_0_1.contains
+  have hh := S_column_derivative_contains (m:=node12) h0 h1
+  change lentry8_2.Contains (S (columnVector node4 false) (node12,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry3_2 : RBox := ⟨(-607660233060482493251090964),(-607660233060482482498102625)⟩
+lemma lentry3_2_contains : lentry3_2.Contains (Lmat 3 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) false false cm4_13_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) false true cm4_13_0_1.contains
+  have hh := S_column_value_contains (m:=node13) h0
+  change lentry3_2.Contains (S (columnVector node4 false) (node13,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry9_2 : RBox := ⟨109451628144957371825678763,109451628144957424719076512⟩
+lemma lentry9_2_contains : lentry9_2.Contains (Lmat 9 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) false false cm4_13_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) false true cm4_13_0_1.contains
+  have hh := S_column_derivative_contains (m:=node13) h0 h1
+  change lentry9_2.Contains (S (columnVector node4 false) (node13,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry4_2 : RBox := ⟨(-232443036487199701392321254),(-232443036487199691183528398)⟩
+lemma lentry4_2_contains : lentry4_2.Contains (Lmat 4 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) false false cm4_15_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) false true cm4_15_0_1.contains
+  have hh := S_column_value_contains (m:=node15) h0
+  change lentry4_2.Contains (S (columnVector node4 false) (node15,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry10_2 : RBox := ⟨667100822413377830267050569,667100822413377880297221997⟩
+lemma lentry10_2_contains : lentry10_2.Contains (Lmat 10 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) false false cm4_15_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) false true cm4_15_0_1.contains
+  have hh := S_column_derivative_contains (m:=node15) h0 h1
+  change lentry10_2.Contains (S (columnVector node4 false) (node15,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry5_2 : RBox := ⟨39065964993206543259829543,39065964993206548649635729⟩
+lemma lentry5_2_contains : lentry5_2.Contains (Lmat 5 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) false false cm4_16_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) false true cm4_16_0_1.contains
+  have hh := S_column_value_contains (m:=node16) h0
+  change lentry5_2.Contains (S (columnVector node4 false) (node16,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry11_2 : RBox := ⟨(-515958726858467410477971212),(-515958726858467377164471438)⟩
+lemma lentry11_2_contains : lentry11_2.Contains (Lmat 11 2) := by
+  have h0 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) false false cm4_16_0_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) false true cm4_16_0_1.contains
+  have hh := S_column_derivative_contains (m:=node16) h0 h1
+  change lentry11_2.Contains (S (columnVector node4 false) (node16,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry0_5 : RBox := ⟨2615176994895548135832210442,2615176994895548142063566693⟩
+lemma lentry0_5_contains : lentry0_5.Contains (Lmat 0 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) true false cm4_7_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) true true cm4_7_1_1.contains
+  have hh := S_column_value_contains (m:=node7) h0
+  change lentry0_5.Contains (S (columnVector node4 true) (node7,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry6_5 : RBox := ⟨(-10633079943167156175729829310),(-10633079943167156148566371119)⟩
+lemma lentry6_5_contains : lentry6_5.Contains (Lmat 6 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) true false cm4_7_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=7) (by decide) (by decide) true true cm4_7_1_1.contains
+  have hh := S_column_derivative_contains (m:=node7) h0 h1
+  change lentry6_5.Contains (S (columnVector node4 true) (node7,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry1_5 : RBox := ⟨(-641704209447256286883620943),(-641704209447256281007240349)⟩
+lemma lentry1_5_contains : lentry1_5.Contains (Lmat 1 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) true false cm4_9_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) true true cm4_9_1_1.contains
+  have hh := S_column_value_contains (m:=node9) h0
+  change lentry1_5.Contains (S (columnVector node4 true) (node9,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry7_5 : RBox := ⟨(-6401538002129311513332102913),(-6401538002129311487912931512)⟩
+lemma lentry7_5_contains : lentry7_5.Contains (Lmat 7 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) true false cm4_9_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=9) (by decide) (by decide) true true cm4_9_1_1.contains
+  have hh := S_column_derivative_contains (m:=node9) h0 h1
+  change lentry7_5.Contains (S (columnVector node4 true) (node9,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry2_5 : RBox := ⟨5673870684468758906815253281,5673870684468758951656584385⟩
+lemma lentry2_5_contains : lentry2_5.Contains (Lmat 2 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) true false cm4_12_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) true true cm4_12_1_1.contains
+  have hh := S_column_value_contains (m:=node12) h0
+  change lentry2_5.Contains (S (columnVector node4 true) (node12,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry8_5 : RBox := ⟨4515061100882060574473274188,4515061100882060849421864762⟩
+lemma lentry8_5_contains : lentry8_5.Contains (Lmat 8 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) true false cm4_12_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=12) (by decide) (by decide) true true cm4_12_1_1.contains
+  have hh := S_column_derivative_contains (m:=node12) h0 h1
+  change lentry8_5.Contains (S (columnVector node4 true) (node12,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry3_5 : RBox := ⟨(-5984619825577872881362402157),(-5984619825577872795340231432)⟩
+lemma lentry3_5_contains : lentry3_5.Contains (Lmat 3 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) true false cm4_13_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) true true cm4_13_1_1.contains
+  have hh := S_column_value_contains (m:=node13) h0
+  change lentry3_5.Contains (S (columnVector node4 true) (node13,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry9_5 : RBox := ⟨27617495594282279521247988788,27617495594282279936739730868⟩
+lemma lentry9_5_contains : lentry9_5.Contains (Lmat 9 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) true false cm4_13_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=13) (by decide) (by decide) true true cm4_13_1_1.contains
+  have hh := S_column_derivative_contains (m:=node13) h0 h1
+  change lentry9_5.Contains (S (columnVector node4 true) (node13,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry4_5 : RBox := ⟨832688775810658666830659423,832688775810658757889595712⟩
+lemma lentry4_5_contains : lentry4_5.Contains (Lmat 4 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) true false cm4_15_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) true true cm4_15_1_1.contains
+  have hh := S_column_value_contains (m:=node15) h0
+  change lentry4_5.Contains (S (columnVector node4 true) (node15,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry10_5 : RBox := ⟨17872500092793652677529018879,17872500092793653116898410653⟩
+lemma lentry10_5_contains : lentry10_5.Contains (Lmat 10 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) true false cm4_15_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=15) (by decide) (by decide) true true cm4_15_1_1.contains
+  have hh := S_column_derivative_contains (m:=node15) h0 h1
+  change lentry10_5.Contains (S (columnVector node4 true) (node15,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry5_5 : RBox := ⟨(-1227193748716980633078098857),(-1227193748716980582381799584)⟩
+lemma lentry5_5_contains : lentry5_5.Contains (Lmat 5 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) true false cm4_16_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) true true cm4_16_1_1.contains
+  have hh := S_column_value_contains (m:=node16) h0
+  change lentry5_5.Contains (S (columnVector node4 true) (node16,false))
+  convert hh using 1
+  decide +kernel
+noncomputable def lentry11_5 : RBox := ⟨(-2872552850724879556441069579),(-2872552850724879247571465752)⟩
+lemma lentry11_5_contains : lentry11_5.Contains (Lmat 11 5) := by
+  have h0 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) true false cm4_16_1_0.contains
+  have h1 := K_column_contains (n:=node4) (m:=16) (by decide) (by decide) true true cm4_16_1_1.contains
+  have hh := S_column_derivative_contains (m:=node16) h0 h1
+  change lentry11_5.Contains (S (columnVector node4 true) (node16,true))
+  convert hh using 1
+  decide +kernel
+noncomputable def lEntries : Matrix (Fin 12) (Fin 6) RBox := ![![lentry0_0,lentry0_1,lentry0_2,lentry0_3,lentry0_4,lentry0_5],
+![lentry1_0,lentry1_1,lentry1_2,lentry1_3,lentry1_4,lentry1_5],
+![lentry2_0,lentry2_1,lentry2_2,lentry2_3,lentry2_4,lentry2_5],
+![lentry3_0,lentry3_1,lentry3_2,lentry3_3,lentry3_4,lentry3_5],
+![lentry4_0,lentry4_1,lentry4_2,lentry4_3,lentry4_4,lentry4_5],
+![lentry5_0,lentry5_1,lentry5_2,lentry5_3,lentry5_4,lentry5_5],
+![lentry6_0,lentry6_1,lentry6_2,lentry6_3,lentry6_4,lentry6_5],
+![lentry7_0,lentry7_1,lentry7_2,lentry7_3,lentry7_4,lentry7_5],
+![lentry8_0,lentry8_1,lentry8_2,lentry8_3,lentry8_4,lentry8_5],
+![lentry9_0,lentry9_1,lentry9_2,lentry9_3,lentry9_4,lentry9_5],
+![lentry10_0,lentry10_1,lentry10_2,lentry10_3,lentry10_4,lentry10_5],
+![lentry11_0,lentry11_1,lentry11_2,lentry11_3,lentry11_4,lentry11_5]]
+lemma lEntries_contains (i : Fin 12) (j : Fin 6) : (lEntries i j).Contains (Lmat i j) := by
+  fin_cases i <;> fin_cases j
+  · exact lentry0_0_contains
+  · exact lentry0_1_contains
+  · exact lentry0_2_contains
+  · exact lentry0_3_contains
+  · exact lentry0_4_contains
+  · exact lentry0_5_contains
+  · exact lentry1_0_contains
+  · exact lentry1_1_contains
+  · exact lentry1_2_contains
+  · exact lentry1_3_contains
+  · exact lentry1_4_contains
+  · exact lentry1_5_contains
+  · exact lentry2_0_contains
+  · exact lentry2_1_contains
+  · exact lentry2_2_contains
+  · exact lentry2_3_contains
+  · exact lentry2_4_contains
+  · exact lentry2_5_contains
+  · exact lentry3_0_contains
+  · exact lentry3_1_contains
+  · exact lentry3_2_contains
+  · exact lentry3_3_contains
+  · exact lentry3_4_contains
+  · exact lentry3_5_contains
+  · exact lentry4_0_contains
+  · exact lentry4_1_contains
+  · exact lentry4_2_contains
+  · exact lentry4_3_contains
+  · exact lentry4_4_contains
+  · exact lentry4_5_contains
+  · exact lentry5_0_contains
+  · exact lentry5_1_contains
+  · exact lentry5_2_contains
+  · exact lentry5_3_contains
+  · exact lentry5_4_contains
+  · exact lentry5_5_contains
+  · exact lentry6_0_contains
+  · exact lentry6_1_contains
+  · exact lentry6_2_contains
+  · exact lentry6_3_contains
+  · exact lentry6_4_contains
+  · exact lentry6_5_contains
+  · exact lentry7_0_contains
+  · exact lentry7_1_contains
+  · exact lentry7_2_contains
+  · exact lentry7_3_contains
+  · exact lentry7_4_contains
+  · exact lentry7_5_contains
+  · exact lentry8_0_contains
+  · exact lentry8_1_contains
+  · exact lentry8_2_contains
+  · exact lentry8_3_contains
+  · exact lentry8_4_contains
+  · exact lentry8_5_contains
+  · exact lentry9_0_contains
+  · exact lentry9_1_contains
+  · exact lentry9_2_contains
+  · exact lentry9_3_contains
+  · exact lentry9_4_contains
+  · exact lentry9_5_contains
+  · exact lentry10_0_contains
+  · exact lentry10_1_contains
+  · exact lentry10_2_contains
+  · exact lentry10_3_contains
+  · exact lentry10_4_contains
+  · exact lentry10_5_contains
+  · exact lentry11_0_contains
+  · exact lentry11_1_contains
+  · exact lentry11_2_contains
+  · exact lentry11_3_contains
+  · exact lentry11_4_contains
+  · exact lentry11_5_contains
+lemma Lmat_column (j : Fin 6) : ∑ i, |Lmat i j| < (88:ℝ)/1000 := by
+  have hh := column_bound_lt (u:=88) (v:=1000) (a:=lEntries) (by norm_num) lEntries_contains (by
+    intro k
+    fin_cases k <;> decide +kernel) j
+  simpa only [Int.cast_one,Int.cast_ofNat] using hh
+end SharpPlanar.Numerical
+
+end OAI

lean/OAI/Analysis/PlanarPacking/Certificate/LowBlock25_11.lean

@@ -0,0 +1,1361 @@
+import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues
+import OAI.Analysis.PlanarPacking.Certificate.HighHeaders25
+
+namespace OAI
+
+/-!
+# Finite interval certificates for the planar Fourier construction
+
+These rational enclosures certify the numerical bounds in the sharp planar
+Fourier construction of OpenAI. All interval endpoints are exact integers.
+-/
+
+namespace SharpPlanar.CachedData
+open IntegerIntervals IntegerBasis IntegerGrid Numerical
+namespace hm25_0_1_8
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk25_1_8 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-685),685⟩,⟨(-685),685⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-2005),2005⟩,⟨(-2005),2005⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-3181),3181⟩,⟨(-3181),3181⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-3990),3990⟩,⟨(-3990),3990⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-5495),5495⟩,⟨(-5495),5495⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-7885),7885⟩,⟨(-7885),7885⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-9822),9822⟩,⟨(-9822),9822⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-10411),10411⟩,⟨(-10411),10411⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-9160),9160⟩,⟨(-9160),9160⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-9849),9849⟩,⟨(-9849),9849⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-10695),10695⟩,⟨(-10695),10695⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-9711),9711⟩,⟨(-9711),9711⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-7168),7168⟩,⟨(-7168),7168⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-3842),3842⟩,⟨(-3842),3842⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-2143),2143⟩,⟨(-2143),2143⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-682),682⟩,⟨(-682),682⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-127),127⟩,⟨(-127),127⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-359),359⟩,⟨(-359),359⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-573),573⟩,⟨(-573),573⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-889),889⟩,⟨(-889),889⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-1363),1363⟩,⟨(-1363),1363⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-1933),1933⟩,⟨(-1933),1933⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-2518),2518⟩,⟨(-2518),2518⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-2967),2967⟩,⟨(-2967),2967⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-3101),3101⟩,⟨(-3101),3101⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-2943),2943⟩,⟨(-2943),2943⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-3517),3517⟩,⟨(-3517),3517⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-3821),3821⟩,⟨(-3821),3821⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-3552),3552⟩,⟨(-3552),3552⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-2808),2808⟩,⟨(-2808),2808⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-1774),1774⟩,⟨(-1774),1774⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-608),608⟩,⟨(-608),608⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-18),16⟩,⟨(-16),19⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-36),26⟩,⟨(-21),38⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-56),60⟩,⟨(-50),69⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-94),97⟩,⟨(-93),98⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-132),132⟩,⟨(-132),132⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-166),166⟩,⟨(-166),166⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-196),196⟩,⟨(-196),196⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-279),279⟩,⟨(-279),279⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-381),381⟩,⟨(-381),381⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-477),477⟩,⟨(-477),477⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-543),543⟩,⟨(-543),543⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-718),718⟩,⟨(-718),718⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-675),675⟩,⟨(-675),675⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-536),536⟩,⟨(-536),536⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-343),343⟩,⟨(-343),343⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-123),123⟩,⟨(-123),123⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨(-7676768073784),(-7676768073766)⟩,⟨(-14605908575067),(-14605908575049)⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨(-21574866152997),(-21574866152976)⟩,⟨(-22895594936842),(-22895594936818)⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨(-20425115398655),(-20425115398625)⟩,⟨(-5897103180259),(-5897103180232)⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨(-6836503890569),(-6836503890536)⟩,⟨3702826151609,3702826151638⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨(-137398183988),(-137398183951)⟩,⟨1703166681214,1703166681254⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨212858138627,212858138673⟩,⟨109744951907,109744951950⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨15167463163,15167463213⟩,⟨(-16788374489),(-16788374441)⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨(-941797688),(-941797638)⟩,⟨(-1214014380),(-1214014328)⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨(-71052687),(-71052627)⟩,⟨39251363,39251423⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨1116546,1116617⟩,⟨3505726,3505799⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨160959,161046⟩,⟨(-2048),(-1962)⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨3224,3304⟩,⟨(-7108),(-7026)⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-269),(-192)⟩,⟨(-457),(-381)⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-76),(-5)⟩,⟨(-48),20⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-31),16⟩,⟨(-16),31⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨616751770922520055281,616751770922536567903⟩,⟨1482854862991955564467,1482854862991972076943⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨2227140030705053388577,2227140030705103753830⟩,⟨2811091316346853721522,2811091316346904086638⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨3122324545627218894018,3122324545627287846717⟩,⟨1160213482858466982272,1160213482858535935207⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨1781214959711994244370,1781214959712061626528⟩,⟨(-845226975331142534760),(-845226975331075152390)⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨83815091482474133773,83815091482527790180⟩,⟨(-824002824982651253021),(-824002824982597596682)⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨(-234515248049863062228),(-234515248049831509059)⟩,⟨(-114665781124479313984),(-114665781124447760814)⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨(-39414894916479227494),(-39414894916467842715)⟩,⟨50835008499109099947,50835008499120484727⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨9352394638330254408,9352394638333052803⟩,⟨8921349247107716579,8921349247110514975⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨1617201512775960563,1617201512776443692⟩,⟨(-1531394414610821368),(-1531394414610338242)⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨(-226107936616013921),(-226107936615951549)⟩,⟨(-266968702210310994),(-266968702210248619)⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨(-44920617178347154),(-44920617178340776)⟩,⟨29613686910600838,29613686910607213⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨2890488222210109,2890488222210734⟩,⟨8262834278641761,8262834278642382⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨1612964942512750,1612964942512837⟩,⟨156651382285152,156651382285234⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨249732482171234,249732482171264⟩,⟨(-257998318309377),(-257998318309345)⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨13887864401581,13887864401602⟩,⟨(-92885084886623),(-92885084886602)⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨(-3411246067695),(-3411246067676)⟩,⟨(-20043166631662),(-20043166631644)⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨(-51324738865890910231936253),(-51324738865890899466044091)⟩,⟨1743804557325643496370478,1743804557325654256451707⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨(-121699531508713537596681915),(-121699531508713506853801867)⟩,⟨37858675808076932449688413,37858675808076963180643968⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨(-99806137148540871412332489),(-99806137148540825702610057)⟩,⟨108322134154961540416555302,108322134154961586121510899⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨1071601520473370361885390,1071601520473422313190676⟩,⟨122271637026096695271180107,122271637026096747229786053⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨65261054410123781472831923,65261054410123830057416538⟩,⟨47023751282192346211455634,47023751282192394798706915⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨38713873600705654787766107,38713873600705691524330906⟩,⟨(-19117704788165572514826335),(-19117704788165535780280643)⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨(-1768462483232579756501527),(-1768462483232557306963147)⟩,⟨(-19200916297754188573932758),(-19200916297754166124082852)⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨(-7285825609546130253620689),(-7285825609546118947532712)⟩,⟨(-1325784430690731354070735),(-1325784430690720047922813)⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨(-985878838777635116806878),(-985878838777630329152809)⟩,⟨2356466570227730197513854,2356466570227734985125831⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨679912762304435821367502,679912762304437588343547⟩,⟨473812697317122099988907,473812697317123866974017⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨203284790442247305320326,203284790442247946280156⟩,⟨(-169371084352800423964410),(-169371084352799783005094)⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨(-26469016767670348781515),(-26469016767670072007590)⟩,⟨(-82402717058841964933459),(-82402717058841688159543)⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨(-28965635325874585647497),(-28965635325874443904255)⟩,⟨(-7241640527719329474726),(-7241640527719187731739)⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨(-9322655857780219666001),(-9322655857780128495494)⟩,⟨5775207484890879581659,5775207484890970752195⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨(-1831791022237130214984),(-1831791022237088434513)⟩,⟨3662757122745000809050,3662757122745042589584⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨(-192086501853903899251),(-192086501853889920738)⟩,⟨1048237592671383464929,1048237592671397443463⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  · exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨(-29500010089432878658202031),(-29500010089432834273028701)⟩,⟨46693512599924699469545568,46693512599924743852349535⟩⟩
+lemma checked : cachedMomentRuleBox density0 hk25_1_8 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule false true 25 8) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density0 hk25_1_8 (tableDensity false) (fullFactor true 25 8) density0_contains hk25_1_8_contains
+noncomputable def atomAnswer : CBox := ⟨⟨(-6354439451167105921739511),(-6354439451167104929123573)⟩,⟨184690033411148593441137213,184690033411148594436267600⟩⟩
+lemma atomChecked : tableAtomBox false ha25_1_8 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 25 8) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains false true ha25_1_8 25 8 ha25_1_8_contains
+ def realAnswer : RBox := ⟨(-35854449540599984679941542),(-35854449540599939102152274)⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment false true 25 8) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm25_0_1_8
+namespace hm25_1_1_8
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk25_1_8 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-126),126⟩,⟨(-126),126⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-355),355⟩,⟨(-355),355⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-563),563⟩,⟨(-563),563⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-701),701⟩,⟨(-701),701⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-940),940⟩,⟨(-940),940⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-1298),1298⟩,⟨(-1298),1298⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-1569),1569⟩,⟨(-1569),1569⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-1643),1643⟩,⟨(-1643),1643⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-1464),1464⟩,⟨(-1464),1464⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-1617),1617⟩,⟨(-1617),1617⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-1809),1809⟩,⟨(-1809),1809⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-1676),1676⟩,⟨(-1676),1676⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-1241),1241⟩,⟨(-1241),1241⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-659),659⟩,⟨(-659),659⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-363),363⟩,⟨(-363),363⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-120),120⟩,⟨(-120),120⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-52),52⟩,⟨(-52),52⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-78),78⟩,⟨(-78),78⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-118),118⟩,⟨(-118),118⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-182),182⟩,⟨(-182),182⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-264),264⟩,⟨(-264),264⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-354),354⟩,⟨(-354),354⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-434),434⟩,⟨(-434),434⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-474),474⟩,⟨(-474),474⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-467),467⟩,⟨(-467),467⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-583),583⟩,⟨(-583),583⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-664),664⟩,⟨(-664),664⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-645),645⟩,⟨(-645),645⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-527),527⟩,⟨(-527),527⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-342),342⟩,⟨(-342),342⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-123),123⟩,⟨(-123),123⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-24),21⟩,⟨(-16),27⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-32),32⟩,⟨(-32),32⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-43),43⟩,⟨(-43),43⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-60),60⟩,⟨(-60),60⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-73),73⟩,⟨(-73),73⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-80),80⟩,⟨(-80),80⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-80),80⟩,⟨(-80),80⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-107),107⟩,⟨(-107),107⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-95),95⟩,⟨(-95),95⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-75),75⟩,⟨(-75),75⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-51),51⟩,⟨(-51),51⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨861676183919,861676183936⟩,⟨(-5448869053761),(-5448869053744)⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨(-1157989798948),(-1157989798927)⟩,⟨(-10308074515190),(-10308074515171)⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨(-4090609945207),(-4090609945188)⟩,⟨(-5462989756003),(-5462989755985)⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨(-2380970497123),(-2380970497099)⟩,⟨(-356850528185),(-356850528162)⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨(-334197316792),(-334197316768)⟩,⟨384758286092,384758286118⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨31782844958,31782844987⟩,⟨61613856966,61613856994⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨6252411133,6252411162⟩,⟨(-1470817209),(-1470817180)⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨(-26121805),(-26121777)⟩,⟨(-429127623),(-429127594)⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨(-22280499),(-22280469)⟩,⟨(-2079341),(-2079307)⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨(-282969),(-282936)⟩,⟨957397,957431⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨36128,36170⟩,⟨23496,23536⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨1738,1779⟩,⟨(-1117),(-1084)⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-11),26⟩,⟨(-146),(-109)⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-25),12⟩,⟨(-27),11⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨227359884076426880794,227359884076439950272⟩,⟨476125968365471891230,476125968365484960739⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨786794745958991330976,786794745959031603344⟩,⟨908670678829485118849,908670678829525391256⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨1090559076453108451211,1090559076453164090330⟩,⟨376408882170586664842,376408882170642303915⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨641048964971322172596,641048964971376968481⟩,⟨(-294887916103751527527),(-294887916103696731693)⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨47259258197446015781,47259258197489898396⟩,⟨(-298771883119306298232),(-298771883119262415604)⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨(-81901946142870778962),(-81901946142844906881)⟩,⟨(-50088433228463265640),(-50088433228437393555)⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨(-16745772686414216410),(-16745772686404873583)⟩,⟨16888263636004630280,16888263636013973103⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨2987169462382624136,2987169462384920903⟩,⟨3819512908793402683,3819512908795699451⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨715598521914763594,715598521915159944⟩,⟨(-469604156360907440),(-469604156360511089)⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨(-63217265707900152),(-63217265707849029)⟩,⟨(-122460556759833334),(-122460556759782209)⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨(-20557504048847648),(-20557504048842429)⟩,⟨6167518816445238,6167518816450454⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨(-91587075485558),(-91587075485054)⟩,⟨3454767487686541,3454767487687045⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨536433423945462,536433423945526⟩,⟨307920572529349,307920572529416⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨123669722671570,123669722671595⟩,⟨(-43561267662115),(-43561267662089)⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨19422109662551,19422109662568⟩,⟨(-26712964295246),(-26712964295225)⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨2180799719891,2180799719910⟩,⟨(-6656272720241),(-6656272720223)⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨(-1521003464240919405131984),(-1521003464240919058377116)⟩,⟨123262173642242573139752,123262173642242916002173⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨(-3158360230645504660084094),(-3158360230645503559198189)⟩,⟨1915582437373322800699405,1915582437373323894133462⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨84183593999868541896134,84183593999870295836785⟩,⟨4323622728685922334296666,4323622728685924086414540⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨6102174534539146150962910,6102174534539148741314601⟩,⟨793135977881053378530836,793135977881055974988923⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨4710376108348077888264080,4710376108348083134201821⟩,⟨(-7122614559022398685570274),(-7122614559022393437995466)⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨(-3244831077766239683271314),(-3244831077766233027392998)⟩,⟨(-7365811607238131853343417),(-7365811607238125199365834)⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨(-5314098728522780194677406),(-5314098728522774488129488)⟩,⟨(-636294730838900363116319),(-636294730838894656138017)⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨(-1495318061555654459556207),(-1495318061555650887620278)⟩,⟨2266491511725308264850597,2266491511725311836830549⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨617129341274432708905877,617129341274434439560126⟩,⟨945404910029166974567871,945404910029168705158451⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨402763465965768049069643,402763465965768746815402⟩,⟨(-76597696184578994796343),(-76597696184578297027428)⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨31095479164993499429333,31095479164993779469186⟩,⟨(-134482011362263582567804),(-134482011362263302533014)⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨(-34545803995592339570281),(-34545803995592192614915)⟩,⟨(-29938136619997791240533),(-29938136619997644285059)⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨(-15255410870042103634844),(-15255410870042013470482)⟩,⟨3836082697331024013341,3836082697331114178210⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨(-3000796403209440189027),(-3000796403209374260240)⟩,⟨4955309569413451460012,4955309569413517388725⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨7948080068034709121,7948080068065947923⟩,⟨2185524982807686161775,2185524982807717400505⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨161663849647828891046,161663849647839607630⟩,⟨550541955916711797137,550541955916722513710⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  · exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨(-472637240831807026294180),(-472637240831801981069773)⟩,⟨(-830928993313816052005850),(-830928993313811007930622)⟩⟩
+lemma checked : cachedMomentRuleBox density1 hk25_1_8 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule true true 25 8) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density1 hk25_1_8 (tableDensity true) (fullFactor true 25 8) density1_contains hk25_1_8_contains
+noncomputable def atomAnswer : CBox := ⟨⟨8309651589987752599623134,8309651589987753897659360⟩,⟨(-241517735999194315801273015),(-241517735999194314499948664)⟩⟩
+lemma atomChecked : tableAtomBox true ha25_1_8 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 25 8) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains true true ha25_1_8 25 8 ha25_1_8_contains
+ def realAnswer : RBox := ⟨7837014349155945473328954,7837014349155952016589587⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment true true 25 8) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm25_1_1_8
+namespace hm25_0_1_9
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk25_1_9 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-681),681⟩,⟨(-681),681⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-2058),2058⟩,⟨(-2058),2058⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-3482),3482⟩,⟨(-3482),3482⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-4792),4792⟩,⟨(-4792),4792⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-5588),5588⟩,⟨(-5588),5588⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-6442),6442⟩,⟨(-6442),6442⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-9188),9188⟩,⟨(-9188),9188⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-10887),10887⟩,⟨(-10887),10887⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-10431),10431⟩,⟨(-10431),10431⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-9165),9165⟩,⟨(-9165),9165⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-10490),10490⟩,⟨(-10490),10490⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-9944),9944⟩,⟨(-9944),9944⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-7458),7458⟩,⟨(-7458),7458⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-4000),4000⟩,⟨(-4000),4000⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-2214),2214⟩,⟨(-2214),2214⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-701),701⟩,⟨(-701),701⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-122),122⟩,⟨(-122),122⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-360),360⟩,⟨(-360),360⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-624),624⟩,⟨(-624),624⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-920),920⟩,⟨(-920),920⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-1217),1217⟩,⟨(-1217),1217⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-1431),1431⟩,⟨(-1431),1431⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-1632),1632⟩,⟨(-1632),1632⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-2370),2370⟩,⟨(-2370),2370⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-3067),3067⟩,⟨(-3067),3067⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-3419),3419⟩,⟨(-3419),3419⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-3257),3257⟩,⟨(-3257),3257⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-2758),2758⟩,⟨(-2758),2758⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-2812),2812⟩,⟨(-2812),2812⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-2486),2486⟩,⟨(-2486),2486⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-1680),1680⟩,⟨(-1680),1680⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-595),595⟩,⟨(-595),595⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-16),26⟩,⟨(-21),17⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-32),37⟩,⟨(-37),32⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-52),56⟩,⟨(-56),52⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-87),87⟩,⟨(-87),87⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-130),130⟩,⟨(-130),130⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-182),182⟩,⟨(-182),182⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-241),241⟩,⟨(-241),241⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-293),293⟩,⟨(-293),293⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-325),325⟩,⟨(-325),325⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-319),319⟩,⟨(-319),319⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-436),436⟩,⟨(-436),436⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-486),486⟩,⟨(-486),486⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-438),438⟩,⟨(-438),438⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-307),307⟩,⟨(-307),307⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-114),114⟩,⟨(-114),114⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨(-6204925147183),(-6204925147167)⟩,⟨6409759271405,6409759271422⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨(-8092517904973),(-8092517904952)⟩,⟨15015876496612,15015876496631⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨529993774665,529993774686⟩,⟨11581081041331,11581081041352⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨3160993706753,3160993706776⟩,⟨2879298144861,2879298144882⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨916582946742,916582946771⟩,⟨(-250175183121),(-250175183096)⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨15550658199,15550658228⟩,⟨(-134055389585),(-134055389555)⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨(-12123085946),(-12123085907)⟩,⟨(-4544612374),(-4544612337)⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨(-442687705),(-442687663)⟩,⟨776897981,776898028⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨38134346,38134393⟩,⟨29292126,29292176⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨1641981,1642036⟩,⟨(-1492788),(-1492731)⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨(-43904),(-43846)⟩,⟨(-88585),(-88526)⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨(-4880),(-4824)⟩,⟨126,183⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-193),(-143)⟩,⟨228,280⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-18),31⟩,⟨4,49⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-16),19⟩,⟨(-16),16⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨625008908554432864278,625008908554440890303⟩,⟨(-396660879788578540683),(-396660879788570514620)⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨1101422268895487191364,1101422268895510698533⟩,⟨(-1238394082583559355393),(-1238394082583535848234)⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨272361234252560808939,272361234252590473404⟩,⟨(-1522928526175221084076),(-1522928526175191419776)⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨(-542856805626791665189),(-542856805626758076233)⟩,⟨(-745979569788014898264),(-745979569787981309371)⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨(-389627947465243859716),(-389627947465219109382)⟩,⟨36701301545329104166,36701301545353854544⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨(-30688517175610520625),(-30688517175595632360)⟩,⟨120961659296873786132,120961659296888674392⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨28184873263560164636,28184873263565917085⟩,⟨13296041661326626735,13296041661332379181⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨3209953699459899132,3209953699461310472⟩,⟨(-5483500113380357454),(-5483500113378946118)⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨(-938269289593843692),(-938269289593602081)⟩,⟨(-596594973880895731),(-596594973880654120)⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨(-101281875385217548),(-101281875385186696)⟩,⟨145650256809403489,145650256809434343⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨20939550989190625,20939550989193763⟩,⟨18135304554707824,18135304554710958⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨3711360993579797,3711360993580117⟩,⟨(-2668666381206948),(-2668666381206630)⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨(-171162535546478),(-171162535546425)⟩,⟨(-839544670914796),(-839544670914742)⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨(-171623472374182),(-171623472374153)⟩,⟨(-85530291368123),(-85530291368097)⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨(-49827476692902),(-49827476692884)⟩,⟨8273951834356,8273951834374⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨(-9710046713639),(-9710046713622)⟩,⟨5113636011072,5113636011090⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨1782348040395987077790417,1782348040395991484618412⟩,⟨20567492407999219541586758,20567492407999223950658016⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨17906627159285202802127737,17906627159285215413820640⟩,⟨48128105524584444553121432,48128105524584457169248574⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨46135113352059665889481871,46135113352059684717609176⟩,⟨37747307915938162771297904,37747307915938181600805379⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨49676173996093278724786375,49676173996093300238610058⟩,⟨(-3663190986947985112119743),(-3663190986947963601544142)⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨17323259471135103060145005,17323259471135123294895650⟩,⟨(-28142253560527911252682333),(-28142253560527891018750820)⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨(-9220472596068107241502139),(-9220472596068091855861352)⟩,⟨(-15365531348627319509309049),(-15365531348627304122811832)⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨(-7958968269284523336225287),(-7958968269284513887944705)⟩,⟨1480759452311368048823376,1480759452311377496925071⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨(-241500691706948799187861),(-241500691706944025399526)⟩,⟨3139225008268803384162813,3139225008268808157945162⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨1057143628180672202776997,1057143628180674226460577⟩,⟨305707528221164678493123,305707528221166702191283⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨167851147879401865442486,167851147879402611677725⟩,⟨(-320536111084055909440513),(-320536111084055163209095)⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨(-86510709151127178190114),(-86510709151126907706647)⟩,⟨(-78820968763640800303614),(-78820968763640529819986)⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨(-34749922713656947196070),(-34749922713656830352458)⟩,⟨17134287315850219288858,17134287315850336132521⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨(-1200930215034073427585),(-1200930215034010061007)⟩,⟨13453100275934075120043,13453100275934138486748⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨3289273414353832365990,3289273414353871396200⟩,⟨3769518045176926457363,3769518045176965487540⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨1797480167153812337583,1797480167153831344788⟩,⟨548348647446260357393,548348647446279364559⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨490484747722228280057,490484747722235138821⟩,⟨5463276702692905267,5463276702699764022⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  · exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨19418626152145879733154726,19418626152145898171582404⟩,⟨10638239442503857852476633,10638239442503876291683122⟩⟩
+lemma checked : cachedMomentRuleBox density0 hk25_1_9 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule false true 25 9) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density0 hk25_1_9 (tableDensity false) (fullFactor true 25 9) density0_contains hk25_1_9_contains
+noncomputable def atomAnswer : CBox := ⟨⟨74234610592612814090287912,74234610592612814510514290⟩,⟨(-1303744538788490291130486),(-1303744538788489872076423)⟩⟩
+lemma atomChecked : tableAtomBox false ha25_1_9 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 25 9) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains false true ha25_1_9 25 9 ha25_1_9_contains
+ def realAnswer : RBox := ⟨93653236744758693723442638,93653236744758712782096694⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment false true 25 9) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm25_0_1_9
+namespace hm25_1_1_9
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk25_1_9 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-125),125⟩,⟨(-125),125⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-363),363⟩,⟨(-363),363⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-616),616⟩,⟨(-616),616⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-841),841⟩,⟨(-841),841⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-955),955⟩,⟨(-955),955⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-1061),1061⟩,⟨(-1061),1061⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-1466),1466⟩,⟨(-1466),1466⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-1718),1718⟩,⟨(-1718),1718⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-1665),1665⟩,⟨(-1665),1665⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-1504),1504⟩,⟨(-1504),1504⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-1774),1774⟩,⟨(-1774),1774⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-1712),1712⟩,⟨(-1712),1712⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-1290),1290⟩,⟨(-1290),1290⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-686),686⟩,⟨(-686),686⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-379),379⟩,⟨(-379),379⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-124),124⟩,⟨(-124),124⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-52),52⟩,⟨(-52),52⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-84),84⟩,⟨(-84),84⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-123),123⟩,⟨(-123),123⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-162),162⟩,⟨(-162),162⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-197),197⟩,⟨(-197),197⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-233),233⟩,⟨(-233),233⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-344),344⟩,⟨(-344),344⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-466),466⟩,⟨(-466),466⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-543),543⟩,⟨(-543),543⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-543),543⟩,⟨(-543),543⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-483),483⟩,⟨(-483),483⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-510),510⟩,⟨(-510),510⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-466),466⟩,⟨(-466),466⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-323),323⟩,⟨(-323),323⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-120),120⟩,⟨(-120),120⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-18),18⟩,⟨(-18),18⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-32),32⟩,⟨(-32),32⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-34),34⟩,⟨(-34),34⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-62),62⟩,⟨(-62),62⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-64),64⟩,⟨(-64),64⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-51),51⟩,⟨(-51),51⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-62),62⟩,⟨(-62),62⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-64),64⟩,⟨(-64),64⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-64),64⟩,⟨(-64),64⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-45),45⟩,⟨(-45),45⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨(-2944064042679),(-2944064042662)⟩,⟨477774669954,477774669970⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨(-5106101999692),(-5106101999675)⟩,⟨2358115565822,2358115565839⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨(-2105340048474),(-2105340048456)⟩,⟨3068869587140,3068869587160⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨245897132160,245897132182⟩,⟨1300951563079,1300951563097⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨264367445120,264367445137⟩,⟨102011124260,102011124277⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨26169388869,26169388887⟩,⟨(-29006141380),(-29006141357)⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨(-2096730455),(-2096730433)⟩,⟨(-3018677205),(-3018677180)⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨(-224864049),(-224864025)⟩,⟨109692604,109692628⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨4144801,4144829⟩,⟨12591147,12591173⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨596053,596079⟩,⟨(-85295),(-85267)⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨3392,3425⟩,⟨(-26264),(-26231)⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨(-1121),(-1089)⟩,⟨(-687),(-659)⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-89),(-59)⟩,⟨19,46⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-16),14⟩,⟨(-6),19⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨198377623305587919107,198377623305594313717⟩,⟨(-140683659786474947227),(-140683659786468552632)⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨350685798399569333426,350685798399588203534⟩,⟨(-430753932295538632171),(-430753932295519762070)⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨81955362353255776957,81955362353279719707⟩,⟨(-529563047315878459536),(-529563047315854516755)⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨(-191099273780070464776),(-191099273780043133903)⟩,⟨(-269295036560884515008),(-269295036560857184116)⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨(-142827852729996046894),(-142827852729975822463)⟩,⟨5484894091724748171,5484894091744972597⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨(-15418421626896351917),(-15418421626884150163)⟩,⟨43229410001970271292,43229410001982473046⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨9747715152581982791,9747715152586702813⟩,⟨6144383356685550036,6144383356690270055⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨1489402151403464918,1489402151404623166⟩,⟨(-1861289367885666783),(-1861289367884508536)⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨(-314484302321943496),(-314484302321745296)⟩,⟨(-289330774894520015),(-289330774894321817)⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨(-51753589176059638),(-51753589176034352)⟩,⟨46969934205428946,46969934205454233⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨5922639711030221,5922639711032787⟩,⟨9330120968098603,9330120968101169⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨1743996421669560,1743996421669822⟩,⟨(-464509582009339),(-464509582009078)⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨72397403025472,72397403025515⟩,⟨(-318916341898380),(-318916341898336)⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨(-42119556424453),(-42119556424431)⟩,⟨(-55936457464350),(-55936457464329)⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨(-16884383534821),(-16884383534803)⟩,⟨(-5515002542421),(-5515002542403)⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨(-3780764428865),(-3780764428849)⟩,⟨(-1754152301),(-1754152285)⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨81562333434599196285690,81562333434599336835312⟩,⟨608000093598605699712418,608000093598605841755030⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨840129750240621015954059,840129750240621465020058⟩,⟨1228319141465078976463171,1228319141465079428258352⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨1744324775574823320000172,1744324775574824041748315⟩,⟨(-137558044308561280080994),(-137558044308560557977591)⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨159485028645015311622135,159485028645016386719623⟩,⟨(-2502359152008130456031763),(-2502359152008129383610034)⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨(-3061436979009555014913064),(-3061436979009552828892329)⟩,⟨(-1717234739732084041803594),(-1717234739732081856237883)⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨(-2937988925688314462908446),(-2937988925688311675519281)⟩,⟨1593705062802402484920137,1593705062802405273104859⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨(-60492324885329956907556),(-60492324885327554855504)⟩,⟨2247382139570685894547750,2247382139570688296376742⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨1024477782254277617325723,1024477782254279125555676⟩,⟨533254435400563074360018,533254435400564582593991⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨374312715445455012592076,374312715445455744198155⟩,⟨(-310851007226989010413653),(-310851007226988278786489)⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨(-55318136232184336296528),(-55318136232184041298758)⟩,⟨(-170286437072436972671545),(-170286437072436677683133)⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨(-60813742544122928118295),(-60813742544122809427094)⟩,⟨(-5492832871199879389029),(-5492832871199760695454)⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨(-10989161723053665880465),(-10989161723053603409510)⟩,⟨17264599544554267176898,17264599544554329647587⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨2786109433081478704283,2786109433081519892343⟩,⟨6548066672165112870027,6548066672165154057937⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨2452635289558503008083,2452635289558531399521⟩,⟨984335785808601460573,984335785808629852066⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨988241195664510796610,988241195664525153705⟩,⟨(-170941220315577646550),(-170941220315563289430)⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨237149538982605449453,237149538982610770307⟩,⟨(-116232526820481102421),(-116232526820475781566)⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  �� exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨(-325998366208086735556053),(-325998366208084621841141)⟩,⟨231678492621187848583747,231678492621189962638151⟩⟩
+lemma checked : cachedMomentRuleBox density1 hk25_1_9 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule true true 25 9) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density1 hk25_1_9 (tableDensity true) (fullFactor true 25 9) density1_contains hk25_1_9_contains
+noncomputable def atomAnswer : CBox := ⟨⟨(-97076029236493680513749456),(-97076029236493679964222654)⟩,⟨1704896704569563678869169,1704896704569564226862943⟩⟩
+lemma atomChecked : tableAtomBox true ha25_1_9 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 25 9) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains true true ha25_1_9 25 9 ha25_1_9_contains
+ def realAnswer : RBox := ⟨(-97402027602701767349305509),(-97402027602701764486063795)⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment true true 25 9) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm25_1_1_9
+end SharpPlanar.CachedData
+
+end OAI

lean/OAI/Analysis/PlanarPacking/Certificate/LowBlock27_11.lean

@@ -0,0 +1,1361 @@
+import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues
+import OAI.Analysis.PlanarPacking.Certificate.HighHeaders27
+
+namespace OAI
+
+/-!
+# Finite interval certificates for the planar Fourier construction
+
+These rational enclosures certify the numerical bounds in the sharp planar
+Fourier construction of OpenAI. All interval endpoints are exact integers.
+-/
+
+namespace SharpPlanar.CachedData
+open IntegerIntervals IntegerBasis IntegerGrid Numerical
+namespace hm27_0_1_8
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk27_1_8 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-685),685⟩,⟨(-685),685⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-2005),2005⟩,⟨(-2005),2005⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-3181),3181⟩,⟨(-3181),3181⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-3990),3990⟩,⟨(-3990),3990⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-5495),5495⟩,⟨(-5495),5495⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-7885),7885⟩,⟨(-7885),7885⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-9822),9822⟩,⟨(-9822),9822⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-10411),10411⟩,⟨(-10411),10411⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-9160),9160⟩,⟨(-9160),9160⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-9849),9849⟩,⟨(-9849),9849⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-10695),10695⟩,⟨(-10695),10695⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-9711),9711⟩,⟨(-9711),9711⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-7168),7168⟩,⟨(-7168),7168⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-3842),3842⟩,⟨(-3842),3842⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-2143),2143⟩,⟨(-2143),2143⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-682),682⟩,⟨(-682),682⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-127),127⟩,⟨(-127),127⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-359),359⟩,⟨(-359),359⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-573),573⟩,⟨(-573),573⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-889),889⟩,⟨(-889),889⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-1363),1363⟩,⟨(-1363),1363⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-1933),1933⟩,⟨(-1933),1933⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-2518),2518⟩,⟨(-2518),2518⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-2967),2967⟩,⟨(-2967),2967⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-3101),3101⟩,⟨(-3101),3101⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-2943),2943⟩,⟨(-2943),2943⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-3517),3517⟩,⟨(-3517),3517⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-3821),3821⟩,⟨(-3821),3821⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-3552),3552⟩,⟨(-3552),3552⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-2808),2808⟩,⟨(-2808),2808⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-1774),1774⟩,⟨(-1774),1774⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-608),608⟩,⟨(-608),608⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-21),21⟩,⟨(-21),21⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-42),42⟩,⟨(-42),42⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-69),69⟩,⟨(-69),69⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-98),98⟩,⟨(-98),98⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-132),132⟩,⟨(-132),132⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-166),166⟩,⟨(-166),166⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-196),196⟩,⟨(-196),196⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-279),279⟩,⟨(-279),279⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-381),381⟩,⟨(-381),381⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-477),477⟩,⟨(-477),477⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-543),543⟩,⟨(-543),543⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-718),718⟩,⟨(-718),718⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-675),675⟩,⟨(-675),675⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-536),536⟩,⟨(-536),536⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-343),343⟩,⟨(-343),343⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-123),123⟩,⟨(-123),123⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨236112322393,236112322411⟩,⟨752945715858,752945715874⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨809982657286,809982657311⟩,⟨1202399369009,1202399369029⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨834886991323,834886991354⟩,⟨362818083004,362818083033⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨272903421122,272903421157⟩,⟨(-121150752964),(-121150752930)⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨5320808497,5320808532⟩,⟨(-56642865238),(-56642865199)⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨(-6139104037),(-6139103997)⟩,⟨(-2671717441),(-2671717402)⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨(-282636547),(-282636501)⟩,⟨431438485,431438534⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨21996128,21996175⟩,⟨17081288,17081336⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨754090,754154⟩,⟨(-864973),(-864910)⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨(-27485),(-27409)⟩,⟨(-29296),(-29223)⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨(-1196),(-1112)⟩,⟨662,747⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨(-33),49⟩,⟨11,91⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-47),60⟩,⟨(-46),49⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-46),46⟩,⟨(-48),44⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-35),35⟩,⟨(-35),35⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-18),18⟩,⟨(-18),18⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨294576238142774249127,294576238142778877390⟩,⟨(-255974358991331596549),(-255974358991326968277)⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨453453443324143670368,453453443324156184050⟩,⟨(-719725241826272427742),(-719725241826259914089)⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨(-12856716101884329746),(-12856716101870056633)⟩,⟨(-752955844147620856714),(-752955844147606583695)⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨(-316412453746031383328),(-316412453746015405931)⟩,⟨(-268922943294803632242),(-268922943294787654854)⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨(-147264790396274625238),(-147264790396264520982)⟩,⟨60085542357670240030,60085542357680344301⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨5046645637292126842,5046645637297314298⟩,⟨44527765178562586959,44527765178567774410⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨9701262747200185482,9701262747201976638⟩,⟨17781497910310811,17781497912101969⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨9463231443001830,9463231443399706⟩,⟨(-1688077599428520873),(-1688077599428122995)⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨(-249010561232552111),(-249010561232492828)⟩,⟨11749884785992002,11749884786051283⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨3215564948673529,3215564948680029⟩,⟨33221476367416798,33221476367423300⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨4365537719480623,4365537719481199⟩,⟨(-342750009175150),(-342750009174571)⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨45114132171305,45114132171374⟩,⟨(-611207172884612),(-611207172884540)⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨(-90410952933849),(-90410952933816)⟩,⟨(-40867829892762),(-40867829892728)⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨(-16895924803466),(-16895924803442)⟩,⟨10136826288714,10136826288742⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨(-1693244002066),(-1693244002042)⟩,⟨4457733906017,4457733906040⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨(-21694277060),(-21694277038)⟩,⟨991252395052,991252395068⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨(-19662312071973024759792959),(-19662312071973011439382558)⟩,⟨29117239336694176868997888,29117239336694190189909187⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨(-26247939183699406581431109),(-26247939183699368950121320)⟩,⟨81682036838688558073001525,81682036838688595709129200⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨23221593452584256406341245,23221593452584311176211106⟩,⟨93168950887152633504219841,93168950887152688283093802⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨65665130973662808452845225,65665130973662868740319412⟩,⟨38326164346566111295265122,38326164346566171583820983⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨41994650237887456292144595,41994650237887510219509465⟩,⟨(-21204440835605693314217171),(-21204440835605639389714586)⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨(-1166200229600422216203994),(-1166200229600383679111485)⟩,⟨(-23426151099771962983287750),(-23426151099771924445655610)⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨(-9353446672643497766776397),(-9353446672643475781194526)⟩,⟨(-2265220585521287764806082),(-2265220585521265779150537)⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨(-1380698069735461998780636),(-1380698069735451782509652)⟩,⟨3070298238625530265337561,3070298238625540481537142⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨897845552074783892617918,897845552074787840980470⟩,⟨547261112422990571101415,547261112422994519483634⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨190649410661887214687849,190649410661888527029872⟩,⟨(-242137746545053965491353),(-242137746545052653152586)⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨(-59167822588784997228078),(-59167822588784581920494)⟩,⟨(-66555990279542634306614),(-66555990279542218998853)⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨(-24151003966289567186528),(-24151003966289423791741)⟩,⟨10984872650313859691454,10984872650314003086265⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨(-467148560373953879465),(-467148560373894824431)⟩,⟨8416861998310154958353,8416861998310214013444⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨2084556537399657060184,2084556537399685169954⟩,⟨2011418006127594448232,2011418006127622557980⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨1016611071111604109228,1016611071111617247963⟩,⟨178341056106930522420,178341056106943661141⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨259926403925193274655,259926403925197614156⟩,⟨(-34039841866933531118),(-34039841866929191620)⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  · exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨12346522421619665348916831,12346522421619714793022473⟩,⟨33121184560818814384562889,33121184560818863830851977⟩⟩
+lemma checked : cachedMomentRuleBox density0 hk27_1_8 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule false true 27 8) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density0 hk27_1_8 (tableDensity false) (fullFactor true 27 8) density0_contains hk27_1_8_contains
+noncomputable def atomAnswer : CBox := ⟨⟨99788163041752915565671784,99788163041752916537381313⟩,⟨78463998134343735704008124,78463998134343736677470080⟩⟩
+lemma atomChecked : tableAtomBox false ha27_1_8 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 27 8) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains false true ha27_1_8 27 8 ha27_1_8_contains
+ def realAnswer : RBox := ⟨112134685463372580814588615,112134685463372631430403786⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment false true 27 8) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm27_0_1_8
+namespace hm27_1_1_8
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk27_1_8 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-126),126⟩,⟨(-126),126⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-355),355⟩,⟨(-355),355⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-563),563⟩,⟨(-563),563⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-701),701⟩,⟨(-701),701⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-940),940⟩,⟨(-940),940⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-1298),1298⟩,⟨(-1298),1298⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-1569),1569⟩,⟨(-1569),1569⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-1643),1643⟩,⟨(-1643),1643⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-1464),1464⟩,⟨(-1464),1464⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-1617),1617⟩,⟨(-1617),1617⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-1809),1809⟩,⟨(-1809),1809⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-1676),1676⟩,⟨(-1676),1676⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-1241),1241⟩,⟨(-1241),1241⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-659),659⟩,⟨(-659),659⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-363),363⟩,⟨(-363),363⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-120),120⟩,⟨(-120),120⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-52),52⟩,⟨(-52),52⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-78),78⟩,⟨(-78),78⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-118),118⟩,⟨(-118),118⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-182),182⟩,⟨(-182),182⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-264),264⟩,⟨(-264),264⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-354),354⟩,⟨(-354),354⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-434),434⟩,⟨(-434),434⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-474),474⟩,⟨(-474),474⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-467),467⟩,⟨(-467),467⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-583),583⟩,⟨(-583),583⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-664),664⟩,⟨(-664),664⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-645),645⟩,⟨(-645),645⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-527),527⟩,⟨(-527),527⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-342),342⟩,⟨(-342),342⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-123),123⟩,⟨(-123),123⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-29),29⟩,⟨(-29),29⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-32),32⟩,⟨(-32),32⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-43),43⟩,⟨(-43),43⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-60),60⟩,⟨(-60),60⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-73),73⟩,⟨(-73),73⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-80),80⟩,⟨(-80),80⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-80),80⟩,⟨(-80),80⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-107),107⟩,⟨(-107),107⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-95),95⟩,⟨(-95),95⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-75),75⟩,⟨(-75),75⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-51),51⟩,⟨(-51),51⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨(-87205508971),(-87205508954)⟩,⟨248992425873,248992425889⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨(-24401660957),(-24401660939)⟩,⟨477459425260,477459425278⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨143652892734,143652892759⟩,⟨254580385431,254580385450⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨90112505859,90112505881⟩,⟨20869941689,20869941707⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨11303546990,11303547015⟩,⟨(-12664928077),(-12664928053)⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨(-999338476),(-999338452)⟩,⟨(-1661437938),(-1661437912)⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨(-135700284),(-135700261)⟩,⟨55091684,55091709⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨2388687,2388714⟩,⟨7419196,7419222⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨306093,306125⟩,⟨(-80128),(-80096)⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨(-1727),(-1692)⟩,⟨(-10769),(-10736)⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨(-382),(-344)⟩,⟨(-36),4⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨(-24),13⟩,⟨(-7),31⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-19),30⟩,⟨(-19),28⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-19),19⟩,⟨(-19),19⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨92332586169843482925,92332586169847049222⟩,⟨(-88952826275509791522),(-88952826275506225227)⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨141271309712307492275,141271309712317259245⟩,⟨(-247613533525929818169),(-247613533525920051196)⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨(-10635209895209032160),(-10635209895197754940)⟩,⟨(-260594669020849474331),(-260594669020838197091)⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨(-112132265950515388646),(-112132265950502496285)⟩,⟨(-97539055794490040297),(-97539055794477147936)⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨(-54914717326021221023),(-54914717326012998513)⟩,⟨18954298919410743469,18954298919418965972⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨315353929886153300,315353929890395635⟩,⟨16479700318581383752,16479700318585626086⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨3559707395039822824,3559707395041290856⟩,⟨440456629570585309,440456629572053340⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨94872566724960790,94872566725287120⟩,⟨(-626052949633101460),(-626052949632775128)⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨(-94981335223055993),(-94981335223007381)⟩,⟨(-12375305583453617),(-12375305583405005)⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨(-1688702305844315),(-1688702305838991)⟩,⟨13038597821940537,13038597821945861⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨1708124884053305,1708124884053774⟩,⟨367848263553175,367848263553645⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨102239912293084,102239912293138⟩,⟨(-219442633977278),(-219442633977225)⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨(-25050940826606),(-25050940826581)⟩,⟨(-28429336436991),(-28429336436966)⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨(-7176222746488),(-7176222746469)⟩,⟨556815683978,556815683998⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨(-1252544708529),(-1252544708510)⟩,⟨1115343329500,1115343329518⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨(-165882517783),(-165882517767)⟩,⟨298604072812,298604072829⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨(-543080047417653689364608),(-543080047417653266220497)⟩,⟨891563804176995794995361,891563804176996218820007⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨(-168925954024356589988177),(-168925954024355264402010)⟩,⟨2479258481118213233416588,2479258481118214562862453⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨2374234808323165205770214,2374234808323167274407868⟩,⟨1502913960595526476745446,1502913960595528551631184⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨2346421908589903737832226,2346421908589906724295340⟩,⟨(-2994663583764687008194769),(-2994663583764684021644958)⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨(-2434587179379825525129684),(-2434587179379819730224551)⟩,⟨(-4337559998320114582392286),(-4337559998320108789803654)⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨(-4360899687644662128797837),(-4360899687644655168711179)⟩,⟨43695135597818795571941,43695135597825756284628⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨(-1147703551911646123825880),(-1147703551911640547517367)⟩,⟨2407443116945315241822803,2407443116945320818157633⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨839176608393561086927075,839176608393564308439609⟩,⟨903853402433109856561290,903853402433113077994402⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨422366317637304671092803,422366317637306094153939⟩,⟨(-193657660318822582476849),(-193657660318821159384747)⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨(-20014303704967351557327),(-20014303704966838770045)⟩,⟨(-151182572608669417104512),(-151182572608668904325613)⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨(-45606151437551968668538),(-45606151437551794544313)⟩,⟨(-8955099522440308364415),(-8955099522440134238472)⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨(-7885331436977376603827),(-7885331436977308111818)⟩,⟨11590805752117633252227,11590805752117701744080⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨1876308541377181690864,1876308541377215528410⟩,⟨4026181687815098803484,4026181687815132640926⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨1463737073783230631404,1463737073783249127390⟩,⟨446066062829412879425,446066062829431375449⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨527213226583975308327,527213226583984607025⟩,⟨(-159478752235177218149),(-159478752235167919437)⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨116723084400583848216,116723084400587053607⟩,⟨(-79354356151785915247),(-79354356151782709854)⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  · exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨(-457076464224024169751780),(-457076464224019061117122)⟩,⟨92978959305191460965158,92978959305196571125740⟩⟩
+lemma checked : cachedMomentRuleBox density1 hk27_1_8 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule true true 27 8) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density1 hk27_1_8 (tableDensity true) (fullFactor true 27 8) density1_contains hk27_1_8_contains
+noncomputable def atomAnswer : CBox := ⟨⟨(-130492213208446121625806332),(-130492213208446120355109256)⟩,⟨(-102606766791064886424383951),(-102606766791064885151395239)⟩⟩
+lemma atomChecked : tableAtomBox true ha27_1_8 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 27 8) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains true true ha27_1_8 27 8 ha27_1_8_contains
+ def realAnswer : RBox := ⟨(-130949289672670145895558112),(-130949289672670139316226378)⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment true true 27 8) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm27_1_1_8
+namespace hm27_0_1_9
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk27_1_9 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-681),681⟩,⟨(-681),681⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-2058),2058⟩,⟨(-2058),2058⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-3482),3482⟩,⟨(-3482),3482⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-4792),4792⟩,⟨(-4792),4792⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-5588),5588⟩,⟨(-5588),5588⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-6442),6442⟩,⟨(-6442),6442⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-9188),9188⟩,⟨(-9188),9188⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-10887),10887⟩,⟨(-10887),10887⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-10431),10431⟩,⟨(-10431),10431⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-9165),9165⟩,⟨(-9165),9165⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-10490),10490⟩,⟨(-10490),10490⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-9944),9944⟩,⟨(-9944),9944⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-7458),7458⟩,⟨(-7458),7458⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-4000),4000⟩,⟨(-4000),4000⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-2214),2214⟩,⟨(-2214),2214⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-701),701⟩,⟨(-701),701⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-122),122⟩,⟨(-122),122⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-360),360⟩,⟨(-360),360⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-624),624⟩,⟨(-624),624⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-920),920⟩,⟨(-920),920⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-1217),1217⟩,⟨(-1217),1217⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-1431),1431⟩,⟨(-1431),1431⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-1632),1632⟩,⟨(-1632),1632⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-2370),2370⟩,⟨(-2370),2370⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-3067),3067⟩,⟨(-3067),3067⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-3419),3419⟩,⟨(-3419),3419⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-3257),3257⟩,⟨(-3257),3257⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-2758),2758⟩,⟨(-2758),2758⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-2812),2812⟩,⟨(-2812),2812⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-2486),2486⟩,⟨(-2486),2486⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-1680),1680⟩,⟨(-1680),1680⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-595),595⟩,⟨(-595),595⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-27),27⟩,⟨(-27),27⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-38),38⟩,⟨(-38),38⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-56),56⟩,⟨(-56),56⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-87),87⟩,⟨(-87),87⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-130),130⟩,⟨(-130),130⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-182),182⟩,⟨(-182),182⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-241),241⟩,⟨(-241),241⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-293),293⟩,⟨(-293),293⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-325),325⟩,⟨(-325),325⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-319),319⟩,⟨(-319),319⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-436),436⟩,⟨(-436),436⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-486),486⟩,⟨(-486),486⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-438),438⟩,⟨(-438),438⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-307),307⟩,⟨(-307),307⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-114),114⟩,⟨(-114),114⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨346829739229,346829739246⟩,⟨(-248440525004),(-248440524986)⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨480213697897,480213697915⟩,⟨(-622324883743),(-622324883725)⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨41239738829,41239738851⟩,⟨(-494653927569),(-494653927547)⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨(-112311890896),(-112311890874)⟩,⟨(-119756405729),(-119756405706)⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨(-30619737894),(-30619737867)⟩,⟨7921612839,7921612861⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨(-188967957),(-188967926)⟩,⟨3767239344,3767239373⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨288935832,288935869⟩,⟨59815177,59815214⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨4282417,4282460⟩,⟨(-15626593),(-15626556)⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨(-647996),(-647946)⟩,⟨(-204916),(-204868)⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨(-9184),(-9128)⟩,⟨22361,22418⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨667,726⟩,⟨425,483⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨0,54⟩,⟨(-47),9⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-30),32⟩,⟨(-32),30⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-32),30⟩,⟨(-30),32⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-22),22⟩,⟨(-22),22⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨(-139410161232082608565),(-139410161232080491696)⟩,⟨(-113671983906713966011),(-113671983906711849138)⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨(-363821524760744250882),(-363821524760738758429)⟩,⟨(-148850529235210073768),(-148850529235204581286)⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨(-343063726911643098136),(-343063726911636494660)⟩,⟨68069235365225414985,68069235365232018507⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨(-96278272229776343138),(-96278272229768900823)⟩,⟨168764159738014142319,168764159738021584626⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨41344275133015645195,41344275133020533236⟩,⟨62742698699909795868,62742698699914683902⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨20337066981278014905,20337066981280461300⟩,⟨(-6719045853649141621),(-6719045853646695223)⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨(-1010785992466241264),(-1010785992465388547)⟩,⟨(-4588787561458447194),(-4588787561457594474)⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨(-808452732503857726),(-808452732503664711)⟩,⟨186297401282777214,186297401282970226⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨35969849082085549,35969849082114778⟩,⟨119102073005919587,119102073005948815⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨15854386283414124,15854386283417387⟩,⟨(-5910111733275270),(-5910111733272007)⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨(-778030636759837),(-778030636759534)⟩,⟨(-2115461129617714),(-2115461129617412)⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨(-312735604606155),(-312735604606110)⟩,⟨67677485466042,67677485466089⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨(-6625568611872),(-6625568611848)⟩,⟨52030818831265,52030818831290⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨7884709962322,7884709962343⟩,⟨6966560578888,6966560578909⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨2561237469068,2561237469086⟩,⟨128306375433,128306375450⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨512169624290,512169624308⟩,⟨(-155219202691),(-155219202674)⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨12103693735386307946974102,12103693735386313402205328⟩,⟨7279398790399329656213894,7279398790399335111120487⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨33437888706612282049135630,33437888706612297493437121⟩,⟨8763595748629700409461611,8763595748629715851535953⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨37087331181481161452073896,37087331181481184017769040⟩,⟨(-11595964851384707334113813),(-11595964851384684771950173)⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨13845538355480008213204074,13845538355480033175717022⟩,⟨(-27703233706622658188277528),(-27703233706622633225917968)⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨(-9938999983014026627967353),(-9938999983014004171016559)⟩,⟨(-16573735676687918765090806),(-16573735676687896306992597)⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨(-9649127696226172450366985),(-9649127696226156310057787)⟩,⟨1276400699187510761333633,1276400699187526901359245⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨(-585792527308086938379573),(-585792527308077685732376)⟩,⟨3997114252616242577108220,3997114252616251829754300⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨1358619804080255334448995,1358619804080259647995562⟩,⟨449334375578711093321661,449334375578715406890966⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨189904566938030715362957,189904566938032384211058⟩,⟨(-411160382425238084972142),(-411160382425236416131803)⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨(-115331960110284278987456),(-115331960110283725048965)⟩,⟨(-69256645131386839776072),(-69256645131386285836167)⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨(-25577665402910931218572),(-25577665402910756353971)⟩,⟨29945757392369332405424,29945757392369507269965⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨6449756565654819633056,6449756565654879807768⟩,⟨9971389513682993388415,9971389513683053563100⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨3793817555392554702561,3793817555392580439671⟩,⟨(-382564506846314832120),(-382564506846289095039)⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨751240659844113827934,751240659844125698296⟩,⟨(-1087083385433870977953),(-1087083385433859107576)⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨2851598485552892019,2851598485559099276⟩,⟨(-473613341760896737008),(-473613341760890529744)⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨(-35693914132444902836),(-35693914132442907802)⟩,⟨(-115259438334297273881),(-115259438334295278846)⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  · exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨12953037638256431880880231,12953037638256452401740004⟩,⟨(-5758270454393402619375745),(-5758270454393382099408907)⟩⟩
+lemma checked : cachedMomentRuleBox density0 hk27_1_9 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule false true 27 9) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density0 hk27_1_9 (tableDensity false) (fullFactor true 27 9) density0_contains hk27_1_9_contains
+noncomputable def atomAnswer : CBox := ⟨⟨29399797670114527021713545,29399797670114527432676744⟩,⟨(-41674510757300143431950949),(-41674510757300143021628487)⟩⟩
+lemma atomChecked : tableAtomBox false ha27_1_9 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 27 9) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains false true ha27_1_9 27 9 ha27_1_9_contains
+ def realAnswer : RBox := ⟨42352835308370958802593776,42352835308370979934416748⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment false true 27 9) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm27_0_1_9
+namespace hm27_1_1_9
+noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk27_1_9 j i k))
+noncomputable def s0_0 : CBox := ⟨⟨(-125),125⟩,⟨(-125),125⟩⟩
+lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel
+noncomputable def s0_1 : CBox := ⟨⟨(-363),363⟩,⟨(-363),363⟩⟩
+lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel
+noncomputable def s0_2 : CBox := ⟨⟨(-616),616⟩,⟨(-616),616⟩⟩
+lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel
+noncomputable def s0_3 : CBox := ⟨⟨(-841),841⟩,⟨(-841),841⟩⟩
+lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel
+noncomputable def s0_4 : CBox := ⟨⟨(-955),955⟩,⟨(-955),955⟩⟩
+lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel
+noncomputable def s0_5 : CBox := ⟨⟨(-1061),1061⟩,⟨(-1061),1061⟩⟩
+lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel
+noncomputable def s0_6 : CBox := ⟨⟨(-1466),1466⟩,⟨(-1466),1466⟩⟩
+lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel
+noncomputable def s0_7 : CBox := ⟨⟨(-1718),1718⟩,⟨(-1718),1718⟩⟩
+lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel
+noncomputable def s0_8 : CBox := ⟨⟨(-1665),1665⟩,⟨(-1665),1665⟩⟩
+lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel
+noncomputable def s0_9 : CBox := ⟨⟨(-1504),1504⟩,⟨(-1504),1504⟩⟩
+lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel
+noncomputable def s0_10 : CBox := ⟨⟨(-1774),1774⟩,⟨(-1774),1774⟩⟩
+lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel
+noncomputable def s0_11 : CBox := ⟨⟨(-1712),1712⟩,⟨(-1712),1712⟩⟩
+lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel
+noncomputable def s0_12 : CBox := ⟨⟨(-1290),1290⟩,⟨(-1290),1290⟩⟩
+lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel
+noncomputable def s0_13 : CBox := ⟨⟨(-686),686⟩,⟨(-686),686⟩⟩
+lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel
+noncomputable def s0_14 : CBox := ⟨⟨(-379),379⟩,⟨(-379),379⟩⟩
+lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel
+noncomputable def s0_15 : CBox := ⟨⟨(-124),124⟩,⟨(-124),124⟩⟩
+lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel
+noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15]
+lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by
+  fin_cases i
+  · exact c0_0
+  · exact c0_1
+  · exact c0_2
+  · exact c0_3
+  · exact c0_4
+  · exact c0_5
+  · exact c0_6
+  · exact c0_7
+  · exact c0_8
+  · exact c0_9
+  · exact c0_10
+  · exact c0_11
+  · exact c0_12
+  · exact c0_13
+  · exact c0_14
+  · exact c0_15
+noncomputable def s1_0 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel
+noncomputable def s1_1 : CBox := ⟨⟨(-52),52⟩,⟨(-52),52⟩⟩
+lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel
+noncomputable def s1_2 : CBox := ⟨⟨(-84),84⟩,⟨(-84),84⟩⟩
+lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel
+noncomputable def s1_3 : CBox := ⟨⟨(-123),123⟩,⟨(-123),123⟩⟩
+lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel
+noncomputable def s1_4 : CBox := ⟨⟨(-162),162⟩,⟨(-162),162⟩⟩
+lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel
+noncomputable def s1_5 : CBox := ⟨⟨(-197),197⟩,⟨(-197),197⟩⟩
+lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel
+noncomputable def s1_6 : CBox := ⟨⟨(-233),233⟩,⟨(-233),233⟩⟩
+lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel
+noncomputable def s1_7 : CBox := ⟨⟨(-344),344⟩,⟨(-344),344⟩⟩
+lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel
+noncomputable def s1_8 : CBox := ⟨⟨(-466),466⟩,⟨(-466),466⟩⟩
+lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel
+noncomputable def s1_9 : CBox := ⟨⟨(-543),543⟩,⟨(-543),543⟩⟩
+lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel
+noncomputable def s1_10 : CBox := ⟨⟨(-543),543⟩,⟨(-543),543⟩⟩
+lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel
+noncomputable def s1_11 : CBox := ⟨⟨(-483),483⟩,⟨(-483),483⟩⟩
+lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel
+noncomputable def s1_12 : CBox := ⟨⟨(-510),510⟩,⟨(-510),510⟩⟩
+lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel
+noncomputable def s1_13 : CBox := ⟨⟨(-466),466⟩,⟨(-466),466⟩⟩
+lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel
+noncomputable def s1_14 : CBox := ⟨⟨(-323),323⟩,⟨(-323),323⟩⟩
+lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel
+noncomputable def s1_15 : CBox := ⟨⟨(-120),120⟩,⟨(-120),120⟩⟩
+lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel
+noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15]
+lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by
+  fin_cases i
+  · exact c1_0
+  · exact c1_1
+  · exact c1_2
+  · exact c1_3
+  · exact c1_4
+  · exact c1_5
+  · exact c1_6
+  · exact c1_7
+  · exact c1_8
+  · exact c1_9
+  · exact c1_10
+  · exact c1_11
+  · exact c1_12
+  · exact c1_13
+  · exact c1_14
+  · exact c1_15
+noncomputable def s2_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel
+noncomputable def s2_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel
+noncomputable def s2_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel
+noncomputable def s2_3 : CBox := ⟨⟨(-18),18⟩,⟨(-18),18⟩⟩
+lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel
+noncomputable def s2_4 : CBox := ⟨⟨(-32),32⟩,⟨(-32),32⟩⟩
+lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel
+noncomputable def s2_5 : CBox := ⟨⟨(-34),34⟩,⟨(-34),34⟩⟩
+lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel
+noncomputable def s2_6 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel
+noncomputable def s2_7 : CBox := ⟨⟨(-48),48⟩,⟨(-48),48⟩⟩
+lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel
+noncomputable def s2_8 : CBox := ⟨⟨(-62),62⟩,⟨(-62),62⟩⟩
+lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel
+noncomputable def s2_9 : CBox := ⟨⟨(-64),64⟩,⟨(-64),64⟩⟩
+lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel
+noncomputable def s2_10 : CBox := ⟨⟨(-51),51⟩,⟨(-51),51⟩⟩
+lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel
+noncomputable def s2_11 : CBox := ⟨⟨(-62),62⟩,⟨(-62),62⟩⟩
+lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel
+noncomputable def s2_12 : CBox := ⟨⟨(-64),64⟩,⟨(-64),64⟩⟩
+lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel
+noncomputable def s2_13 : CBox := ⟨⟨(-64),64⟩,⟨(-64),64⟩⟩
+lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel
+noncomputable def s2_14 : CBox := ⟨⟨(-45),45⟩,⟨(-45),45⟩⟩
+lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel
+noncomputable def s2_15 : CBox := ⟨⟨(-23),23⟩,⟨(-23),23⟩⟩
+lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel
+noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15]
+lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by
+  fin_cases i
+  · exact c2_0
+  · exact c2_1
+  · exact c2_2
+  · exact c2_3
+  · exact c2_4
+  · exact c2_5
+  · exact c2_6
+  · exact c2_7
+  · exact c2_8
+  · exact c2_9
+  · exact c2_10
+  · exact c2_11
+  · exact c2_12
+  · exact c2_13
+  · exact c2_14
+  · exact c2_15
+noncomputable def s3_0 : CBox := ⟨⟨142610518316,142610518332⟩,⟨2733150506,2733150522⟩⟩
+lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel
+noncomputable def s3_1 : CBox := ⟨⟨249842898759,249842898775⟩,⟨(-69065115734),(-69065115717)⟩⟩
+lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel
+noncomputable def s3_2 : CBox := ⟨⟨106327903398,106327903414⟩,⟨(-118738312002),(-118738311983)⟩⟩
+lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel
+noncomputable def s3_3 : CBox := ⟨⟨(-5477857305),(-5477857285)⟩,⟨(-50563417624),(-50563417604)⟩⟩
+lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel
+noncomputable def s3_4 : CBox := ⟨⟨(-8757033692),(-8757033672)⟩,⟨(-3516661973),(-3516661954)⟩⟩
+lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel
+noncomputable def s3_5 : CBox := ⟨⟨(-677371751),(-677371732)⟩,⟨856848926,856848947⟩⟩
+lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel
+noncomputable def s3_6 : CBox := ⟨⟨57808116,57808140⟩,⟨60644848,60644869⟩⟩
+lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel
+noncomputable def s3_7 : CBox := ⟨⟨3455755,3455780⟩,⟨(-2936054),(-2936025)⟩⟩
+lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel
+noncomputable def s3_8 : CBox := ⟨⟨(-115902),(-115873)⟩,⟨(-147270),(-147244)⟩⟩
+lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel
+noncomputable def s3_9 : CBox := ⟨⟨(-5482),(-5454)⟩,⟨3620,3650⟩⟩
+lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel
+noncomputable def s3_10 : CBox := ⟨⟨72,103⟩,⟨190,222⟩⟩
+lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel
+noncomputable def s3_11 : CBox := ⟨⟨(-7),22⟩,⟨(-16),16⟩⟩
+lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel
+noncomputable def s3_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel
+noncomputable def s3_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel
+noncomputable def s3_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel
+noncomputable def s3_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),16⟩⟩
+lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel
+noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15]
+lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by
+  fin_cases i
+  · exact c3_0
+  · exact c3_1
+  · exact c3_2
+  · exact c3_3
+  · exact c3_4
+  · exact c3_5
+  · exact c3_6
+  · exact c3_7
+  · exact c3_8
+  · exact c3_9
+  · exact c3_10
+  · exact c3_11
+  · exact c3_12
+  · exact c3_13
+  · exact c3_14
+  · exact c3_15
+noncomputable def s4_0 : CBox := ⟨⟨(-47657411184425964179),(-47657411184424319908)⟩,⟨(-34944287852181586385),(-34944287852179942113)⟩⟩
+lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel
+noncomputable def s4_1 : CBox := ⟨⟨(-123992961490085935684),(-123992961490081629233)⟩,⟨(-44504380589132904570),(-44504380589128598123)⟩⟩
+lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel
+noncomputable def s4_2 : CBox := ⟨⟨(-118226064154645758623),(-118226064154640523566)⟩,⟨26386705742767143620,26386705742772378667⟩⟩
+lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel
+noncomputable def s4_3 : CBox := ⟨⟨(-35150493455491571288),(-35150493455485567329)⟩,⟨60004017678160870449,60004017678166874405⟩⟩
+lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel
+noncomputable def s4_4 : CBox := ⟨⟨13817758987589870254,13817758987593843569⟩,⟨23714524861303863492,23714524861307836805⟩⟩
+lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel
+noncomputable def s4_5 : CBox := ⟨⟨7679038192310822543,7679038192312821332⟩,⟨(-1760361925414144720),(-1760361925412145932)⟩⟩
+lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel
+noncomputable def s4_6 : CBox := ⟨⟨(-165713200480049106),(-165713200479350542)⟩,⟨(-1729433169965335588),(-1729433169964637026)⟩⟩
+lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel
+noncomputable def s4_7 : CBox := ⟨⟨(-310173628923344858),(-310173628923186588)⟩,⟨25397330915171164,25397330915329438⟩⟩
+lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel
+noncomputable def s4_8 : CBox := ⟨⟨5561216272473930,5561216272497892⟩,⟨47483422688674226,47483422688698188⟩⟩
+lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel
+noncomputable def s4_9 : CBox := ⟨⟨6608115253217682,6608115253220357⟩,⟨(-874067925667197),(-874067925664523)⟩⟩
+lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel
+noncomputable def s4_10 : CBox := ⟨⟨(-55651131425187),(-55651131424939)⟩,⟨(-897738693692888),(-897738693692641)⟩⟩
+lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel
+noncomputable def s4_11 : CBox := ⟨⟨(-124995001738667),(-124995001738632)⟩,⟨(-18799349190581),(-18799349190545)⟩⟩
+lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel
+noncomputable def s4_12 : CBox := ⟨⟨(-10481694194206),(-10481694194184)⟩,⟨17070153290210,17070153290229⟩⟩
+lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel
+noncomputable def s4_13 : CBox := ⟨⟨1440446123786,1440446123806⟩,⟨3563403327007,3563403327027⟩⟩
+lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel
+noncomputable def s4_14 : CBox := ⟨⟨778060387319,778060387337⟩,⟨456227364140,456227364157⟩⟩
+lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel
+noncomputable def s4_15 : CBox := ⟨⟨181026471841,181026471857⟩,⟨34989974336,34989974352⟩⟩
+lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel
+noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15]
+lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by
+  fin_cases i
+  · exact c4_0
+  · exact c4_1
+  · exact c4_2
+  · exact c4_3
+  · exact c4_4
+  · exact c4_5
+  · exact c4_6
+  · exact c4_7
+  · exact c4_8
+  · exact c4_9
+  · exact c4_10
+  · exact c4_11
+  · exact c4_12
+  · exact c4_13
+  · exact c4_14
+  · exact c4_15
+noncomputable def s5_0 : CBox := ⟨⟨369367665879580202393273,369367665879580375883565⟩,⟨199212744585614001297050,199212744585614174433273⟩⟩
+lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel
+noncomputable def s5_1 : CBox := ⟨⟨1001030338273275909586722,1001030338273276454834522⟩,⟨13353493361891725680138,13353493361892269180773⟩⟩
+lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel
+noncomputable def s5_2 : CBox := ⟨⟨550146572974299569649039,550146572974300424297950⟩,⟨(-994927036538584056348085),(-994927036538583204136519)⟩⟩
+lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel
+noncomputable def s5_3 : CBox := ⟨⟨(-1280239346918605901175569),(-1280239346918604664396418)⟩,⟨(-873992444766664778110412),(-873992444766663541160144)⟩⟩
+lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel
+noncomputable def s5_4 : CBox := ⟨⟨(-1704951756388985981561905),(-1704951756388983568475735)⟩,⟨1128215079978809204715988,1128215079978811618725125⟩⟩
+lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel
+noncomputable def s5_5 : CBox := ⟨⟨166538236428215005562745,166538236428217921361890⟩,⟨1803079047090733285217644,1803079047090736200710345⟩⟩
+lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel
+noncomputable def s5_6 : CBox := ⟨⟨1051201484630934839197165,1051201484630937186191880⟩,⟨386824651870590747166202,386824651870593094178576⟩⟩
+lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel
+noncomputable def s5_7 : CBox := ⟨⟨345541298688379222647412,345541298688380582882702⟩,⟨(-394589667221981741496225),(-394589667221980381236665)⟩⟩
+lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel
+noncomputable def s5_8 : CBox := ⟨⟨(-103722052756287769112652),(-103722052756287167584167)⟩,⟨(-171241321172821364562544),(-171241321172820763045824)⟩⟩
+lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel
+noncomputable def s5_9 : CBox := ⟨⟨(-64387079854660342107058),(-64387079854660125555649)⟩,⟨16973916574994970793781,16973916574995187348677⟩⟩
+lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel
+noncomputable def s5_10 : CBox := ⟨⟨(-1166182044524953386151),(-1166182044524879879907)⟩,⟨20523651105845281590295,20523651105845355095746⟩⟩
+lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel
+noncomputable def s5_11 : CBox := ⟨⟨5649958961856081441395,5649958961856110325251⟩,⟨2730472258024140572856,2730472258024169456835⟩⟩
+lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel
+noncomputable def s5_12 : CBox := ⟨⟨1667310118995860689951,1667310118995875768943⟩,⟨(-1121250489393632693418),(-1121250489393617614408)⟩⟩
+lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel
+noncomputable def s5_13 : CBox := ⟨⟨92538141776312096268,92538141776319968097⟩,⟨(-691871420209300020391),(-691871420209292148580)⟩⟩
+lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel
+noncomputable def s5_14 : CBox := ⟨⟨(-112522698152170396692),(-112522698152165906418)⟩,⟨(-226323866405440247888),(-226323866405435757619)⟩⟩
+lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel
+noncomputable def s5_15 : CBox := ⟨⟨(-45092469266346435137),(-45092469266344942048)⟩,⟨(-46766734199651946062),(-46766734199650452975)⟩⟩
+lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel
+noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15]
+lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by
+  fin_cases i
+  · exact c5_0
+  · exact c5_1
+  · exact c5_2
+  · exact c5_3
+  · exact c5_4
+  · exact c5_5
+  · exact c5_6
+  · exact c5_7
+  · exact c5_8
+  · exact c5_9
+  · exact c5_10
+  · exact c5_11
+  · exact c5_12
+  · exact c5_13
+  · exact c5_14
+  · exact c5_15
+noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5]
+lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by
+  fin_cases j
+  · exact s0_eq i
+  · exact s1_eq i
+  · exact s2_eq i
+  · exact s3_eq i
+  · exact s4_eq i
+  · exact s5_eq i
+noncomputable def ans : CBox := ⟨⟨56051229487997091442157,56051229487999228071322⟩,⟨189017268752003850466894,189017268752005986476396⟩⟩
+lemma checked : cachedMomentRuleBox density1 hk27_1_9 = ans := by
+  change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans
+  simp_rw [sums_eq]
+  decide +kernel
+lemma contains : ans.Contains (fullMomentRule true true 27 9) := by
+  rw [← checked]
+  exact @cached_density_rule_contains density1 hk27_1_9 (tableDensity true) (fullFactor true 27 9) density1_contains hk27_1_9_contains
+noncomputable def atomAnswer : CBox := ⟨⟨(-38445889260918997411961895),(-38445889260918996874548482)⟩,⟨54497437144161725489821868,54497437144161726026397394⟩⟩
+lemma atomChecked : tableAtomBox true ha27_1_9 = atomAnswer := by decide +kernel
+lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 27 9) := by
+  rw [← atomChecked]
+  exact @fullAtomBox_contains true true ha27_1_9 27 9 ha27_1_9_contains
+ def realAnswer : RBox := ⟨(-38389838031431000420519738),(-38389838031430997546477160)⟩
+lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel
+lemma realContains : realAnswer.Contains (fullMoment true true 27 9) := by
+  rw [← realChecked]
+  exact fullMoment_contains atomContains contains (by norm_num) (by norm_num)
+end hm27_1_1_9
+end SharpPlanar.CachedData
+
+end OAI