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 |
|---|---|---|---|---|---|
1,409 | lean_file_chunk | 0842a9dbe667443236824f8201edc064e46d467039e2b0e18ce2ab7e5dccbbf6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Evan Chen, Kenny Lau, Seewoo Lee, Ken Ono, Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Evan Chen, Kenny Lau, Seewoo Lee, Ken Ono, Jujian Zhang
-/
import LeanPool.PartialRegularity.Extension
/-!
# Almost all primes are partially ... |
11,825 | lean_file_chunk | dd8bcb1495ad4090ac5bb142df7d0defbbbfe0573f768be2e8156a207348f35d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Algebra.Order.BigOperators.Group.Finset
/-!
# Basic definitions for graph pebbling
This file sets up the object... |
9,859 | lean_file_chunk | 3e579dfb83ab44fd0042913e2d5ec028aeb87ba2cb97d9380c0bf257aa6b6eb2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Analysis.MeanInequalities
import Mathlib.Analysis.SpecialFunctions.Exp
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import LeanPool.PebblingLean.Fin... |
9,843 | lean_file_chunk | e6e402fd0ed9586220e3fd12b4da68a96944e5b991432bc234970f6251f600ec | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Tactic.Linarith
import LeanPool.PebblingLean.Basic
/-!
# Direct delivery along paths
This file formalizes the elementary deterministic fact used inside ... |
926 | lean_file_chunk | 36652af2a42e72f10dda987eea91521777f6ecd2ade533078749be0ab5db1a53 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import LeanPool.PebblingLean.Hypercube
/-!
# Small examples
These definitions give named vertices and distributions for testing the basic
API on low-dimensional cubes.... |
3,148 | lean_file_chunk | 6d78930527d4c34817467726d2da73ee840a4ed81c943d7ea5e0b86ec3750923 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.BigOperators.Field
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Da... |
4,864 | lean_file_chunk | 3beda01b69009f310fdae19af6eb3802e264b552a233ad0695ebab97bf386c8a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import LeanPool.PebblingLean.Basic
/-!
# Transport across graph isomorphisms
The recursive upper bound is naturally proved on Cartesian products. To apply
those produ... |
4,951 | lean_file_chunk | 8bb20dfefc93c5ec0727329208798b79d1c0aae1796ff4e6f049cfdaa137fb14 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Data.Fintype.Powerset
import LeanPool.PebblingLean.Basic
/-!
# Hypercubes
The `n`-dimensional hypercube is represented as Boolean coordinate functions
`... |
3,087 | lean_file_chunk | 4eb8d4c19b6872ac759646a4277a02954b6fd253b59bd373fe804073d46b6ff8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import LeanPool.PebblingLean.Hypercube
import LeanPool.PebblingLean.Delivery
/-!
# Paths in hypercubes
This file connects Hamming distance to the graph-walk API: verti... |
19,623 | lean_file_chunk | 65dc98f8d1d9befd3d1a4118a76112e97cc06d25db7c3dc8e2469894232fdd48 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import LeanPool.PebblingLean.GraphIso
import LeanPool.PebblingLean.Hypercube
import LeanPool.PebblingLean.Product
import LeanPool.PebblingLean.UpperBound
import Mathlib.... |
6,228 | lean_file_chunk | d5d5cc4427b7a7d0f62489216b0ef34f26389535b5174965840c1673b0a0b4db | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import LeanPool.PebblingLean.Hypercube
import LeanPool.PebblingL... |
5,979 | lean_file_chunk | cd3d4d9b0a1a788eae9a19dbf4eac64eb0e2c595aa0597bb362df3b1d17a0451 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import LeanPool.PebblingLean.UpperBoundParameters
/-!
# Paper-facing formulation
This file contains wrappers whose statements follow the exposition in the
paper. The ... |
14,374 | lean_file_chunk | 3af460eacf5d41ef5766ccb6e12e19b49c273366e065dc53bd8fed0f46204265 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import LeanPool.PebblingLean.Basic
/-!
# Product constructions
This file begins the deterministic part of the up... |
7,162 | lean_file_chunk | 67c3f231778176c12b5fe116f3a380361b03310c715a6a07d7eefc165ba29f8d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Algebra.Order.Group.Nat
import LeanPool.PebblingLean.Hypercube
import LeanPool.PebblingLean.Product
/-!
# Upper-bound scaffolding
This file records the ... |
6,368 | lean_file_chunk | 9e91e5c28f6cb5efb2875ed25dcfedf3059cc484ef5ded7d9f04fd9b739d8dce | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Tactic.Ring
import LeanPool.PebblingLean.UpperBound
import LeanPool.PebblingLean.HypercubePath
/-!
# Delivery interpretation of annulus contributions
Th... |
17,978 | lean_file_chunk | 03595e129997d17c9794b13906ba2cc81383f1cd22625b3893f0f0eb915167c3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Analysis.SpecialFunctions.Exp
import LeanPool.PebblingLean.UpperBoundRecurrence
/-!
# Loss bookkeeping for t... |
23,965 | lean_file_chunk | afa7ce97c55cb77f5c027baa05b125b8a0252aedfb7ea7252e4ffcf8fa3834f8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Analysis.Complex.Exponential
import Mathlib.Analysis.Complex.ExponentialBounds
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.R... |
23,976 | lean_file_chunk | 3184be317b5c208be774195f4a6aba3033f9d847ae21926f2b534899e57d6cea | lean_source_file | lean_pool_source_file_chunks | 9 ≤ annulusWidthCore A K n := by
have hlog_nonneg : 0 ≤ Real.log (n : ℝ) :=
Real.log_natCast_nonneg n
have hinner :
((3 : ℝ) * (n : ℝ) / 4) * Real.log (n : ℝ) ≤
(splitA K n : ℝ) * Real.log (n : ℝ) :=
mul_le_mul_of_nonneg_right ha_lower hlog_nonneg
have hcoarse :
A ^ 2 * (((3 : ℝ) * (n ... |
23,984 | lean_file_chunk | 512053ab7be131d05968d121db3f5efcf72fbbac7dc082fad0af95e648da9efc | lean_source_file | lean_pool_source_file_chunks | Real.log 2 + 2 * Real.log (n : ℝ) +
(((splitA K n / 3 : ℕ) : ℝ) + annulusWidthCore A K n + 1) *
Real.log 2 ≤
((splitM K n / 5 : ℕ) : ℝ) * Real.log 2 +
(splitA K n : ℝ) * Real.log ((4 : ℝ) / 3) := by
have hlog2_nonneg : 0 ≤ Real.log 2 :=
(Real.log_pos (by norm_num : (1 : ℝ) < 2)).le... |
23,964 | lean_file_chunk | 32dc774600e466042fe537c986c935061901418a1cd8fa88d7c7bbf31a0f5cec | lean_source_file | lean_pool_source_file_chunks | (hstack :
(2 ^ rOut A K n : ℝ) ≤
(loss n / 2) * (t : ℝ) * (((4 : ℝ) / 3) ^ splitA K n)) :
(sampleCountForDemand A K n t : ℝ) *
(annulusMean (splitA K n) (rIn A K n) (rOut A K n) : ℝ) ≤
2 * (t : ℝ) := by
let delta : ℝ := loss n
let pow43 : ℝ := (((4 : ℝ) / 3) ^ splitA K n)
let pow34... |
23,979 | lean_file_chunk | 05ece35346b046b2443bb80199cc122ee0ff8b8f8b8902c376875405e1f0348a | lean_source_file | lean_pool_source_file_chunks | (splitA_add_splitM_of_four_mul_le (hquarter n hn))
(hcostReal n hn))
/-- Specialization of the concrete parameter theorem to the recursively
defined integer cost bound. The finite base cost and the integer product
recurrence are discharged by `recursiveCostBound_base_cost` and
`recursiveCostBound_step_cost`; ... |
23,954 | lean_file_chunk | 41ce8db7206193bbb78e7507318e26fb8c231ef9577d3c5d7767988610c0707b | lean_source_file | lean_pool_source_file_chunks | (splitA K n) (rIn A K n) (rOut A K n))
hlogMin
hstackMin
hminExp
hceilSlack
/-- Version of the reduced wrapper using the coarser but simpler Bernstein
denominator `2^(2w)`, where `w = annulusWidth A K n`. -/
theorem hasRealUpperBound_of_recursiveCostBound_annulusLower_widthBound_finiteBase
{K A : ℝ... |
23,991 | lean_file_chunk | 7d9aca1cb0e5d3a20c705c780fc2d08453ec518c8c57b8f2f3d8112b20411f16 | lean_source_file | lean_pool_source_file_chunks | assumption `9≤w` absorbs the one-unit floor slack in `rOut`. -/
theorem right_standard_chernoff_log_le_of_width_exponent
{A K : ℝ} {n : ℕ} {E : ℝ}
(hwidth : 9 ≤ (annulusWidth A K n : ℝ))
(hlam_le_one : annulusChernoffLambda A K n ≤ 1)
(hE :
E ≤ (1 / 2) *
((annulusWidth A K n : ℝ) ^ 2 / ((s... |
23,982 | lean_file_chunk | 56bc2a92b88d07b5294025c435369b294231b5fe11d76c08a47a944c5398c078 | lean_source_file | lean_pool_source_file_chunks | ∀ n : ℕ, n0 ≤ n →
K ^ 2 * Real.log (n : ℝ) ≤ (n : ℝ) / 64)
(hleftExp :
∀ n : ℕ, n0 ≤ n →
leftChernoffTerm A K (annulusChernoffLambda A K) n ≤
Real.exp (-(tailExponent n)))
(hrightExp :
∀ n : ℕ, n0 ≤ n →
rightChernoffTerm A K (annulusChernoffLambda A K) n ≤
... |
23,978 | lean_file_chunk | ef14831c2228ce80d5521ff47f04efd1a89640ce6a8f735c62db3e87d1e4b212 | lean_source_file | lean_pool_source_file_chunks | (Real.log ((4 : ℝ) / 3) - Real.log 2 / 3)) :
HasRealHypercubePebblingUpperBound
(Real.exp (4 * loss n0) *
finiteBaseNormalizedBound (recursiveCostBound K n0) n0) :=
hasRealUpperBound_of_Kdom_thresholdBudgets_logChernoff_sixLog_finiteBase
(K := K) (A := A) (n0 := n0) (tailExponent := tailExponent... |
8,820 | lean_file_chunk | f63884b9f613300eb326f46718b04e3ebf1519022a9fcfccd79d04d3627fa591 | lean_source_file | lean_pool_source_file_chunks | (n0 := n0) hsplitThreshold)
hcoreNineCutoff
hwidthConstCutoff
hstackLogThreshold
hstackConstCutoff
/-- For `A=4`, the `core≥9` cutoff follows from the split cutoff. -/
theorem explicit_coreNineCutoff_of_splitThreshold {n0 : ℕ}
(hsplitThreshold : (128 * (217 : ℝ) ^ 2) ^ 2 ≤ (n0 : ℝ)) :
81 ≤ (4 :... |
23,945 | lean_file_chunk | 7d07aab2af030f8d121cf44409e96c1b5fe5f83ef88425ab931f26f5cfe46ae4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Data.List.OfFn
import LeanPool.PebblingLean.Concentration
import LeanPool.PebblingLean.UpperBoundDelivery
/-!
# F... |
23,993 | lean_file_chunk | f64b2d749c502436049517fcaefa35dafa741bd72a3ed51c6e486d75deabed65 | lean_source_file | lean_pool_source_file_chunks | /-- Chernoff bound for the left tail of `Binomial(n,1/3)`, with arbitrary
nonnegative parameter `lam`. -/
theorem binomialLeftTailProbThird_le_chernoff (n rIn : ℕ) {lam : ℝ}
(hlam : 0 ≤ lam) :
binomialLeftTailProbThird n rIn ≤
Real.exp (lam * (rIn : ℝ)) *
(((1 : ℝ) / 3) * Real.exp (-lam) + ((2 : ℝ... |
23,993 | lean_file_chunk | d06d58093883d106f4b8e1b6881c904f4fc0735511382b5a6f619342cecc4222 | lean_source_file | lean_pool_source_file_chunks | classical
have hmaps :
∀ center ∈ (Finset.univ : Finset (HypercubeVertex n)),
dist target center ∈ Finset.range (n + 1) := by
intro center _hcenter
exact Finset.mem_range.mpr (Nat.lt_succ_of_le (dist_le target center))
have hfiber :=
(Finset.sum_fiberwise_of_maps_to
(s := (Finset.uni... |
19,179 | lean_file_chunk | 8bb32736acab3f94bd8c188e3496b4f1a15c8490de417fe6bc33c4ac8c72a5b7 | lean_source_file | lean_pool_source_file_chunks | simpa [sampleContributionExpectation_eq_nat_mul_annulusMean] using hmean
theorem chernoffMeanLowerBound_of_annulusMean {n N rIn rOut T : ℕ}
(hmean : (T : ℚ) ≤ (N : ℚ) * annulusMean n rIn rOut) :
ChernoffMeanLowerBound n N rIn rOut T :=
chernoffMeanLowerBound_iff_annulusMean.mpr hmean
/-- The Bernstein input... |
23,991 | lean_file_chunk | a86f6d419cf110deb427a253f466eea9fdafb192083ba938e5a6d81259b25475 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import LeanPool.PebblingLean.HypercubeProduct
import LeanPool.PebblingLean.UpperBoundProbability
/-!
# Recurrence bridge for the upper bound
This file connects the pro... |
365 | lean_file_chunk | 6fd0c5410e0f856d782e20902ace6e342c838c1b027a65ab8d877ac983be5c54 | lean_source_file | lean_pool_source_file_chunks | minPile n ≤ 2 ^ rOut n) :
HasHypercubePebblingUpperBound costBound :=
hasHypercubePebblingUpperBound_of_highDemandDistribution
(highDemandDistribution_of_recursive_split_schedule_variable_large_constant_base
(n0 := n0) hbase_minPile_pos hbase_cost hsplit hsmaller
hgap_pos hmean hlog hfiberCost hco... |
7,936 | lean_file_chunk | ab1a776742341b613951273d6b77bfbb8f9c2633abd2a59f059023630d3c674d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import Mathlib.Data.Rat.BigOperators
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Tac... |
1,220 | lean_file_chunk | 0449e15991c776d50d592cd52cbfa3d57f6e6398a09b140ee117605751837b24 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lior Pachter. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lior Pachter
-/
import LeanPool.PebblingLean.Basic
import LeanPool.PebblingLean.Hypercube
import LeanPool.PebblingLean.Weight
import LeanPool.PebblingLean.LowerBound
import LeanPool.Peb... |
7,855 | lean_file_chunk | c96b95c00927534a035c81ae61ac8a913cbd5f4fe5d114812ab25729e2d82492 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import LeanPool.PentagonalNumberTheorem.Generic
import Mathlib.Analysis.SpecialFunctions.Log.Summable
import Mathlib.Analysis.RCLike.Basic
/-!
# Pentagonal number theorem ... |
8,398 | lean_file_chunk | a364b46aaa641b98cbc48964014b49d2feed291b2fc1d4b5be5da7d7e3f70f7f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Ring.NegOnePow
import Mathlib.Topology.Algebra.InfiniteSum.Basic
import Mathlib.Topology.Algebra.Infin... |
23,983 | lean_file_chunk | bd5ff0825d5875c4bd632659ee57c4c0c9f57c8801b0132fd063109d7421f73b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Ring.NegOnePow
import Mathlib.Combinatorics.Enumerative.Partition.Basic
import Mathlib.Data.Set... |
23,954 | lean_file_chunk | 671a0e0035f2a857d2ea9745128656452ccc71841639cea45ff6ccb64c3f2e34 | lean_source_file | lean_pool_source_file_chunks | x.diagSize ≤ (x.putLast hn i hi).diagSize := by
unfold diagSize putLast
refine le_trans ?_ (List.lengthWhile_mono _ _ _)
rw [x.delta.updateLast_eq _ (x.delta_ne_nil hn)]
refine List.lengthWhile_set _ _
(by simpa using List.length_pos_iff.mpr (x.delta_ne_nil hn)) ?_ _
rw [List.getLast_eq_getElem] at hlast
... |
23,997 | lean_file_chunk | c14a23e87613803a74b20560aacf017d10fe11e4d301b4a73987e0dcd1bf29b0 | lean_source_file | lean_pool_source_file_chunks | theorem up_notPosPentagonal (hn : 0 < n) (x : FerrersDiagram n)
(hdown : ¬ x.IsToDown hn)
(hpospen : ¬ x.IsPosPentagonal hn) :
¬ (x.up hn hdown hpospen).IsPosPentagonal hn := by
rw [IsPosPentagonal, and_comm, not_and]
intro h
obtain hnot := x.up_notPentagonal hn hdown hpospen h
contrapose! hnot
si... |
9,193 | lean_file_chunk | e565dfda47697c62d657af0f6aec84085b68b5ada29412587e993cdc4a8a1f5c | lean_source_file | lean_pool_source_file_chunks | unfold IsPosPentagonal at ha hb
by_cases hi : i < a.delta.length - 1
· rw [ha.2 i hi, hb.2 i (h ▸ hi)]
· have hai' : i = a.delta.length - 1 :=
le_antisymm (Nat.le_sub_one_of_lt hai) (Nat.le_of_not_lt hi)
have hbi' : i = b.delta.length - 1 := h ▸ hai'
conv => left; left; rw [hai']
c... |
6,659 | lean_file_chunk | a81713fc4d3947575e87bdda16e05a376246b64cdd8e3eb13c699bcc5ceff4be | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import LeanPool.PentagonalNumberTheorem.PowerSeries
import Mathlib.Combinatorics.Enumerative.Partition.Glaisher
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Orde... |
6,281 | lean_file_chunk | e29f9a3c0cfe5802fff7d8c76d0d5c066d254eeac2cbc6e47f5fd40bb71fa2f8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import LeanPool.PentagonalNumberTheorem.Generic
import Mathlib.RingTheory.PowerSeries.Basic
import Mathlib.RingTheory.PowerSeries.Order
import Mathlib.RingTheory.PowerSeries... |
732 | lean_file_chunk | 75dc456e3c2c8ff1abb96958d7175f7dc8c5d9f26eccff2aa789744153392542 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Weiyi Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Weiyi Wang
-/
import LeanPool.PentagonalNumberTheorem.Complex
import LeanPool.PentagonalNumberTheorem.Generic
import LeanPool.PentagonalNumberTheorem.Old
import LeanPool.PentagonalNumberT... |
17,085 | lean_file_chunk | d84d5e4eca856d869979a9b4f9fe552c755391d06091083b7f5af9334b73e5ca | 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
-/
/-
# AnnulusLocalEstimate.lean
Uniform local estimate on annuli (combining circle + band estimates).
Scaffolding n... |
14,338 | lean_file_chunk | cad4e89834682abc16c4391f3cd1bb5201de4940e2514bdda4e7ba8665c1d726 | 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
-/
/-
# BlockDecomposition.lean
Frequency-block decomposition of polynomials.
Scaffolding notes: BlockDecomposition/b... |
23,975 | lean_file_chunk | bd80f999257346217e9f7ce06cd58867c1ea5068348f46c1a6902c5aafe46de5 | 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 definitions for the Fock-space phase retrieval problem.
Scaffolding notes: Definitions/... |
15,600 | lean_file_chunk | 04e13c2ef1711cab8e9cbaf53bfba8cd4acd108f1c718ec574d94d6e9e613201 | lean_source_file | lean_pool_source_file_chunks | Real.exp (-‖Complex.polarCoord.symm p‖ ^ 2)))
from (Complex.integral_comp_polarCoord_symm _).symm]
rw [polarCoord_target]
-- Step 2: Rewrite the integrand using helper lemmas
-- For (r, θ) ∈ Ioi 0 ×ˢ Ioo(-π, π):
-- ‖pc.symm(r,θ)‖ = |r| = r (since r > 0)
-- polyEval a (pc.symm(r,θ)) = polyEvalCircle a ... |
23,966 | lean_file_chunk | 347ea197f157f98fcad775e0b6ad653ffa7c7b5b175249852aa41d977342744b | 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
-/
/-
# HighFreqBandEstimate.lean
High-frequency band estimate using Poincaré + rotational averaging.
Scaffolding not... |
21,249 | lean_file_chunk | 174f80a67b1b1e846a5fbd6b2d0047fbf1bf01cf2f182954c29d229cc38ba75c | lean_source_file | lean_pool_source_file_chunks | Continuous (fun x : ℝ => ∑ m : Fin L,
b m * ((2 * Real.pi * Complex.I * ↑(m.val : ℤ) / (T : ℂ)) *
fourier (m.val : ℤ) (↑(x + a) : AddCircle T))) :=
continuous_finsetSum Finset.univ fun m _ =>
continuous_const.mul
(continuous_const.mul
((fourier (m.val : ℤ)).cont... |
13,948 | lean_file_chunk | 31a5a14eb07db5e7ddc641173f36ddc6e789aac6c942a221eed0293e68df8d3c | 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
-/
/-
# LaplaceFactorial.lean
Laplace/Stirling-type bounds for factorials via saddle-point estimates.
Scaffolding not... |
23,994 | lean_file_chunk | 065ec1651e38987051125d35949ecb8ccec3e692460838f4f4ed88f452c10af5 | 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
-/
/-
# LeakageEstimate.lean
Leakage estimates for block-to-annulus energy transfer.
Scaffolding notes: BlockDecompos... |
23,973 | lean_file_chunk | dbce21a74b5da1e3b9dac8644b0914f72e6bbd75519353b3fa4c32b72458bfcf | lean_source_file | lean_pool_source_file_chunks | · intro ⟨⟨hℓ'1, hℓ'Λ⟩, hℓ'mem⟩
by_contra hne
have hdisj := blocks_disjoint hℓ1 hℓ'1 (Ne.symm hne)
exact Finset.disjoint_left.mp hdisj hℓmem hℓ'mem
· intro h; rw [h]
refine ⟨⟨hℓ1, ?_⟩, hℓmem⟩
unfold maxBlockIndex
rw [Nat.le_sqrt]
have hfb : k.val + 1 ∈ freqBlock ℓ := hℓmem
unfold freqBl... |
609 | lean_file_chunk | 0398f4afca2d03ddd8f4d6fb33ea94d8be4e51f874f09a5b1bcc104d2d9865cd | lean_source_file | lean_pool_source_file_chunks | ∑ m ∈ (Finset.Icc 6 100 : Finset ℕ), Real.exp (-(m : ℝ) ^ 2) :=
add_nonneg (le_of_lt (Real.exp_pos _))
(Finset.sum_nonneg fun m _ => le_of_lt (Real.exp_pos _))
-- 2 · exp(1/4) · sum < 2 · (13/10) · (14/10¹² + 95/10¹⁴) = 3887/10¹⁴ < 4/10¹¹
have step1 : 2 * Real.exp (1 / 4) *
(Real.exp (-25) + ∑ m ∈ (... |
2,496 | lean_file_chunk | 321c9a3cb27d42e4c60b07a9ca39990f7f47f8df4eda4085d55bd10e3b18e131 | 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
-/
/-
# LipschitzRho.lean
Lipschitz property of the function `rho`.
Scaffolding notes: ElementaryLemmas/lipschitz_rho... |
2,281 | lean_file_chunk | 940e070c12d9334f4203953d146e9eb3cc401ddce48f12c6089d1f324d866f13 | 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
-/
/-
# Local.lean
Transparent statement of the local phase-aligned Fock-space phase retrieval estimate.
This is the... |
23,995 | lean_file_chunk | 2c3d0f5330a11caaff1b5053f4471286434c81d7c022ade00c3ce597456ad983 | 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
-/
/-
# LocalCircleEstimate.lean
Quantitative local estimate on S¹.
Scaffolding notes: LocalCircleEstimate/local_circ... |
6,204 | lean_file_chunk | 621ce1d3af61c89df825597aabca566638810afd589d0bbaa1298fa762fd791c | lean_source_file | lean_pool_source_file_chunks | have h_rho_factor : ∀ w : ℂ,
rho w * (‖(1 : ℂ) + w‖ + 1) = |‖(1 : ℂ) + w‖ ^ 2 - 1| := by
intro w; unfold rho
set a := ‖(1 : ℂ) + w‖
have ha1 : 0 ≤ a + 1 := by positivity
rw [show |a - 1| * (a + 1) = |a - 1| * |a + 1| from by
rw [abs_of_nonneg ha1]]
rw [← abs_mul]; congr 1; ring
-- Cont... |
23,951 | lean_file_chunk | baaef974c82d83a61140fb0cfc0336a9016f412ad12d61ecaefa5201febaad42 | 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
-/
/-
# LocalCore.lean
The analytic core of the local Fock-space phase retrieval estimate.
This file upgrades the or... |
23,968 | lean_file_chunk | 781630cd0b352e0aedbf5093af59e1d8a5bf3463e1e8c7e1cdb1c8cfefb4b3de | lean_source_file | lean_pool_source_file_chunks | (∫ x : ℝ, Real.exp (-x ^ 2)) * ∫ y : ℝ, Real.exp (-y ^ 2)
= Real.sqrt Real.pi * Real.sqrt Real.pi := by simp [hgauss']
_ = Real.pi := by nlinarith [Real.sq_sqrt Real.pi_pos.le]
private lemma gaussian_integral_normalized :
(1 / Real.pi) * ∫ z : ℂ, Real.exp (-‖z‖ ^ 2) = 1 := by
rw [gaussian_integral_eq... |
23,954 | lean_file_chunk | 10dc8ff28eabd9f79656fcbb38b8913eb05f50ccd74b9c519c7d6bb1b10745cf | lean_source_file | lean_pool_source_file_chunks | private lemma integrable_gaussianWeight :
Integrable gaussianWeight volume := by
let a : Fin 0 → ℂ := fun i => nomatch i
convert (integrable_gaussian_sq_real_const_add_polyEval a 1).const_mul (1 / Real.pi) using 1
ext z
simp [gaussianWeight, polyEval]
private lemma gaussianMeasure_isFinite : IsFiniteMeasur... |
5,297 | lean_file_chunk | 32072552dd2de55d4552998dbe6b8755b6d475e0793a8fb521c5fc12ced14752 | lean_source_file | lean_pool_source_file_chunks | have hN2_int : Integrable (fun z => N z ^ 2) gaussianMeasure := by
simpa [N, hp_eval] using integrable_sq_gaussianMeasure_real_const_add_polyEval a u
have hR2_int : Integrable (fun z => R z ^ 2) gaussianMeasure := by
simpa [R, hp_eval] using integrable_sq_gaussianMeasure_rho_real_const_add_polyEval a u
have... |
8,245 | lean_file_chunk | 352ab5d2de3a1ee9841fce52ca4d3f64e34c4e31095332809101c679ab51683a | 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
-/
/-
# LocalHelpers.lean
Helper lemmas for the local phase-aligned Fock-space phase retrieval estimate.
The public ... |
23,991 | lean_file_chunk | d4842f27cddb5366f3ba749f256f2227d77f0b2cd332aff5f685cec7984f8df5 | 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
-/
/-
# MainTheorem.lean
Assembly of the main Fock-space coercivity theorem.
Scaffolding notes: Assembly/main_theorem... |
17,021 | lean_file_chunk | 7d6a64810252cb8fd2e9c8b4cca14d291a6320a2ea31b6ddb747a500cf633e89 | lean_source_file | lean_pool_source_file_chunks | fun a b => hf_cont.intervalIntegrable a b
have h_telescope := sum_intervalIntegral_telescope hf_ii
-- ∫_0^J f → ∫_{Ioi 0} f as J → ∞ (via intervalIntegral_tendsto_integral_Ioi)
have h_tends : Filter.Tendsto (fun (b : ℝ) => ∫ r in (0 : ℝ)..b, f r)
Filter.atTop (nhds (∫ r in Set.Ioi (0 : ℝ), f r)) :=
inte... |
9,910 | lean_file_chunk | 4ed7b9f3f331e9b909a4e5bbc1ba51e7d896a4eb754fbe9e3a592b051899f180 | 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
-/
/-
# Poincare.lean
Weak Poincaré inequality on intervals — the ONLY missing Mathlib result.
Scaffolding notes: Mis... |
7,744 | lean_file_chunk | 5edd33be399602b62030d2ac021c0023a67edf53ff7e0d2e7378d6e625775a73 | 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
-/
/-
# RotationalAveraging.lean
Rotational averaging lower bound for `rho`.
Scaffolding notes: ElementaryLemmas/rota... |
1,846 | lean_file_chunk | 5a77b4d165176008e5b98c2d1000891b732e5af9c9abd7f2a4e92a3e44787219 | 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
-/
/-
# SafeSquare.lean
Safe-square inequalities — pure real-number estimates.
Scaffolding notes: ElementaryLemmas/sa... |
2,292 | lean_file_chunk | 16f3881715be5622df92316634f45f61d4a61084936c93676679e884c46c8e98 | 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.Internal.Local
/-!
# Showcase
This file packages the local Fock-space argument... |
23,953 | lean_file_chunk | 04ab5e1c047abc5631b8bb16b7bba61dcfa3120402a05e523e9be5d7b0969d7a | 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.PhaseStability
/-! # Auxiliary -/
open scoped BigOperators
noncompu... |
11,881 | lean_file_chunk | 732e72ef6daa7e6f0d02aef0d2d0774545266470aa1f183cdecc10530af368fc | lean_source_file | lean_pool_source_file_chunks | have hPQθ_mem : MeasureTheory.MemLp (fun z => P z - θ * Q z) 2
(explicitGamma d) :=
hP_mem.sub hθQ_mem
have hPQnθ_mem : MeasureTheory.MemLp (fun z => P z - θ * Qn n z) 2
(explicitGamma d) :=
hP_mem.sub hθQn_mem
have hQnQ_mem : MeasureTheory.MemLp (fun z => Qn n z - Q z) 2
(ex... |
23,966 | lean_file_chunk | 16509e20c112ce4e6af0cf6934de39e33a3a04d03cab80366b64bf4188f3e3d4 | 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.Topology.MetricSpace.Sequences
import LeanPool.PhaseRetrieval.DimdPoly.Internal.FiniteBaseAnnulusEstimate... |
23,984 | lean_file_chunk | f0f13fbabbaeca29f641e6164215f9120e2947d1e4e72f9443f8c6311d76d4ec | lean_source_file | lean_pool_source_file_chunks | refine norm_tsum_subtype_compl_le_of_finset_bound_wip
(E := E)
(f := fun alpha : Idx d =>
(coeffPkappa (H m) alpha - coeffSkappa U alpha) * Phi kappa alpha z)
(hf := hdiff_summ.subtype _) ?_
intro T hdis
exact le_of_lt (hE T hdis (hH_norm m) hU_partial)
have hsplit := hdiff_summ.sum_... |
23,985 | lean_file_chunk | 8853a55bca054bfcea2abf79e5c260e5bed0f9adb571cc604cf4d7a4e29cf040 | lean_source_file | lean_pool_source_file_chunks | have hdelta_pos : 0 < delta := by
dsimp [delta]
positivity
by_contra hno
apply hbad
refine ⟨delta, hdelta_pos, ?_⟩
intro H t hpos hH_norm hmass ht_pos ht_le_four
by_contra hnot
have hlt : defect F (t • H) < delta * t := lt_of_not_ge hnot
exact hno ⟨H, t, hpos, hH_norm, hmass, ht_pos, ht_le_four, h... |
23,945 | lean_file_chunk | ead437594b250246d8751febec0fa747fbb977d6d1189e5e3fa7b05f943ac211 | lean_source_file | lean_pool_source_file_chunks | defectFunctionPkappa_coeff_wip kappa F (t (φ m) • H (φ m)) z / t (φ m)
have hf_eq :
∀ m,
f m =
((t (φ m))⁻¹ : ℝ) •
defectFunctionPkappa_coeff_wip kappa F (t (φ m) • H (φ m)) := by
intro m
funext z
simp [f, Pi.smul_apply, div_eq_mul_inv, mul_comm]
have hf_meas :
... |
23,962 | lean_file_chunk | 93568b49a323b31194aceda6006993bd898bd5d32ded7f5cb77e755310c0d1f8 | lean_source_file | lean_pool_source_file_chunks | have hminus := norm_sq_add_real_smul_wip f u (-1)
have hplus' :
‖f + u‖ ^ 2 =
‖f‖ ^ 2 + 1 ^ 2 * ‖u‖ ^ 2 + 2 * 1 * Complex.re (u * star f) := by simpa using hplus
have hminus' :
‖f + (-1 : ℂ) * u‖ ^ 2 =
‖f‖ ^ 2 + (-1 : ℝ) ^ 2 * ‖u‖ ^ 2 +
2 * (-1 : ℝ) ... |
7,196 | lean_file_chunk | f664a72412379ca452b9099ea36d66d905dfc47493bd70014e784988eab7c7ff | lean_source_file | lean_pool_source_file_chunks | ‖(0 : Pkappa d kappa)‖ = 0 := by
change Real.sqrt (Finset.sum (0 : Pkappa d kappa).support
(fun alpha => ‖(0 : Pkappa d kappa) alpha‖ ^ 2)) = 0
simp
rw [hzero]
exact mul_nonneg (le_of_lt hC_F_pos) (Real.sqrt_nonneg _)
· let t : ℝ := ‖G‖
let H : Pkappa d kappa := (((t : ℂ)⁻¹) : ℂ) • G
... |
10,346 | lean_file_chunk | 54fa6e193d29474e6ffd930f08312297a46138ab1fb4326a71b64ab71024b682 | 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.Complex.UpperHalfPlane.Measure
import Mathlib.Analysis.Fourier.AddCircle
import Mathlib.Analysis... |
23,988 | lean_file_chunk | 7c4677505be105b5b74b4a97198d82a9c3044d203ce16b5c84ee8194e110f834 | 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.Calculus.Deriv.Star
import Mathlib.Analysis.Calculus.ParametricIntegral
import Mathlib.Analysis.... |
23,966 | lean_file_chunk | 991eff469dd11b700f1c9d3d6e1d2d633a38967ed84776ecfa5dd7cac5027cdd | lean_source_file | lean_pool_source_file_chunks | congr 1
ring
have hsum : Integrable (fun t : ℝ =>
Real.sqrt 2 * (|t| * Real.exp (-(t ^ 2) / 2)) +
(1 + B) * Real.exp (-(t ^ 2) / 2)) volume :=
(integrable_abs_mul_exp_neg_half_sq_wip25.const_mul (Real.sqrt 2)).add
(hgauss.const_mul (1 + B))
exact (hsum.const_mul C).congr (by
filter_u... |
23,932 | lean_file_chunk | cc0c0e9b9da07b78f2a259a69d00b881dd25286162ab0f2a4f195d41cf63c052 | lean_source_file | lean_pool_source_file_chunks | Complex.exp (-(2 * Real.pi : ℂ) * Complex.I *
((inner ℝ ω t : ℝ) : ℂ)))
(∫ t : ℝ,
(phi t *
(((Real.sqrt 2 : ℂ) * ((t - (1 / 2 : ℝ) * x : ℝ) : ℂ) - w0) *
realHermiteGenerating (t - (1 / 2 : ℝ) * x) w0)) *
Complex.exp (-(2 * Real.pi : ℂ) * Complex.I *
... |
23,970 | lean_file_chunk | 03f49cbe801ff34e19721f38278996fce44e3e41f5468183874b8571880faacd | lean_source_file | lean_pool_source_file_chunks | rw [show Complex.exp (-(((t : ℂ) ^ 2) / 2) + (Real.sqrt 2 : ℂ) *
(t : ℂ) * 0 - 0 ^ 2 / 2) =
Complex.exp (-(((t : ℂ) ^ 2) / 2)) by
ring_nf]
simp only [star_mul, RCLike.star_def, Complex.conj_ofReal]
rw [← Complex.exp_conj]
simp only [map_neg, map_div₀, map_pow, Complex.conj_ofReal, ma... |
23,931 | lean_file_chunk | 09ef0e42b3d44b6d90f2c16bb4333d871bee2adec0f3537182ed18a53b4d966e | lean_source_file | lean_pool_source_file_chunks | · have hlt : n < k := Nat.lt_of_not_ge hk
rw [Polynomial.coeff_hermite_of_lt hlt]
simp [realHermiteGeneratingExpansionCoeff, Nat.choose_eq_zero_of_lt hlt]
/-- `standardGaussianMoment`: standard Gaussian Moment. -/
noncomputable def standardGaussianMoment (r : ℕ) : ℂ :=
if Even r then ((r - 1)‼ : ℂ) else 0
p... |
23,994 | lean_file_chunk | 42770ffcb0d930e3479ee6f412ea280074ca2e0e674f4787a02f37889e388d10 | lean_source_file | lean_pool_source_file_chunks | theorem realHermiteGenerating_iteratedDeriv_zero_star (n : ℕ) (t : ℝ) :
star (iteratedDeriv n (realHermiteGenerating t) 0) =
iteratedDeriv n (realHermiteGenerating t) 0 := by
have hcont : ContDiff ℂ (⊤ : WithTop ℕ∞) (realHermiteGenerating t) := by
unfold realHermiteGenerating
fun_prop
have h := st... |
23,983 | lean_file_chunk | 674f8770136025cab29239576c2c46eb23a2a2a54ccca7c2af13e722d7be50b1 | lean_source_file | lean_pool_source_file_chunks | refine realHermite1D_memLp_inner_orthonormal_of_no_conj_interchange ?_ ?_
· intro n
exact realHermite1D_memLp n
· intro n m
exact realHermiteGenerating_no_conj_interchange_of_finite_sum n m
theorem realHermiteTensorRep_memLp_of_realHermite1D_memLp
{d : Nat} (alpha : Idx d)
(hmem1 : ∀ n : Nat, MemLp... |
23,990 | lean_file_chunk | 2a1a6329efb8ad1a0c5f7caf89add83718e00c3ed06611799797193d2f897b82 | lean_source_file | lean_pool_source_file_chunks | Complex.exp (-(Real.pi : ℂ) * Complex.I * ((inner ℝ ξ.1 ξ.2 : ℝ) : ℂ)) := by
calc
(∏ q : Fin d,
Complex.exp (-(Real.pi : ℂ) * Complex.I *
(((ξ.1 q : ℝ) : ℂ) * (ξ.2 q : ℂ)))) =
Complex.exp
(∑ q : Fin d,
-(Real.pi : ℂ) * Complex.I * (((ξ.1 q : ℝ) : ℂ) * (ξ.2... |
23,964 | lean_file_chunk | 51d12723132e646f7d11a847e3f0cbc60dc187677b9c0ff18d75eb6290c4fee7 | lean_source_file | lean_pool_source_file_chunks | A * ∫ t : ℝ, f2 t ∂μ + C * ∫ t : ℝ, f0 t ∂μ := by ring
rw [hsplit]
simp only [f4, f2, f0, μ]
rw [gaussian_half_moment_four, gaussian_half_moment_two, gaussian_half_moment_zero]
ring
private theorem gaussian_half_sextic_exp_integral (A B C z : ℂ) :
(∫ t : ℝ,
((4 / 3 : ℂ) * (t : ℂ) ^ 6 - A * (t : ℂ) ... |
23,971 | lean_file_chunk | 816a234e7d8c1e044935fc02f8a65ed8592c0a5332db08b83b478cfc2f032da0 | lean_source_file | lean_pool_source_file_chunks | ((Nat.choose m l : ℂ) * (Real.sqrt 2 : ℂ) ^ l *
iteratedDeriv (m - l) (fun w : ℂ => Complex.exp (-(w ^ 2) / 2)) 0) *
(∑ i ∈ Finset.range (k + 1), ∑ j ∈ Finset.range (l + 1),
(Nat.choose k i : ℂ) * (Nat.choose l j : ℂ) *
((x : ℂ) / 2) ^ (k - i) * (-(x : ℂ) / 2) ^ (l ... |
23,970 | lean_file_chunk | 17ef2b327e07dbda7189daaeeb9db53c186cd058a27c11024eae792c1dfcf09c | lean_source_file | lean_pool_source_file_chunks | oneDWindowAmbiguityShiftedModulatedGaussian x ω t := by
rw [oneDWindowAmbiguityMonomialKernel_eq_shifted_monomial 0 0,
oneDWindowAmbiguityMonomialKernel_eq_shifted_monomial 0 2,
oneDWindowAmbiguityMonomialKernel_eq_shifted_monomial 2 0,
oneDWindowAmbiguityMonomialKernel_eq_shifted_monomial 2 2]
ring
pr... |
23,982 | lean_file_chunk | b442ce5709d9ef8d7084e95533efe92635f2e3aebacfe8a81bcb69da83a73e8d | lean_source_file | lean_pool_source_file_chunks | intro alpha
rw [map_smul]
simp [hstft]
_ = ∑' alpha : Idx d,
coeffSkappa U alpha *
(stftModelPhase kappa ξ *
(((WKappa ξ : ℝ) : ℂ) *
Phi kappa alpha (TKappa ξ))) := by
simp_all
_ = ∑' alpha : Idx d,
(stftModelPhase kappa ξ * ((WKa... |
23,954 | lean_file_chunk | ab5b43b7c8c8a108f52fa53129f7dfbc4a8bb16d4d21bae551f6f6ae32546cbe | lean_source_file | lean_pool_source_file_chunks | (((x : ℂ) - (2 * Real.pi : ℂ) * Complex.I * (ω : ℂ)) /
(Real.sqrt 2 : ℂ)) *
star (((x : ℂ) - (2 * Real.pi : ℂ) * Complex.I * (ω : ℂ)) /
(Real.sqrt 2 : ℂ)) +
(1 / 2 : ℂ) *
((((x : ℂ) - (2 * Real.pi : ℂ) * Complex.I * (ω : ℂ)) /
(Real.sqrt ... |
23,968 | lean_file_chunk | 6dea3724f961f8d940f14f5311bd6a867180b6c4d4233c23cf4d8157ff623f2d | lean_source_file | lean_pool_source_file_chunks | star (realHermiteTensorRep kappa (t - ((1 / 2 : ℝ) • ξ.1))) *
Complex.exp (-(2 * Real.pi : ℂ) * Complex.I *
((inner ℝ ξ.2 t : ℝ) : ℂ))) =
∫ t : RealVec d,
(fun y : Fin d → ℝ => ∏ q : Fin d, f q (y q)) (WithLp.ofLp t) := by
apply MeasureTheory.integral_congr_ae... |
23,967 | lean_file_chunk | 1b2342c4d0c0330c6c8a20612c579f7cccb4b263b075a2b6c698d2cecc160559 | lean_source_file | lean_pool_source_file_chunks | simp [ambiguityRep, Fsec, Gsec, phase, real_inner_comm, mul_assoc, mul_comm]
theorem equalAmbiguity_to_rankOneKernel_ae
{d : Nat} {f g : L2Real d} {fRep gRep : RealVec d -> ℂ}
(hf_rep : IsL2Rep f fRep) (hg_rep : IsL2Rep g gRep)
(hAmb : ∀ ξ : PhaseSpace d, ambiguityRep f f ξ = ambiguityRep g g ξ) :
(fun... |
2,862 | lean_file_chunk | 9a8683ae66490692e4a6663dff82cd0b708e715141ac0e03756de6df289d5aee | lean_source_file | lean_pool_source_file_chunks | have hpoint := ae_modulus_to_pointwise_modulus hd kappa hmod
by_cases hU_zero : U = 0
· have hV_toFun_zero : ∀ z, toFun kappa V z = 0 := by
intro z
have hz_norm : ‖toFun kappa V z‖ = 0 := by
simpa [hU_zero, toFun_zero_exact_wip] using (hpoint z).symm
exact norm_eq_zero.mp hz_norm
have ... |
23,959 | lean_file_chunk | 05a94c946b98e5cfd9b70d08f50345d6329d440a20e1cbff0e6cfc87f3be50e4 | 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.FiniteBaseCircleEstimate
import LeanPool.PhaseRetrieval.DimdPoly.Intern... |
23,982 | lean_file_chunk | 2ffa2d399cb23157bad85e723293adee45eaec7d320a44f4a8e9f76b7c02ceb6 | lean_source_file | lean_pool_source_file_chunks | (Hermite1DimdLEAN.localPart j M ⟨G⟩).support =
Hermite1DimdLEAN.localCoeffSet j M ⟨G⟩ :=
(Hermite1DimdLEAN.explicitLocalAndFarSupport (j := j) (M := M) (G := ⟨G⟩)).2.2.1
have halpha_local :
alpha ∈ Hermite1DimdLEAN.localCoeffSet j M ⟨G⟩ := by
have halpha_support :
alpha ∈ (Hermite1DimdLE... |
23,962 | lean_file_chunk | d0069ba3929b7dd8fa6db35fe267e7ac389936154608e6e8a4bc247a81b19b1c | lean_source_file | lean_pool_source_file_chunks | ∂ gammaD d) := by
rw [MeasureTheory.integral_add hrightDef hrightMass,
MeasureTheory.integral_const_mul, MeasureTheory.integral_const_mul]
_ = 2 * (∫ z : Cd d,
Set.indicator (productAnnulus j)
(fun w =>
(‖evalPkappa kappa F w + evalPkappa kappa G w‖ -
... |
23,936 | lean_file_chunk | db242ad693c579756b219e88fe37b8a2830a18e99c05573384c130632d136bd3 | lean_source_file | lean_pool_source_file_chunks | (q0 : Fin d) (D N L : Nat)
(F H : Pkappa d kappa) (z : Cd d)
(hL : 1 ≤ L)
(hsep : circleGap D * L ≤ N)
(hD : ∀ alpha ∈ F.support, alpha q0 ≤ D)
(hband : ∀ alpha ∈ H.support, N ≤ alpha q0 ∧ alpha q0 < N + L) :
circleL2Sq
(fun x : Circle =>
evalPkappa kappa H
(Function.upda... |
11,166 | lean_file_chunk | 532b664c53f22d324571059a178b9441af5a8fc6eb3a4931c606085ba06a662f | lean_source_file | lean_pool_source_file_chunks | simp [Finsupp.smul_apply, Real.norm_eq_abs, sq_abs, mul_pow]
rw [hsum, Real.sq_sqrt (mul_nonneg (sq_nonneg t) (by positivity)), Real.sq_sqrt (by positivity)]
private theorem finite_base_product_annulus_estimate_large_eps
{d : Nat} (hd : 0 < d) (kappa : MultiIndex d)
(F : Pkappa d kappa) (_hF : basePointNor... |
23,971 | lean_file_chunk | 04cbc516124f031685cc1f00cb44aec7b18b6ed1dd38bca5b7285c9f3d1ab6bd | 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.Algebra.Order.Chebyshev
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Order.Interval.Se... |
23,992 | lean_file_chunk | 2fccc01c0240578399e49bb6e75b34a28e62b9681438c8e46a9fd4c528c1d2ae | lean_source_file | lean_pool_source_file_chunks | (hclose : ‖Qx - c‖ <= theta * ‖c‖) :
∃ lam : ℂ, Qx = lam * c ∧ ‖lam - 1‖ <= theta := by
refine ⟨Qx * c⁻¹, ?_, ?_⟩
· field_simp [hc]
· have hc_norm_pos : 0 < ‖c‖ := norm_pos_iff.mpr hc
have hrewrite : Qx * c⁻¹ - 1 = (Qx - c) * c⁻¹ := by field_simp [hc]
calc
‖Qx * c⁻¹ - 1‖ = ‖(Qx - c) * c⁻¹‖ := by... |
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