chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
23,928 | lean_file_chunk | 47c85453428239f57a7f2fdfb32e357aae96ecf270ed09133f81eb68d4015339 | lean_source_file | lean_pool_source_file_chunks | have hmtheta : 2 * (m : ℝ) * eps <= theta := hmleD.trans hthetaD
exact (one_add_eps_pow_sub_one_le_two_nat_mul heps hsmallm).trans hmtheta
private theorem one_add_degree_eps_pow_sub_one_le_one_div_sixtyfour
{m D : Nat} (hmD : m <= D) :
(1 + (1 / (128 * ((D + 1 : Nat) : ℝ)))) ^ m - 1 <=
(1 / 64 : ℝ) := ... |
23,999 | lean_file_chunk | a12f27baf96be0fede6e856a670fa7ebc22f91b925a9cbf6e316a82f17e19ca3 | lean_source_file | lean_pool_source_file_chunks | private theorem carrierIocImage_subset_arcSet {N : Nat} (k : Fin N) :
carrierIocImage k ⊆ arcSet (carrierArc N k) := by
unfold carrierIocImage
rw [carrierArc_arcSet_eq_mk_image_Icc_wip k]
exact Set.image_mono Set.Ioc_subset_Icc_self
private theorem carrierIocImage_subset_closedBall_of_arc_mem
{N : Nat} (... |
23,970 | lean_file_chunk | 59a4cbf87deabc26450ae55bea8a0c1ba8f109bd7ccd5af9fa310f47fba32f3c | lean_source_file | lean_pool_source_file_chunks | simp_all
have hsum := carrierIocImage_setIntegral_biUnion_finset_wip
(N := N) K (fun _ : Circle => (1 : ℝ)) hf
have hleft :
(∫ x in U, (1 : ℝ) ∂ μCircle) = μCircle.real U := by
simp_all
have hright :
(∑ k ∈ K, ∫ x in carrierIocImage k, (1 : ℝ) ∂ μCircle) =
∑ k ∈ K, (N : ℝ)⁻¹ := by
... |
23,940 | lean_file_chunk | 802c3968792f940ea349e2ec31e0f5d0bb84800612aae2256d35e4d33f479dc8 | lean_source_file | lean_pool_source_file_chunks | ∀ x ∈ arcSet (carrierArc N k),
‖slowBandPoly p x - slowBandPoly p (carrierBase k)‖ <=
(∑ m : Fin L, ‖p m‖ * (m.1 : ℝ)) *
arcLength (carrierArc N k) := by
intro x hx
have hchord := carrierArc_chord_le_length k x hx
let S : ℝ := ∑ m : Fin L, ‖p m‖ * (m.1 : ℝ)
have hS_nonneg : 0 <= S := by ... |
23,961 | lean_file_chunk | 5e7baaa18d2cdada57345963d38cf70e2b80a96bfae8c7535eb3ba5e07f641b8 | lean_source_file | lean_pool_source_file_chunks | carrierAverage (N := N) k (slowBandPoly p)‖ ^ 2 ∂ μCircle
have hraw :
X <= 4 * Crot * Dint + 4 * Crot * E + 2 * Crot * V := by
exact goodCarrier_average_mass_le_actual_defect_plus_errors
(q := q) hq p hdelta_pos htheta_nonneg htheta_le hgood hosc
have hE :
4 * Crot * E <= (1 / 2) * X +
... |
23,986 | lean_file_chunk | f603823d44e061a20f9ab24d821d483b8023212b6cc404f9840f6535e34b50df | lean_source_file | lean_pool_source_file_chunks | have hperiod_nonneg : 0 <= (2 * Real.pi : ℝ) := by positivity
have hmul :
(2 * Real.pi) *
(∫ x in s, ‖slowBandPoly p x‖ ^ 2 ∂ μCircle) <=
(2 * Real.pi) *
(((L : ℝ) * circleL2Sq (bandPoly N p)) * (N : ℝ)⁻¹) := by
rw [hband]
exact mul_le_mul_of_nonneg_left hband_bound hperiod_n... |
23,989 | lean_file_chunk | 06085e3333b3b1bcfc832b2c8527244fda690715db530f6c2d999c33f7e8bb03 | lean_source_file | lean_pool_source_file_chunks | (1 / (128 * ((D + 1 : Nat) : ℝ))) * delta) :
circleL2Sq (slowBandPoly p) <=
(1 / (2 * Real.pi)) *
(8 * Crot * defectSq (lowPoly q) (bandPoly N p) +
(8 * Crot * (4 * (1 / 64 : ℝ)) ^ 2 + 4 * Crot) *
((4 * Real.pi ^ 2 * ((L : ℝ) - 1) ^ 2 / (N : ℝ) ^ 2) *
circleL2Sq (sl... |
1,062 | lean_file_chunk | e768f6f478f50645f45c215797b74d5d180ce1f00987b9d25e9f78bd7b932925 | lean_source_file | lean_pool_source_file_chunks | have hmain : M <= 256 * Def + (3 / 4) * M := by nlinarith
have hM_le : M <= 1024 * Def := by nlinarith
have hconst : (1024 : ℝ) <= circleConst D :=
one_thousand_twenty_four_le_circleConst D
have hDef_nonneg : 0 <= Def := by
dsimp [Def]
exact defectSq_nonneg (lowPoly q) (bandPol... |
7,374 | lean_file_chunk | 3e5032f38684a32993d48d9ff974a38a52ef08f63da15f7622954760f04bbe98 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
/-
# Definitions.lean
Core shared definitions for the Hermite phase-retrieval scaffold.
Scaffolding notes:
- `B... |
6,302 | lean_file_chunk | d598b808e403d8c74b2c3b9a788af8f3107df3fa911717c4db99caef2f8536ed | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
/-
# ImportedAnalyticInputs.lean
Black-box analytic inputs reused from the verified Fock-space development.
Scaff... |
4,408 | lean_file_chunk | 4bd8d810b53ad90d250577f59903438257451fd7b2bff674c78ca43ce7e6d5a4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
/-
# MissingMathlib.lean
Small convenience lemmas likely to stay project-local.
This file collects small reusable... |
23,985 | lean_file_chunk | 93d28069310af55d27a5320de1b80304b1ee308f3c0dd80853f67d2f70ce7c65 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Hermite1Dimd.ProductBasisAndAnnuli
import LeanPool.PhaseRetrieval.DimdP... |
23,991 | lean_file_chunk | 59c2804da4e0f5bd7e0a9939fee62a0af9c2852d268b7514af782d22a669f3ba | lean_source_file | lean_pool_source_file_chunks | {d : ℕ} (hd : d ≠ 0) (ℓ : MultiIndex d) {r : ℕ} (hr : 1 ≤ r) :
∃ f : {j : MultiIndex d // blockDistance j ℓ = r} → {x // x ∈ shellFinset d r},
Function.Injective f := by
refine ⟨fun j => ⟨(fun q => (j.1 q : ℤ) - ℓ q), by
simpa [shellFinset, Finset.mem_sdiff] using shell_offset_mem_cube_sdiff hd j.2 hr... |
13,510 | lean_file_chunk | b57bd823e9fff7b9804a4c3e1cdd94fe1f48ab154540d493a214d58216c806a9 | lean_source_file | lean_pool_source_file_chunks | else 0) ≤
localizationLeakageCoefficient C c B d M)
(s : Finset (MultiIndex d)) (M : ℕ) (G : FiniteHermiteSum d) :
Finset.sum s (fun j => annulusMass j (evalHermiteSum κ (remainderPart j M G))) ≤
localizationLeakageCoefficient C c B d M * hermiteNormSq κ G := by
have hpoint :
∀ j : Multi... |
13,229 | lean_file_chunk | 3ab96c9ce99c828530cf48c8dc66585d171ae8092e2396e5525d3b72267bcc37 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import Mathlib.Analysis.Fourier.AddCircle
import Mathlib.Analysis.SpecialFunctions.PolarCoord
import Mathlib.LinearAlgeb... |
18,382 | lean_file_chunk | 158b0c68cec8cf3c770e05e11450a2241629874605b619e9af890aaf3fcf2ed8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Hermite1Dimd.BlockLocalization
/-! # DegreeBookkeeping -/
open Compl... |
23,964 | lean_file_chunk | d30f3e3368f9f9fc09400a5c7292a45a69e15bb99372e0ca9a8464f66d2e9cb2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Hermite1Dimd.Definitions
import Mathlib.MeasureTheory.Integral.Pi
impor... |
23,970 | lean_file_chunk | 105cd8e6db299594f6d64c9c57aa59cfbabbf324af93ee8f8f7aeff90deb2054 | lean_source_file | lean_pool_source_file_chunks | HermiteLEAN.circleL2Sq (HermiteLEAN.positiveTrigonometricPolynomial E b) by
rfl]
rw [show circleL2NormSq (fun t => rho 1 (positiveFrequencyPolynomial E b t)) =
HermiteLEAN.circleRhoNormSq (HermiteLEAN.positiveTrigonometricPolynomial E b) by
simp [circleL2NormSq, rho, positiveFrequencyPolynomial, Her... |
2,779 | lean_file_chunk | 8a1035afd0f4f76a344643321e9c41a567d17f782efc12c8374dec7315fec409 | lean_source_file | lean_pool_source_file_chunks | (volume : Measure ℂ) := by
intro q
exact integrable_weighted_coord_of_integrable_gaussian (F q) (G q) (hFG q)
have hprod_volume :
Integrable
(fun z : CSpace d =>
∏ q : Fin d,
((((1 / Real.pi) * Real.exp (-‖z q‖ ^ 2) : ℝ) : ℂ) *
(F q (z q) * conj (G q (z q)))))... |
23,950 | lean_file_chunk | 475c3059a69998bda5679c9db3417bb03f991a4db1db6a830e31bfac5f9e244a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Hermite1Dimd.DegreeBookkeeping
/-! # ProductAnnulusCircle -/
open C... |
12,863 | lean_file_chunk | 65cfad5420673614f8c2d7e44848e7507050aaa69b77385de84795556bb6a704 | lean_source_file | lean_pool_source_file_chunks | ENNReal.ofReal (defectAnnulusMass κ j (evalHermiteSum κ (localPart j M G))) =
∫⁻ z : CSpace d,
Set.indicator (productAnnulus j)
(fun z =>
ENNReal.ofReal
(circleL2NormSq (fun t : Circle => rho (nuKappa κ z) (localOrbit κ j M G z t)))) z
∂ gaussianMeasure d := by
... |
23,990 | lean_file_chunk | fc490eb87f067de5676a305e45e1b3409bda745e9ce70a86cf5d9a60f47c2d8c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Hermite1Dimd.ImportedAnalyticInputs
import LeanPool.PhaseRetrieval.Dimd... |
19,145 | lean_file_chunk | 989822f5044c9b7c8b3b5af24bb0ff53ad02ce5c29a01649d64c72bbb923deee | lean_source_file | lean_pool_source_file_chunks | z ∈ productAnnulus j ↔
(fun q => Complex.exp (Complex.I * t) * z q) ∈ productAnnulus j := by
have hnorm : ‖Complex.exp (Complex.I * t)‖ = 1 := by simp []
simp [productAnnulus, hnorm]
private def mulCircleLIE (ω : _root_.Circle) : ℂ ≃ₗᵢ[ℝ] ℂ := by
refine LinearIsometryEquiv.mk
(LinearEquiv.ofBijective
... |
23,978 | lean_file_chunk | 2f5736c1d64976899466c302e08e1ab4b04fa96e3093f8e1322221ec1e4859f6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
/-
# BasisLocalization.lean
Statement-only scaffold for annulus localization of the true-level basis.
Scaffolding... |
23,987 | lean_file_chunk | f9fddfb21f0db02bb2a80b9f9bed018e1716c9ba77ab5f965ed60bf175d38e78 | lean_source_file | lean_pool_source_file_chunks | circleL2Sq (finiteCirclePoly k r a)) := by
let F : ℂ → ℝ := fun z => ‖finiteHermiteSum k a z‖ ^ 2 * Real.exp (-‖z‖ ^ 2)
have hannulus_meas : MeasurableSet (annulus j) := by
refine (measurableSet_le measurable_const measurable_norm).inter ?_
exact measurableSet_lt measurable_norm measurable_const
unfold He... |
23,954 | lean_file_chunk | 08eebd011a735d6ed97aa5cc03de2e5136565d24b31e9405e0227494348a6386 | lean_source_file | lean_pool_source_file_chunks | simp_all
calc
2 * ∫ r in (j : ℝ)..(((j + 1 : ℕ) : ℝ)), phi0AnnulusIntegrand k (‖g 0‖ ^ 2) r
≤
2 * ∫ r in (j : ℝ)..(((j + 1 : ℕ) : ℝ)),
(‖g 0‖ ^ 2 / (Nat.factorial k : ℝ)) *
((((j + 1 : ℕ) : ℝ) ^ (2 * k + 1))) * Real.exp (-(j : ℝ) ^ 2) := by gcongr
_ =
(2 * (‖g 0‖ ^ 2 / (Nat.facto... |
23,956 | lean_file_chunk | aa9ccd09efa49ee5cbc5cf6bd396c6c91d5146762b9bf1c87ceab7aec48e3fbf | lean_source_file | lean_pool_source_file_chunks | have hS1_nn : 0 ≤ Real.sqrt ((m : ℝ) + 1) + |x - ((m : ℝ) + 1)| := by positivity
calc |(Pkn k N).eval x|
≤ Ak * ((m : ℝ) + 1) ^ ((k : ℝ) / 2) *
(1 + |x - ((m : ℝ) + 1)| / Real.sqrt ((m : ℝ) + 1)) ^ k := hIH0
_ = Ak * (Real.sqrt ((m : ℝ) + 1) + |x - ((m : ℝ) + 1)|) ^ k := by rw [mul... |
23,961 | lean_file_chunk | afccf79ba36e8c6fe3d83f6f69a530a9c551668129b007d9195e155d3ef0e368 | lean_source_file | lean_pool_source_file_chunks | (1 + |r ^ 2 - (↑n - ↑k + 1)| / √(↑n - ↑k + 1)) ^ (2 * k))
≤ (1 / (↑k.factorial * ↑n.factorial)) *
(Ak ^ 2 * (↑n - ↑k + 1) ^ k * (1 + |r - √↑(α + 1)|) ^ (4 * k)) :=
mul_le_mul_of_nonneg_left hmid (by positivity)
exact mul_le_mul_of_nonneg_right hmid' (by positivity)
_ =
... |
3,477 | lean_file_chunk | 950f055d07803fc4bb75aed32cb2dea5772e73d56097ba9a6c1312c9cdad4c80 | lean_source_file | lean_pool_source_file_chunks | ((((r ^ k) / Real.sqrt ((Nat.factorial k : ℕ) : ℝ)) ^ 2) * |qkn k n r| ^ 2))
volume (j : ℝ) ((j + 1 : ℕ) : ℝ) := intervalIntegrable_basisRadialTerm k n j
-- Bound the integral pointwise: replace integrand by the shell-level Gaussian.
have hbound_int :
∫ r in (j : ℝ)..((j + 1 : ℕ) : ℝ),
r * Real.... |
2,447 | lean_file_chunk | c0207c5d3bc50c68636054bfa400f5834b69b96d1cb9cf3ad035f0525f54cc1d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
/-
# ImportedAnalyticInputs.lean
Re-exported analytic inputs reused from the existing formalizations.
Scaffolding... |
23,972 | lean_file_chunk | f25cf932c55e1fc74bf82fa81b35deed659ef0325eb1c4a8d834033664ffad39 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
/-
# ModulusRigidity.lean
Statement-only scaffold for modulus rigidity over a finite Hermite base point.
Scaffold... |
23,975 | lean_file_chunk | 057be53f395a79f2d3b3326153d39d964328b856e92098c25950a79ab381c98b | lean_source_file | lean_pool_source_file_chunks | simp [fourier_apply, Circle.norm_coe]
rw [hfour, one_mul]
rw [circle_series_norm_eq_of_modulus_eq (k := k) (d := d) (a := a) (G := G) hG hmod r
hr_pos t]
exact hpoly_bound t
have hInt0 :
‖∫ t : Circle, fourier (-(n : ℤ)) t • circleSeries k (hermiteCoeff k G) r t
... |
23,983 | lean_file_chunk | f8d4783424d8f2c7d91488d76ef2cd640ff85aa05c573d103c70277a281d507b | lean_source_file | lean_pool_source_file_chunks | have hsq' : ‖fourierCoeff fLp (-(m + 1 : ℤ))‖ ^ 2 = 0 := by simpa [s] using hsq
exact norm_eq_zero.mp (sq_eq_zero_iff.mp hsq')
exact (fourierCoeff_toLp (f := fcont) (-(m + 1 : ℤ))).symm.trans hsqLp
/-- Positive Fourier modes of the conjugate mixed product only keep indices `i ≥ ell`. -/
private theorem fourierCo... |
8,873 | lean_file_chunk | 861067fd2d042d3919eb0e4cac72023ea0773e85d08cd801408d4d323b8dd5e1 | lean_source_file | lean_pool_source_file_chunks | · simp [hidx, mul_assoc, mul_comm]
field_simp [hd, hn]
· simp [hidx]
private theorem finitePositiveModeErrorSum_mul_den
{k d : ℕ} (a b : Fin (d + 1) → ℂ) (n : Fin (d + 1)) {r : ℝ}
(hd : (qkn k d r : ℂ) ≠ 0) (hn : (qkn k n.1 r : ℂ) ≠ 0) :
((qkn k d r : ℂ) * (qkn k n.1 r : ℂ)) * finitePositiveModeError... |
23,985 | lean_file_chunk | cd657c192ee4df1c632dd25ab785daadc94cfa71da7d0e81da7953d970de51dd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
/-
# TrueLevelBasis.lean
WIP merged implementation for the true Hermite level `k` basis.
Scaffolding notes:
- `... |
23,968 | lean_file_chunk | 30ce8d0bb6e9b204479c81ceeabd23d35e1c24d7ad4e0ed51f8210b6f1d2a315 | lean_source_file | lean_pool_source_file_chunks | Finset.abs_sum_le_sum_abs _ _
_ ≤ ∑ j ∈ (Finset.range (min k n + 1)).erase 0,
((Nat.choose k j : ℝ) *
((Nat.factorial n : ℝ) / (Nat.factorial (n - j) : ℝ)) /
r ^ 2) := by
apply Finset.sum_le_sum
intro j hj
have hj_pos : 1 ≤ j := by
... |
23,979 | lean_file_chunk | 0eb51030e9dda323265bd874602486c2c66c5497106fa72895e91883d6367391 | lean_source_file | lean_pool_source_file_chunks | (-1 : ℝ) ^ (i + j) * (Nat.choose k i : ℝ) * (Nat.choose k j : ℝ) *
(Nat.descFactorial m i : ℝ) * (Nat.descFactorial m j : ℝ) *
(‖z‖ ^ (2 * (m + k - i - j)) * Real.exp (-‖z‖ ^ 2)) := by
intro z
suffices h : ‖Phi k m z‖ ^ 2 =
(1 / ((↑k.factorial : ℝ) * ↑m.factorial)) *
∑ i ∈ Finset... |
23,943 | lean_file_chunk | e50b1416584241ba8acc2ee0ed307b61431082871200d24c04b0d1140a5137fb | lean_source_file | lean_pool_source_file_chunks | have hEq :
(fun z : ℂ =>
(Finset.sum s (fun b => f b z)) * (starRingEnd ℂ) (g z) *
(Real.exp (-‖z‖ ^ 2) : ℂ)) =
fun z : ℂ =>
Finset.sum s
(fun b => f b z * (starRingEnd ℂ) (g z) * (Real.exp (-‖z‖ ^ 2) : ℂ)) := by
funext ... |
23,954 | lean_file_chunk | d38431904ec4010e2c03a53c1d244a3d55a9eb1b4083577caf05088f42ab0fea | lean_source_file | lean_pool_source_file_chunks | /-- Circle Parseval identity for finite Hermite sums. -/
theorem finiteCirclePoly_l2_identity :
∀ {k D : ℕ} (r : ℝ) (a : Fin D → ℂ),
circleL2Sq (finiteCirclePoly k r a) =
∑ n : Fin D, ‖a n‖ ^ 2 * |qkn k n.1 r| ^ 2 := by
intro k D r a
by_cases hD : D = 0
· subst hD
simp [finiteCirclePoly, Her... |
23,938 | lean_file_chunk | 9c35c0ebc79275812c14a09fb1813212a842aeb1811f75f89cf7fb1fb8ea9f12 | lean_source_file | lean_pool_source_file_chunks | ENNReal.ofReal (Real.pi * weightedNormSq F) := by
have hIntEq :
∫ z : ℂ, ‖F z‖ ^ 2 * rexp (-‖z‖ ^ 2) = Real.pi * weightedNormSq F := by
unfold weightedNormSq HermiteLEAN.weightedNormSq
field_simp [Real.pi_ne_zero]
rw [(MeasureTheory.ofReal_integral_eq_lintegral_ofReal hF
(Filter.Eventually.of_fora... |
23,976 | lean_file_chunk | e08541ec4f9a1c410ccb485a6fe73aa5fbccaee03205eb735b058a98b7cb6c7c | lean_source_file | lean_pool_source_file_chunks | Filter.Tendsto (fun J => ∑ n ∈ Finset.range J, a n)
Filter.atTop (nhds (circleSeries k (hermiteCoeff k G) r t)) := by
simpa [circleSeries, a] using hs.hasSum.tendsto_sum_nat
have hEqFun :
(fun J => truncCirclePoly k r J G t) =
(fun J => ∑ n ∈ Finset.range (J + 1), a n) := by
ext J
si... |
23,990 | lean_file_chunk | 6c96a23f13bee37854ca09ac31964894b5d4309a319f1a73a0781dcafffd24fc | lean_source_file | lean_pool_source_file_chunks | have hεsq : 0 < ε ^ 2 := sq_pos_of_pos hε
obtain ⟨N, hN⟩ := hTendsto (ε ^ 2) hεsq
refine ⟨N, fun J hJ => ?_⟩
rw [hDiffNormSq, hShift]
have hJN := hN (J + 1) (by omega)
rw [dist_zero_right] at hJN
linarith [abs_nonneg (∑' n, ‖hermiteCoeff k G (n + (J + 1))‖ ^ 2),
(abs_lt.mp hJN).2]
/-- Truncations conve... |
23,954 | lean_file_chunk | 4dc45cfe839ab204feb872dacfccddc07da620bd236a60bae0ff24fc4719c678 | lean_source_file | lean_pool_source_file_chunks | obtain ⟨Cz, _, hCz⟩ := point_eval_bounded (k := k) z
have hRK_partial : ∀ J : ℕ, ∑ n : Fin (J + 1), ‖Phi k n z‖ ^ 2 ≤ Cz ^ 2 := by
intro J
let a : Fin (J + 1) → ℂ := fun n => starRingEnd ℂ (Phi k n z)
have hF_mem : finiteHermiteSum k a ∈ Hk k := finiteHermiteSum_mem_Hk k a
have heval := hCz hF_mem
... |
10,791 | lean_file_chunk | f1a93bbe785abcc1994beada6388a39e8b3c9167201f119d45e84e899ab96d90 | lean_source_file | lean_pool_source_file_chunks | apply Filter.liminf_le_of_le hbounded
intro b hb
rw [Filter.eventually_atTop] at hb
obtain ⟨N, hN⟩ := hb
exact le_trans (hN N le_rfl) (hLinEq N)
have htail_nonneg : 0 ≤ ∑' m : ℕ, s m := by
have hs_nonneg_term : ∀ m : ℕ, 0 ≤ s m := by
intro m
by_cases hm : m < J ... |
23,961 | lean_file_chunk | 4af916b583b842d45b9f7098b262251067ccbc10324d483c661440429e8fc62c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import Mathlib.Analysis.Distribution.SchwartzSpace.Deriv
import Mathlib.Analysis.Distribution.SchwartzSpace.Fourier
impo... |
23,990 | lean_file_chunk | d3b182c975f52a52c9ee00cd8d1c4811355ec8ae37b43e189f03a5bbb8f2632b | lean_source_file | lean_pool_source_file_chunks | (a := (carrierArc N k).left) (b := (carrierArc N k).right)
have h_simp : (fun x => g ((↑N : ℝ) * x / ↑N)) = g := by
ext x
show g (↑N * x / ↑N) = g x
congr 1
field_simp [hN_ne]
rw [h_simp] at key
have h_el : (↑N : ℝ) * (carrierArc N k).left =
(2 * Real.pi) * ↑k.val := by
... |
23,955 | lean_file_chunk | 037b1e2f9b6aad7b43200909e04fd7ab7ff6af8e733852894704933d5fe05bba | lean_source_file | lean_pool_source_file_chunks | MeasureTheory.lpNorm f 2 μ
= MeasureTheory.lpNorm
((schwartzApproxRealVec hf n : RealVec d -> ℂ) -
((schwartzApproxRealVec hf n : RealVec d -> ℂ) - f)) 2 μ := by
congr 1
funext t
simp
_ ≤ MeasureTheory.lpNorm (sc... |
23,959 | lean_file_chunk | 4e3c4ec64582ed89f632df0f4715d302dcbf891b79b48e459a8ea6f8aea1bf62 | lean_source_file | lean_pool_source_file_chunks | (star (f p.1) * f (p.1 + x)) *
(h (p.1 - p.2) * star (h (p.1 + x - p.2))))
((MeasureTheory.volume : MeasureTheory.Measure (RealVec d)).prod
(MeasureTheory.volume : MeasureTheory.Measure (RealVec d))) := by
let μ : MeasureTheory.Measure (RealVec d) := MeasureTheory.volume
let A : RealVec d → ... |
23,934 | lean_file_chunk | cfbc97f2bfcea52089f74aa1aa8b9efa4fbb0d819530b16baed56603e8b7b8df | lean_source_file | lean_pool_source_file_chunks | apply MeasureTheory.eLpNorm_congr_norm_ae
filter_upwards [
MeasureTheory.Lp.coeFn_star f,
MeasureTheory.Lp.coeFn_star g] with t hf hg
rw [Pi.sub_apply, Pi.sub_apply, hf, hg]
simp only [Pi.star_apply]
calc
‖star ((f : RealVec d -> ℂ) t) - star ((g : RealVec d -> ℂ) t)‖
= ‖star ((f : RealVec d... |
23,947 | lean_file_chunk | a94569725b26a6df4a22b456cd11c60aad5a5a8dd054e956c739e7ab3ba27a74 | lean_source_file | lean_pool_source_file_chunks | let μP : MeasureTheory.Measure (PhaseSpace d) := MeasureTheory.volume
have hfinite_rhs :
ENNReal.ofReal
(MeasureTheory.lpNorm (f : RealVec d -> ℂ) 2 μ *
MeasureTheory.lpNorm (h : RealVec d -> ℂ) 2 μ) < ⊤ :=
ENNReal.ofReal_lt_top
have hfin : MeasureTheory.eLpNorm (stftRep h f) 2 μP < ⊤ :=... |
15,636 | lean_file_chunk | c04b4cf0cab6ce7c6dbc9aa2c8f91846e2920544aa3a4940d290d05220a5fac4 | lean_source_file | lean_pool_source_file_chunks | rw [integral_signal_autocorr_phase_schwartz_realVec f x ω]
_ = ambiguityRep (f.toLp 2 MeasureTheory.volume)
(f.toLp 2 MeasureTheory.volume) (x, ω) *
star (ambiguityRep hLp hLp (x, ω)) := by ring
/-- Middle of the Moyal calc: collapse the inner `η`-integral of the squared STFT
times the modulati... |
23,971 | lean_file_chunk | f6e6b31791bc2a49c763aff05caadd82e4f02d6a74bd130aa47b3447b17ac47e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.FiniteBaseAnnulusEstimate
import LeanPool.PhaseRetrieval.DimdPoly.Inter... |
864 | lean_file_chunk | 0c5689c8d4929c6ee85dbd36bf957023ab1609dc3dd1763586378b69fedd88d0 | lean_source_file | lean_pool_source_file_chunks | rw [le_div_iff₀ hdelta_pos]
exact le_of_lt (by simpa [mul_comm] using hstrict)
simpa [div_eq_mul_inv, mul_comm, mul_left_comm, mul_assoc] using haux
calc
‖G‖ = t := rfl
_ ≤ delta⁻¹ * defectPk kappa F G := ht_le_delta
_ ≤ C_F_perp * defectPk kappa F G :=
... |
10,358 | lean_file_chunk | 003df59db8034727c43111d8a6d592470f9cc6cad68deb15810b4a363a39cc91 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Hermite.ImportedAnalyticInputs
import Mathlib.MeasureTheory.Function.Ho... |
20,813 | lean_file_chunk | 4683617149a8d2d93413a994aa8783f492149d7975341a84840f8f1d873522e3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.OrthogonalCoercivity
import LeanPool.PhaseRetrieval.DimdPoly.Internal.O... |
23,963 | lean_file_chunk | 500086fbd3dd7958cb2e32b37830e63043dbe85ac73676a229edaac5643daf41 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Hermite1Dimd.BlockLocalization
import LeanPool.PhaseRetrieval.DimdPoly.... |
5,163 | lean_file_chunk | e5e1329599da4afa1ce51e0ca92b6f0bc7ecaf7c203b33980b0624895d8b36b6 | lean_source_file | lean_pool_source_file_chunks | simpa using ofPkappa_total_mass_wip hd kappa H
theorem lowAnnulusProjection
{d : Nat} (hd : 0 < d) (kappa : MultiIndex d)
(J : Nat) :
∃ E : Finset (Idx d), ∃ rho : ℝ, 0 < rho ∧
∀ {H : Pkappa d kappa},
‖H‖ = 1 ->
Finset.sum E (fun alpha => ‖coeffPkappa H alpha‖ ^ 2) <= rho ->
l... |
23,975 | lean_file_chunk | fccabd361e2b31cd02e86b7aaafef8a4109db1a8e85c3cc2c786fe3527fa649a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.ImportedAnalyticInputs
import LeanPool.PhaseRetrieval.DimdPoly.Internal... |
23,996 | lean_file_chunk | d31f96aeda34ce38ae9bf0d679dd4c5a964889a1c98d28867a826a0a95373b9d | lean_source_file | lean_pool_source_file_chunks | /-- `BoxPartialSumsLocallyUniformCauchy`: Box Partial Sums Locally Uniform Cauchy. -/
def BoxPartialSumsLocallyUniformCauchy
{d : Nat} (kappa : MultiIndex d) (U : Skappa d kappa) : Prop :=
(∀ K : Set (Cd d), IsCompact K ->
UniformCauchySeqOn (fun J : MultiIndex d => partialSum kappa U J) Filter.atTop K) ∧
B... |
12,624 | lean_file_chunk | be8d28a3954fbaf1245200f53febb79bbfbd5ce1cbea16dbe3ecf132aff16594 | lean_source_file | lean_pool_source_file_chunks | have hsubset : box J0 ⊆ box N := box_subset_box hN
have htail_eq :
partialSum kappa U N z - partialSum kappa U J0 z =
∑ alpha ∈ box N \ box J0, term alpha := by
unfold partialSum
have hsum :=
Finset.sum_sdiff (s₁ := box J0) (s₂ := box N) (f := term) hsubset
dsimp [term] a... |
5,209 | lean_file_chunk | 0e88a5d2f512d18dc0094c40d92b38603d8533b670159c805d2c3ddf0bd25b15 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.DimdPoly.Internal.Auxiliary
/-! # DimdPoly -/
open scoped BigOperators
noncomputable ... |
1,352 | lean_file_chunk | e8318bbd07148dae37919a9427a9bd420b7a91f0ce01e02cdc7b29717f0a893b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Susanna Bertolini, Jaume de Dios Pont. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Susanna Bertolini, Jaume de Dios Pont
-/
import LeanPool.PhaseRetrieval.Constant
import LeanPool.PhaseRetrieval.DimdPoly
/-!
# Stable phase retrieval for Hermi... |
19,180 | lean_file_chunk | de685525a4cbfc6fefdc07bd7aa331fbd733c0a76d531c1f341efb59dad43f2b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.ActionPoisson
/-!
# Pointwise factorization of the leading integral through the Delaunay actions
The mass-zero leading coefficien... |
23,935 | lean_file_chunk | f973520530613b4fddb46effd9d1a6cae587b8e17437ffa3bf587d2908264c7d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DelaunaySection
/-!
# Poisson brackets and the Cartesian Delaunay action map
This file rewrites the physical Poisson bracket with... |
3,518 | lean_file_chunk | 0c1fd7a5d6c077c4a271dbd84f5f0a79a41be6c5c76369f4fb2d7c4b8895616e | lean_source_file | lean_pool_source_file_chunks | exact IsFirstIntegralFamily.mass_zero_liftedDelaunayPhasePoint_eq
hδ hanalytic hfirstIntegral hfirstAction heccentricity
heccentricityOne hapoapsis (meanAnomaly, angle)
(meanAnomaly, periapsisAngle)
calc
poissonBracket (F 0) cartesianAngularAction state =
fderiv ℝ (F 0) state (angularAct... |
10,996 | lean_file_chunk | 2da74c741d37d1f5521c2371b3b8c7fb4f69c00caf30ee351f1fa60d7d2fba72 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DisturbingRegularBound
/-!
# Blow-up of the collision-aligned disturbing average
Combining the logarithmic singular estimate with... |
8,138 | lean_file_chunk | 818741d20f1ceecaf20a0f9819e11c5259707dd7c820c5941d6f13b373250d35 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.Core
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Analytic.Linear
import Mathlib.Tactic.FieldSimp
import Mathl... |
6,434 | lean_file_chunk | bfb3c8a197c71fd2fddacd4d2f263112741bbb6e50ecae331a58a290322ebd67 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.JointSlabIntegral
/-!
# Analyticity under integration over a compact time set
A finite subcover of the compact time set reduces t... |
2,002 | lean_file_chunk | 5e7075d9ebabf836a48e8036aa8e3aa4c2e6761710e18ce357867a3cc29efbff | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import Mathlib.Analysis.Analytic.Order
import Mathlib.Topology.Algebra.Module.PerfectSpace
/-!
# Density from one-dimensional analytic nonvanishing
This file packa... |
17,351 | lean_file_chunk | 4587be8af571fa9e9562d065dbce49486b41084524d8013d51c3379e768af4fd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DifferentialDependence
import LeanPool.PoincareThreeBody.ParameterDomainTopology
import Mathlib.Analysis.Analytic.Order
import Math... |
14,820 | lean_file_chunk | 8d86c426232e77db2f39afb041100f05dab2601aaf7a3d61959b5f38298175fd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.EnergyLeafObstruction
import Mathlib.Analysis.Analytic.IsolatedZeros
/-!
# Analytic coefficient normalization in the mass paramete... |
4,860 | lean_file_chunk | 2989b825ba467f6ce86202f4ccffe5855f717ee9b6a42d90c7e0799ae649c8bb | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import Mathlib.Analysis.Analytic.Basic
import Mathlib.MeasureTheory.Integral.DominatedConvergence
import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
... |
5,133 | lean_file_chunk | 1f9d6c5c9153f933423191bedcd599917453fe762292c4e9b73bb3630394e626 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.Resonance
import Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus
import Mathlib.Tactic.Linarith
/-!
# Averaging th... |
4,146 | lean_file_chunk | d5d30a3c0bb714656c01712a461928be1075b4fd3f8c5178fda579c7bd2e1036 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DisturbingCertificate
import LeanPool.PoincareThreeBody.PoincareSet
/-!
# Finite certificates for the classical Poincaré set
This... |
10,160 | lean_file_chunk | 39a4c66284a97739ce8575d936603cb7e8717791f9f32f37dcb0b272d0eff93f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.AnalyticNormalization
/-!
# The first Poincaré coefficient-normalization cycle
The dense Poincaré-set obstruction makes the zerot... |
9,596 | lean_file_chunk | 81b54b4b3d634fa9272833728d1a4877af57cc181a4b36ca02372c5ef7dfdd19 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.CollisionBandObstruction
import Mathlib.Analysis.Analytic.Uniqueness
/-!
# Analytic continuation from the collision band
For each... |
7,615 | lean_file_chunk | 32ddf72458f4ceb1ec5119f52b94528ffca1c22b58f2e7984e4f72e063798aa9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.ResonantAverageSeparation
/-!
# The leading obstruction on collision-band resonances
Fiberwise density in eccentricity propagates... |
13,861 | lean_file_chunk | 70b4873cf2e18a8c669809d17171d905a026872c91604772f8a583e283964178 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.ResonantCollisionBoundary
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
/-!
# Logarithmic growth near a resonant collis... |
5,689 | lean_file_chunk | eaf0a2896c7cac0c79a15dbb5a61aadbd2c805e64f4056cc1b39d27773f90ba2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import Mathlib.Analysis.Analytic.Basic
import Mathlib.Analysis.Calculus.FDeriv.Basic
import Mathlib.Analysis.Real.Sqrt
import Mathlib.LinearAlgebra.Matrix.Notation
i... |
12,368 | lean_file_chunk | dbc650b9ecde38615a14db5ae0a75ecdcc8a9b4d88fdd2d2db3c46040e08264d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.Resonance
import Mathlib.Analysis.Calculus.Deriv.Add
import Mathlib.Analysis.Calculus.Deriv.Inv
import Mathlib.Analysis.Calculus.De... |
23,942 | lean_file_chunk | ad6c17903d959c1b8f3842f50249e9a2bb910a5e1e09e91c7eafa493a313c948 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DelaunayChart
import LeanPool.PoincareThreeBody.KeplerHamiltonian
/-!
# Physical realization of the planar Delaunay actions
This ... |
1,631 | lean_file_chunk | 74a7876b2c32b79a32ef06585836112b712876f961a8b4ceac6e6f402c37bfa3 | lean_source_file | lean_pool_source_file_chunks | rw [fderiv_hamiltonian_zero_eq_delaunay_comp_actions hposition henergy]
have hfirstAction : cartesianDelaunayActions state 0 ≠ 0 := by
change 1 / Real.sqrt (-2 * cartesianKeplerEnergy state) ≠ 0
have hpositive : 0 < -2 * cartesianKeplerEnergy state := by linarith
positivity
rw [fderiv_delaunayHamiltonia... |
23,990 | lean_file_chunk | 66474c917e7400ad676dd22690bc62a06c6f9dba2700c6119bad29563edf64b3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.GlobalEnergySection
import LeanPool.PoincareThreeBody.ActionFactorization
import Mathlib.Analysis.Calculus.InverseFunctionTheorem.F... |
8,617 | lean_file_chunk | c64a049a2ee1b4f093760031176e26b90b97164599167f9b9e491f506e714a18 | lean_source_file | lean_pool_source_file_chunks | delaunayAnchorAction_prograde]
rw [eccentricityFromActions_delaunayAnchorAction]
rfl
theorem analyticAt_delaunayAnchorEccentricAngleChart :
AnalyticAt ℝ delaunayAnchorEccentricAngleChart delaunayAnchorMeanAngles := by
have hembedding : AnalyticAt ℝ
(fun angles : ℝ × ℝ ↦ (delaunayAnchorAction, angles))
... |
12,495 | lean_file_chunk | 496fbf25c8399669cf7386b4b1f729bd53d7fe8743620826e42bece68a56630a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.IrrationalTorusFlow
import LeanPool.PoincareThreeBody.KeplerPhaseOrbit
/-!
# The lifted planar Delaunay chart
This file packages ... |
23,948 | lean_file_chunk | 1849bd792721bab977c5e4b0a185bf5b300f9ad20bb1a5c58807de7f2bf7eab4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DelaunayChart
import LeanPool.PoincareThreeBody.KeplerHamiltonian
import Mathlib.Analysis.Calculus.MeanValue
/-!
# The unperturbed... |
12,013 | lean_file_chunk | 0fdf994f5a29fd655c209aa14ce5a0bb39dd111fe48104ac63d44c20fb48144f | lean_source_file | lean_pool_source_file_chunks | have hradius := eccentricRadius_pos (anomaly := anomaly)
hfirstAction heccentricity heccentricityOne
have hpositionSq :
(liftedDelaunayFlowLine firstAction eccentricity meanAnomaly periapsisAngle time 0) ^ 2 +
(liftedDelaunayFlowLine firstAction eccentricity meanAnomaly periapsisAngle time 1... |
23,938 | lean_file_chunk | 0e9584b768bcf5dd1b519ce1031cbe99315cc89d8d4c1941f7c2a9ed9b8cc4e7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DelaunayActions
import LeanPool.PoincareThreeBody.DelaunayFlow
import Mathlib.Analysis.Calculus.FDeriv.Analytic
/-!
# An analytic ... |
8,347 | lean_file_chunk | 803e6e8406f7f9d78c57ca1c7b1c8b4993ba3aceb442f1eaabc24fadb9e3a480 | lean_source_file | lean_pool_source_file_chunks | have heccentricity : 0 ≤ eccentricity := eccentricityFromActions_nonneg action
have heccentricityOne : eccentricity < 1 := eccentricityFromActions_lt_one haction
have hsectionIdentity : state =
liftedDelaunayPhasePoint (action 0) eccentricity 0 0 :=
delaunayActionSection_eq_liftedDelaunayPhasePoint hactio... |
5,261 | lean_file_chunk | e8886f1814fc88f0c32d974448c92f64640982d88a69f629024635cdab37852d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.ResonantActionObstruction
/-!
# Propagating resonant obstructions by density
Positive rational Kepler resonances remain dense aft... |
7,526 | lean_file_chunk | 789d30b465a1a0d24b5ce902f84e4db5154f7da7cd2878388077a56ce8ef40ca | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.PoissonNormalization
/-!
# Coordinate minors and functional dependence
Two phase covectors are dependent exactly when all of thei... |
3,763 | lean_file_chunk | cbf8fceffe00cb1fab92f8eaa6d0aec63022795d6f43dd49a31b02ebcdda07c2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.AnalyticCompactParameterIntegral
import LeanPool.PoincareThreeBody.DisturbingParameterAnalytic
/-!
# Analytic eccentricity depende... |
5,061 | lean_file_chunk | 409c673259be8dd123f61cab3fc48d849200849abef8965757a9c88a4470459e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DisturbingFunction
import LeanPool.PoincareThreeBody.ValidatedQuadrature
/-!
# Finite certificates for nonconstant resonant averag... |
23,981 | lean_file_chunk | e12778f64728cd1a3d11928e62b0cdc41062d58c2e73e9506f9cf0cad603b7c8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.Averaging
import LeanPool.PoincareThreeBody.ResonantOrbit
import Mathlib.Analysis.Calculus.ParametricIntervalIntegral
import Mathli... |
13,657 | lean_file_chunk | b7061e6d8a492930f5ea39e85e6f7eefb63e8067fb9e594595c803f47ce9ecf4 | lean_source_file | lean_pool_source_file_chunks | (orientedResonantEllipsePosition p q eccentricity orientation time 0 - 1) ^ 2 +
(orientedResonantEllipsePosition p q eccentricity orientation time 1) ^ 2 ≠ 0 := by
exact rotatingEllipse_primaryDistance_ne_zero_of_apoapsis_lt_one heccentricity
heccentricityOne hapoapsis
lemma orientedResonantEllipsePositi... |
15,195 | lean_file_chunk | 46c3c4f4d8185d8c473ab1edb06afb82253a026e9b3bfaf6a8669e415c7349e5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.DisturbingFunction
import LeanPool.PoincareThreeBody.JointEccentricAnomaly
/-!
# Analytic eccentricity dependence of the disturbin... |
10,113 | lean_file_chunk | 6664831d6f9318412bfda316d6721174a0101c1abdee4eeb620b4808bfc8104e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.CollisionIntegralBlowup
/-!
# Uniform control of the regular disturbing terms near collision
The two nonsingular terms in the fir... |
10,383 | lean_file_chunk | 8c06843b0d7d3d3ae888dfb37d16c14745c9e4fe0955883f4b699e06a39e09a6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.LeadingObstruction
import LeanPool.PoincareThreeBody.CollisionBandAnalyticContinuation
import Mathlib.Analysis.Calculus.MeanValue
... |
8,681 | lean_file_chunk | b58f7c665cf63133a61c4a4bef8ec7628d66cdbad38e19ccfb72ed99d083e67d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.Polar
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Ring
/-!
# Algebraic foundations of the planar Delaunay generating fun... |
20,758 | lean_file_chunk | 89d7d5d2c6304e434fb61102cff1daabb77a0330044aaac3a74c0d7a39db8bc3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Gershon Bialer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gershon Bialer
-/
import LeanPool.PoincareThreeBody.ParameterDomainTopology
import LeanPool.PoincareThreeBody.Analytic
import LeanPool.PoincareThreeBody.ParameterizedAnalyticDivision
... |
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