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 |
|---|---|---|---|---|---|
2,659 | lean_file_chunk | 298a39117bbc824bd3744c48421c42eb12eac08682955304aea87bcd7824e5c4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Wondermonger-daydreaming. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wondermonger-daydreaming
-/
import Mathlib.GroupTheory.Perm.Fin
import Mathlib.GroupTheory.Perm.Cycle.Type
import Mathlib.Data.Fin.Basic
/-!
`finRotate` arithmetic lemmas... |
23,971 | lean_file_chunk | 16c5c299568c808b6093a37019744665279bd472930294d08f2a21e5e2470b94 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Wondermonger-daydreaming. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wondermonger-daydreaming
-/
import Mathlib.Combinatorics.Enumerative.Catalan.Basic
import Mathlib.GroupTheory.Perm.Fin
import Mathlib.GroupTheory.Perm.Cycle.Type
import Math... |
23,982 | lean_file_chunk | 0f36e44e32f8cc89e21e904c7d19af766c0334a27171f3dba309581bda27a85d | lean_source_file | lean_pool_source_file_chunks | private lemma sign_pairing {n : ℕ} (p : Pairing n) :
Equiv.Perm.sign p.val = (-1) ^ n := by
rw [Equiv.Perm.sign_of_cycleType, Equiv.Perm.sum_cycleType,
support_eq_univ_of_fpf p.val p.property.2, Finset.card_univ, card_fin,
pairing_cycleType_card p]
simp [pow_add, pow_mul]
private theorem numCycles_... |
8,843 | lean_file_chunk | 0aad6e4c138348d90c7731e8c9d970071782af11bb14d6f687773be45c763039 | lean_source_file | lean_pool_source_file_chunks | ∃ x : Fin (2 * (n + 1)), (longCycle (n + 1) * p.val) x = x := by
set σ := longCycle (n + 1) * p.val
have hfp_card := Equiv.Perm.card_fixedPoints σ
have hsum := Equiv.Perm.sum_cycleType σ
have hsum_ge := multiset_sum_ge_two_card
(fun c hc => Equiv.Perm.two_le_of_mem_cycleType hc : ∀ c ∈ σ.cycleType, 2 ≤ c)
... |
1,821 | lean_file_chunk | 83ff7014fa412b5f0d1ed30d6fdbe24958311adbeb3addf76a856df964244d8f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Wondermonger-daydreaming. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wondermonger-daydreaming
-/
import Mathlib.GroupTheory.Perm.Fin
/-!
Group-theoretic helpers used with rotation normalization.
The `finRotate` arithmetic lemmas live in... |
5,750 | lean_file_chunk | 34dc8cc05a362d1594e60eb515e3801568396a4d4fd82f648f3b32ac3071d206 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Wondermonger-daydreaming. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wondermonger-daydreaming
-/
import Mathlib.Data.Fin.Basic
import Mathlib.GroupTheory.Perm.Basic
/-!
CANONICAL DELETION OF THE BOUNDARY PAIR
Canonical deletion of coord... |
838 | lean_file_chunk | a321f06096bd08e78ad5c3a9408ede36b4783c8c933a9cfe23315e2c204f3401 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Wondermonger-daydreaming. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wondermonger-daydreaming
-/
import LeanPool.SemicircleCheck.ShiftTwoEquiv
import LeanPool.SemicircleCheck.FinRotateLemmas
import LeanPool.SemicircleCheck.RotationArithmetic
... |
23,925 | lean_file_chunk | 909a8ea64840c429ebd7a4c5a6a42320cbaa36fc8554ed679bacdf65951a8b01 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 FredRaj3. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: FredRaj3
-/
import Mathlib.Analysis.SpecialFunctions.Sqrt
import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
import Mathlib.Analysis.SpecialFunctions.Integrals.Basic
import Mathlib.MeasureT... |
23,978 | lean_file_chunk | 3991d846922d9b8311e72c9c5f7963acf0af7f805beb8d4a7090cda9f600c0b7 | lean_source_file | lean_pool_source_file_chunks | /-- If `X` has semicircular law with mean `μ` and variance `v`, then `X / c` has
semicircular law with mean `μ / c` and variance `v / c ^ 2`. -/
lemma semicircleReal_div_const (hX : ProbabilityTheory.HasLaw X (semicircleReal μ v) P)
(c : ℝ) :
ProbabilityTheory.HasLaw (fun ω ↦ X ω / c)
(semicircleReal (μ /... |
1,856 | lean_file_chunk | cc87438e6d2b8de9a25789e6a44255418cb42e688ef2ed00765ff73d1f827bfc | lean_source_file | lean_pool_source_file_chunks | lemma variance_fun_id_semicircleReal : Var[fun x ↦ x; semicircleReal μ v] = v :=
variance_id_semicircleReal
/-- The odd central moments of the semicircle distribution vanish. -/
lemma centralMoment_fun_odd_semicircleReal (μ : ℝ) (v : ℝ≥0) (n : ℕ) :
ProbabilityTheory.centralMoment (fun x ↦ x) ((2 * n) + 1) (semic... |
1,690 | lean_file_chunk | 10390af5b1c4e30eab9fe88977089ab36d7dd5659602e7d0292b56b33cb0328e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 FredRaj3. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: FredRaj3
-/
import LeanPool.SemicircleLaw.SemicircleDistribution
/-!
# Wigner Semicircle Distribution
Source: url:https://www.math.ucsd.edu/~tkemp/247A.Notes.pdf
Authors: FredRaj3
Status:... |
2,604 | lean_file_chunk | e77141324b2b2dafedab0cace31017fb91a8f1a45583ebc53a3408bbd318ee78 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
/-!
# Elementary Properties of Sensitivity
Basic bounds and symmetries for the sensitivity of Boolean functions.
## Main r... |
1,246 | lean_file_chunk | bf4465b55d5080a52eaded80eaade7259c2fffa0881bd4c6026d91c5358e9cb5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
import LeanPool.Sensitivity.Basic
import LeanPool.Sensitivity.Multilinear
import LeanPool.Sensitivity.Main
/-!
# Consequence... |
3,985 | lean_file_chunk | 8610a918ff33ee168be926a6a9b68d81c98eb62be3f65b14ead050ea7fff1f06 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import Mathlib.Data.Fin.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Data.Fintype.Pi
import Mathlib.Data.Finset.Lattice.Fold
/-!
# Boolean Function D... |
3,210 | lean_file_chunk | 3bde41df7452e4450eae73c1181a8720d960cab5456f21fa7aae356b6648be4c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
import Archive.Sensitivity
import Mathlib.Data.Fintype.Pi
/-!
# Bridge to Mathlib's Huang Theorem
Repackages Mathlib's `Sen... |
7,056 | lean_file_chunk | 2e1360b0827c5b47351974f63111361fb294750ab84b70c8f107b2eb180c0eb9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
import LeanPool.Sensitivity.Multilinear
import LeanPool.Sensitivity.Subcube
import LeanPool.Sensitivity.Parity
import LeanPoo... |
3,197 | lean_file_chunk | 0c7dbe6afea8f41abb803f53a50004d40a5ca90e249157ff12b5bbf3aeca7e77 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Data.Finset.Powerset
import Mathlib.Data.Fintype.Powers... |
9,577 | lean_file_chunk | 9cbb86d22c85ae5717715f93a8c730352597411aef43cb6d0b63a5c9481cb6b1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
import LeanPool.Sensitivity.Multilinear
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Data.Fintype.Pi... |
5,513 | lean_file_chunk | 205919db1f4ccb5e2e37e69395f604b925d877645658ba2ca662b6e422fcd7fd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
import LeanPool.Sensitivity.Multilinear
/-!
# Subcube Restriction
We define the restriction of a Boolean function to a subc... |
2,651 | lean_file_chunk | aaaeb2ee42b3707b172551cffe35ac9df8b1cc0a3bfb722ae561e4e62b752892 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Sensitivity.Defs
import LeanPool.Sensitivity.Basic
import LeanPool.Sensitivity.Multilinear
import LeanPool.Sensitivity.Subcube
import LeanPoo... |
23,940 | lean_file_chunk | 0c09cf582dfa75566a967e732e0f76b824e8cbfa459b67ab1fff5306c09d5563 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import LeanPool.SetTheory.Realize
import Mathlib.SetTheory.ZFC.VonNeumann
/-!
# Basic theory of models of ZF set theory
This module develops the order-theoretic and membe... |
11,516 | lean_file_chunk | 23459ceedef3fc83680a6aa6a5784ba814e67675292ea05a92720a730055ba44 | lean_source_file | lean_pool_source_file_chunks | @[simp] lemma isPair_pair {x y : M} : IsPair ⸨x, y⸩ := by simp [IsPair]
lemma fst_aux {x y z : M} (hz : z = ⸨x, y⸩) : ExistsUniqueAt x fun x => ∀ w ∈ z, x ∈ w := by
subst hz
simp [ExistsUniqueAt, pair.spec]
@[realize] lemma fst.eu {z : M} (hz : IsPair z) : ∃! x, ∀ w ∈ z, x ∈ w := by
rcases hz with ⟨x, y, h⟩
e... |
8,474 | lean_file_chunk | 06bc8572e3e52dec54cb0cb2d2e9d8838b1c0328f7c4a141ece4181041d72858 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import LeanPool.SetTheory.Omega
/-!
# Elementary embeddings of models of ZF
This module defines nontrivial elementary embeddings of a model of ZF into itself, their
criti... |
14,176 | lean_file_chunk | a0c26ded706feb051f365e094998c104e04174ff1dc6bb1c83e8a2889b97be99 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import LeanPool.SetTheory.ElementaryEmbedding
/-!
# The Kunen inconsistency theorem
This module proves the Kunen inconsistency theorem: there is no nontrivial elementary
... |
6,901 | lean_file_chunk | e9219e6e1955e7b510e87f75d49c30c8a8612a7cd8ba65f82c8b6ce50bb37edf | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import LeanPool.SetTheory.Ordinals
/-!
# The first infinite ordinal in models of ZF
This module develops the theory of `ω` and the natural numbers inside a von Neumann mo... |
4,262 | lean_file_chunk | cd94da6af2443a443d5cda93b335addc2e06a19a76bc1a945fe4cb701e428664 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import Mathlib.Order.ConditionallyCompleteLattice.Basic
/-!
# Order-theoretic preliminaries
This module collects order-theoretic lemmas about infima and suprema in condit... |
11,161 | lean_file_chunk | 405c92df6156510de3d236aef914f4c9c882f30007805acdafafd9d2fc25ff61 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import LeanPool.SetTheory.Basic
import LeanPool.SetTheory.OrderTheory
/-!
# Ordinals in models of ZF
This module develops the theory of ordinals inside a von Neumann mode... |
23,990 | lean_file_chunk | 80afb80d88725e483cd15c7faf3e6ad781056e151b363bfe7000cdda5ba7a9c3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import Mathlib.ModelTheory.ElementaryMaps
import Mathlib.ModelTheory.Semantics
import Mathlib.Tactic.FinCases
import LeanPool.SetTheory.SimpAttr
/-!
# Realization machiner... |
18,572 | lean_file_chunk | 6f6d14c9da833292139719ba47da00f6c153d5b79cd625e14bf85babd8733197 | lean_source_file | lean_pool_source_file_chunks | forallTelescopeReducing constInfo.type fun vars _ => do
unless vars.size ≥ 2 do
throwError m!"Variable list {vars} doesn't starts with `\{M} [ZFStructure M] ...`"
let variableType := vars[0]!
let mut classVars : Array Expr := #[]
let mut classParams : Array Term := #[]
let mut freeVars : Array... |
1,152 | lean_file_chunk | f06e7ad36081986971deda5c02a78a816c2321136abe6262e92fafcbff451d4d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import Lean
/-!
# Simp attributes for the ZF realization machinery
This module registers the custom `simp` attributes used to drive the formula-realization
and elementary... |
767 | lean_file_chunk | 7e1ebb0eb81da7b386d60ed8ea4f8f4254e23701b7b9f7c9eda6c0977088193f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Shuhao Song. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shuhao Song
-/
import LeanPool.SetTheory.KunenInconsistency
/-!
# The Kunen inconsistency theorem
Source: doi:10.2307/2269948, url:https://github.com/znssong/SetTheory
Authors: Shuhao ... |
7,965 | lean_file_chunk | 9c4d1831a20dde39d3f9f1123de79a73f91e9e40d16fe8de6032ecdc5f373d8f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Rational
/-!
# Shannon.Entropy.Approx
Phase 3 of the characterization: continuity extension.
Constructs f... |
3,616 | lean_file_chunk | 37a85e8223d9e36ae7f245b8d699902ee183c5683a91d6cd21fdb8f4ea199a58 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Gibbs
/-!
# Shannon.Entropy.Converse
The converse direction: `entropyNat` satisfies `ShannonEntropyAxioms`... |
5,408 | lean_file_chunk | 81cac68ae2b34b5c312dc2e28e0580790e2cd6f3a6a47d50d80be7d49c2d20aa | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import Mathlib.Analysis.Convex.DoublyStochasticMatrix
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Analysis.SpecialFunctions.Log.NegMulLo... |
2,757 | lean_file_chunk | 699b5c16e4b3a57a5bd8ea67fbfa94b5c76cca224f58e661c01b8a962e74026a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Approx
/-!
# Shannon.Entropy.Final
Final theorem layer.
Combines the rational characterization and contin... |
4,895 | lean_file_chunk | b4dbe2e19ab092ed01425b3395f8a07404ff2fa646bbaf1e9a9ce3eb4d8b72fc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Final
/-!
# Shannon.Entropy.Gibbs
Gibbs inequality and single-variable entropy bounds.
The Gibbs inequali... |
7,330 | lean_file_chunk | 7edd91ab55f42710b08061e2fce308390e3dded1e24408bd13ed59e0afc1603f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Gibbs
/-!
# Shannon.Entropy.Joint
Joint distributions on product types, marginals, conditional entropy,
an... |
11,520 | lean_file_chunk | 51475766a9cc9828b94da1af0a3a213661fbc6fa7d857dbfddda3751d17f0e8e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Joint
/-!
# Shannon.Entropy.Properties
The fundamental properties of Shannon entropy from Section 6 of Sha... |
7,998 | lean_file_chunk | 13e8cc1f2c2741a90e348635ec86e8e2315f01ed614e74de4f40f404bdeceec8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Uniform
/-!
# Shannon.Entropy.Rational
Phase 2 of the characterization: rational probabilities.
This modu... |
13,326 | lean_file_chunk | 029b52e452e7f95acb1adc77cd3cd35ac55528f08f3f94d8dd26e85e18f5cd76 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Core
/-!
# Shannon.Entropy.Uniform
Phase 1 of the characterization: equiprobable distributions.
Main outp... |
867 | lean_file_chunk | ce1b164291c663cc11a4de3725fbdbdbc6f29a556f0d802a095a4816f0ab8ac9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy.Properties
import LeanPool.Shannon1948Formalization.Entropy.Converse
/-!
# Shannon.Entropy
Facade module f... |
577 | lean_file_chunk | 95daec2570ff3e4d2be1befa58489ea89575ebd15a63bcde6ad3a4484867b0cf | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
import LeanPool.Shannon1948Formalization.Entropy
/-!
# Shannon Entropy Characterization
Source: doi:10.1002/j.1538-7305.1948.tb01338.x
Authors: Samuel Schl... |
6,374 | lean_file_chunk | c1f4902d0477498553a14b92f4fbf1d94040284daef5372559cb5acdb147fabf | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import Mathlib.RingTheory.AdjoinRoot
/-!
# The quadratic order `O_d` — definition and power basis
**Thesis.** §1.2 (Notation) and §3.2, the order
`O = O_d... |
10,496 | lean_file_chunk | 3dff82274043d4388aa874e9495639e3b2f7fd646a3a2ecd55be33999469e7d0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Prime
/-!
# Layer 2b: Canonical Form for ideals of `QuadraticOrder` — scaffolding
This file is the first PR ... |
2,833 | lean_file_chunk | 98f40c76894c17a0a1561d4ef53a150aa2c9f2e72a06548af04e407e720b36d0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Norm
/-!
# The discriminant identity `(τ − tauConj)² = d`
**Thesis.** §3.2, the discriminant of the order: f... |
4,492 | lean_file_chunk | fc08049bf1f3ba62b6c0cd66e4608705610826b5a316c2073f71d4a41552f2b1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Basic
/-!
# The norm form on `O_d`
**Thesis.** §3.2, the norm form `N(a + bτ) = a² + d·a·b + ((d² − d)/4)·b²... |
3,774 | lean_file_chunk | 59a7f32b4136f517a93b12180942bab674e97c392dd1e92d8723f5e48b440fa2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Prime.QuotientIso
/-!
# Prime classification, part 3: the inert case
**Thesis.** §3.2, Proposition 3.2.1 — t... |
14,429 | lean_file_chunk | 9f061d3637299873ece72195e642ee22ca87aa502a4e9dfd436c3c79fb078bd8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Basic
import Mathlib.Algebra.QuadraticDiscriminant
import Mathlib.Data.ZMod.Basic
import Mathlib.Data.ZMod.Quo... |
4,767 | lean_file_chunk | c11dca4a2ab45b4dffba6ae4dfc319639afe48a0629512d004d21dd5e21fc166 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Prime.PolyMod
/-!
# Prime classification, part 2: the quotient ring isomorphism
**Thesis.** §3.2, the proof ... |
9,652 | lean_file_chunk | e764d9eaca3715fec88265dcbcb2c2cd2f723e839705215c78120c4c98d4ac55 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Prime.QuotientIso
/-!
# Prime classification, part 4: the ramified case
**Thesis.** §3.2, Proposition 3.2.1 ... |
3,299 | lean_file_chunk | 740017c2cc0ae54c1c3abe9901b866eec915526ec24c88bad58bae4718df0a4a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Prime.Inert
import LeanPool.SingularModuli.QuadraticOrder.Prime.Ramified
/-!
# Prime classification, part 5: ... |
1,495 | lean_file_chunk | e8f26440f32d2021ce3c28fe4b73a5e348e4bbcf67a0d1b0da64ea76cdcecf3e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Prime.PolyMod
import LeanPool.SingularModuli.QuadraticOrder.Prime.QuotientIso
import LeanPool.SingularModuli.Q... |
23,993 | lean_file_chunk | a8d0a85fb5baa00ffff5d79a615a0329df3f4b6a83519699474efe36f9f0d9a0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import Mathlib.NumberTheory.LegendreSymbol.Basic
import Mathlib.RingTheory.Multiplicity
import Mathlib.RingTheory.ZMod.UnitsCyclic
/-!
# Layer 3: Root Coun... |
15,136 | lean_file_chunk | bf07379142fd22f721aeff348f9ea5d47956a164dac8c61b7577cc3851f93634 | lean_source_file | lean_pool_source_file_chunks | rw [← pow_add, Nat.add_sub_cancel' (by omega)]
rw [hnsplit, mul_dvd_mul_iff_left hpne] at hdvd_int
have hy_sq : (↑y' : ZMod (p ^ (n - 2 * r))) ^ 2 = ↑u := by
have h_eq : (((y' : ℤ) ^ 2 - u : ℤ) : ZMod (p ^ (n - 2 * r))) = 0 := by
rwa [ZMod.intCast_zmod_eq_zero_iff_dvd, Nat.cast_pow]
have h_e... |
603 | lean_file_chunk | 6059149eb9ecfd191d7f7b71837eddea4a38ea4d8018b2bdcd9c45981de8d0e2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Basic
/-!
# Quadratic-order verification checks
This file records a small sanity check for the defining mini... |
876 | lean_file_chunk | 94009e7d309bfff572f7824ce85a039be920266e09464cc9fb10f10dbd100bf8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Lean Pool contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Caleb L. Geiger
-/
import LeanPool.SingularModuli.QuadraticOrder.Basic
import LeanPool.SingularModuli.QuadraticOrder.Norm
import LeanPool.SingularModuli.QuadraticOrder.Discrim... |
11,757 | lean_file_chunk | cf69769c61647b2a1975c970d8e1c75c9609734d55d4e9f12a651990f145a24a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Walter Moreira, Joe Stubbs. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Walter Moreira, Joe Stubbs
-/
import Mathlib.Analysis.Complex.ExponentialBounds
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Order.Filter.AtTopBot.Basic... |
7,190 | lean_file_chunk | f1a2c71012184bfb1c3baae558ed2b77eeee0d283bf16de635a16bcf9f07785e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Walter Moreira, Joe Stubbs. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Walter Moreira, Joe Stubbs
-/
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Algebra.NeZero
import Mathlib.Data.Nat.Choose.Sum
/-!
# Eulerian Numbers
This module... |
7,622 | lean_file_chunk | a9052e7acc86bce9a3a2f03b61fdb88c963cd7a1d739bd8e24cdddea105baf8e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Walter Moreira, Joe Stubbs. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Walter Moreira, Joe Stubbs
-/
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Sylvester sequence
This file introduces the Sylvester's sequence.
This is sequence [... |
1,681 | lean_file_chunk | 479d813ccfef84c0be3d0b45a895341b1dfbfda174d907c45acf67fe4d30d753 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Walter Moreira, Joe Stubbs. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Walter Moreira, Joe Stubbs
-/
import LeanPool.SpecialNumbers.Eulerian
import LeanPool.SpecialNumbers.Euclidian
import LeanPool.SpecialNumbers.Sylvester
/-!
# Special Numb... |
18,234 | lean_file_chunk | 92798708fce3ac23f6739f8b818b3cc8481290a1dbd569fb437c4ba8e4fde20e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import LeanPool.SpectralPositivity.Matrix.MetzlerExp
import LeanPool.SpectralPositivity.Matrix.PerronFrobenius
import Mathlib.LinearAlgebra.Matrix.PosDef
imp... |
6,736 | lean_file_chunk | 3bc2b529ec0bf87a1c15ed75d6dd8997a04c46d32d2ec7ef54dc5fbd267a2d88 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import LeanPool.SpectralPositivity.Matrix.NonnegPower
import Mathlib.Analysis.Normed.Algebra.MatrixExponential
import Mathlib.Topology.Algebra.InfiniteSum.Ba... |
3,026 | lean_file_chunk | 8c5b2553d79915edee7fbebf6fd7a90d9e4289a8d205cf1a1250d500ed6fb4b7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Data.Real.Basic
/-!
# Nonneg Matrix Powers and Positivity
Proves that nonneg matrices... |
23,998 | lean_file_chunk | a7c436de2f74df219f7dc2a96a4e499c3f9f70932b6c18bb56c31fd2dc4b7426 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import LeanPool.SpectralPositivity.Matrix.NonnegPower
import LeanPool.SpectralPositivity.Operator.JentzschProof
import Mathlib.Analysis.InnerProductSpace.l2S... |
4,362 | lean_file_chunk | 83a3130040dc727ab4395a27370bddc2b90eab4339d4f4d49e9d87618812c096 | lean_source_file | lean_pool_source_file_chunks | -- The Perron eigenspace of B = A^k (for the eigenvalue μ) is one-dimensional
-- for a matrix with all positive entries. This means Aw = c·w for some scalar c.
-- We establish this via the uniqueness of positive eigenvectors for B.
--
-- Uniqueness argument: If Bx = μx and By = μy with x, y > 0,... |
1,017 | lean_file_chunk | c64eab76854c2cce31c7404fc0c76a4f8c2e92544c844b3ffbb640a0e0cad9ba | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import LeanPool.SpectralPositivity.Operator.JentzschProof
/-!
# Jentzsch's Theorem — Clean API
Re-exports the main results from JentzschProof.lean with cle... |
23,976 | lean_file_chunk | 369934b829febdf2808217233ace19db0b548a573c01781ce3034019bf9b554f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import Mathlib.MeasureTheory.Function.LpSpace.Basic
import Mathlib.MeasureTheory.Function.LpOrder
import Mathlib.MeasureTheory.Function.L2Space
import Mathli... |
23,968 | lean_file_chunk | e3596fe0d27c76652d790edc3c18f69652022bfd2e507813bf868d6fde80f211 | lean_source_file | lean_pool_source_file_chunks | push Not at hmu_nonneg
-- If |μ| < lam₀, done. Otherwise |μ| = lam₀, i.e., μ = -lam₀.
rcases lt_or_eq_of_le h_abs_mu_le with h_done | h_eq
· exact h_done
· -- μ = -lam₀. Derive contradiction using positivity-improving.
exfalso
have hmu_eq : μ = -lam₀ := by linarith [abs_of_neg hmu_nonneg]
... |
2,710 | lean_file_chunk | e218cfd8d2427ccbe9d1d65c565b256415bdfcc0e14f39a761473e2c5ae4ea74 | lean_source_file | lean_pool_source_file_chunks | ∃ c : ℝ, v = c • b i₀ := by
classical
intro v hv hTv
use @inner ℝ _ _ (b i₀) v
-- For j ≠ i₀: use self-adjointness to show inner (b j) v = 0
have h_coeff_zero : ∀ j, j ≠ i₀ → @inner ℝ _ _ (b j) v = 0 := by
intro j hj
-- inner (T (b j)) v = inner (eigenval j • b j) v = eigenval j * inner ... |
9,288 | lean_file_chunk | e387139a8551011bac7d21175330f540ce0a4bb79bc597f919d0cf2764308738 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import LeanPool.SpectralPositivity.Operator.JentzschProof
import Mathlib.MeasureTheory.Integral.Bochner.Basic
import Mathlib.MeasureTheory.Integral.Bochner.S... |
2,305 | lean_file_chunk | 59120868cff684b9b798e7424e0189535fbaf34fa2b73a02351e4544f18b140e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import LeanPool.SpectralPositivity.Operator.JentzschProof
import Mathlib.Analysis.InnerProductSpace.Rayleigh
import Mathlib.Analysis.Normed.Algebra.Spectrum
... |
864 | lean_file_chunk | b5749b74868b294ccc9a385975229da756b3c6a0ec9e72d6e9ff97385a2f4696 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Michael R. Douglas. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael R. Douglas
-/
import LeanPool.SpectralPositivity.Matrix.MetzlerExp
import LeanPool.SpectralPositivity.Matrix.NonnegPower
import LeanPool.SpectralPositivity.Operator.Jentzs... |
23,982 | lean_file_chunk | 2bd8665bfcced861c044f37f18063fdf4c10df32894cce262e2f1c187a07e62e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Dirk Kunert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dirk Kunert
-/
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.BigOperators.Group.Multiset.Basic
import Mathlib.Algebra.Order.Archimedean.Real.Basic
import M... |
23,990 | lean_file_chunk | 6991805f05925433152b288d296fbd7a4b7dd26ba54618b73af9068c968d895c | lean_source_file | lean_pool_source_file_chunks | theorem fract_shift_eq (a : ℝ) (N : ℕ) {p : ℝ} (hp : p ∈ orbit a N)
{mp : ℕ} (hmpval : Int.fract ((mp : ℝ) * a) = etaPos a N) :
Int.fract (((canMul a N p hp + mp : ℕ)) * a) = Int.fract (p + etaPos a N) := by
have hcast : ((canMul a N p hp + mp : ℕ) : ℝ) * a
= (canMul a N p hp : ℝ) * a + (mp : ℝ) * a := ... |
23,980 | lean_file_chunk | e35b957017148fd390c1345041a78704a13e9630bb794c26892c19d7de302f18 | lean_source_file | lean_pool_source_file_chunks | exact Int.fract_eq_self.mpr ⟨by linarith, by linarith⟩
have hmem2 : 1 - (etaPos a N - s) ∈ orbit a N :=
hval2 ▸ (mem_orbit_iff a N _).mpr ⟨k - mPlus a N h2, by omega, rfl⟩
have hle2 : 1 - (etaPos a N - s) ≤ 1 - etaNeg a N :=
le_one_sub_etaNeg a h2 (by rw [mem_posOrbit_iff]; exact ⟨ne_of_gt (by linarith), hm... |
4,373 | lean_file_chunk | aedb1813ff22ab821f62ef54beac21974a3e452b47ab7ceb8a8610fbe761cfd3 | lean_source_file | lean_pool_source_file_chunks | have hqval : Int.fract ((((j + mPlus a N h2) - mMinus a N h2 : ℕ) : ℝ) * a)
= v + etaPos a N + etaNeg a N := by
rw [fract_sub_mMinus a h2 (by omega : mMinus a N h2 ≤ j + mPlus a N h2),
fract_index_shift a h2 j, hjfr, Int.fract_eq_self.mpr ⟨by linarith, hvep1⟩,
show v + etaPos a N - (1 - etaNeg a N... |
440 | lean_file_chunk | 685f27a00998ff42cc11e3a53fd56c86f8cf661e56008b43916075a9a02f0784 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Dirk Kunert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dirk Kunert
-/
import LeanPool.SteinhausThreeGap.Basic
/-!
# The Three-Gap (Steinhaus) Theorem
Source: doi:10.1017/S1446788700031062
Authors: Dirk Kunert
Status: verified
Main declarat... |
6,242 | lean_file_chunk | 85ee37b84255ead9be4c7fa806ce3bd4fa0bb518113f204898cb7c65ecca1f0a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Bhavik Mehta, Pietro Monticone, Abel Doñate Muñoz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Pietro Monticone, Abel Doñate Muñoz
-/
import Mathlib.MeasureTheory.Group.GeometryOfNumbers
import Mathlib.MeasureTheory.Measure.Haar.I... |
23,990 | lean_file_chunk | e39c3a7949e1a6ecd7b8e0f002e5f5a61a139802574491eae331c898cfaf5053 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Bhavik Mehta, Pietro Monticone, Abel Doñate Muñoz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Pietro Monticone, Abel Doñate Muñoz
-/
import LeanPool.SumsThreeSquares.MinkowskiConvex
import Mathlib.Tactic.Common
import Mathlib.Tac... |
23,193 | lean_file_chunk | 200ddef25d53488f67b64e6a5c30e03fd3f4f851119c4d8c3b61cb02e84da1f6 | lean_source_file | lean_pool_source_file_chunks | · simp only [Real.rpow_ofNat, Nat.cast_nonneg, Real.sq_sqrt, Real.rpow_one]
all_goals positivity
rw [this, Real.mul_rpow, mul_comm π, mul_assoc, mul_assoc, mul_lt_mul_iff_right₀]
· rw [← pow_lt_pow_iff_left₀ (n := 2)]
· norm_num1
rw [mul_pow, ← Real.rpow_two, ← Real.rpow_mul (by simp)]
... |
1,776 | lean_file_chunk | dd1007e926f13c995ebdb1fd68bd81e2bd854bed6b80c50d7d722d22ff1e5911 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Bhavik Mehta, Pietro Monticone, Abel Doñate Muñoz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta, Pietro Monticone, Abel Doñate Muñoz
-/
import LeanPool.SumsThreeSquares.MinkowskiConvex
import LeanPool.SumsThreeSquares.SumThreeSquar... |
13,209 | lean_file_chunk | 3014a87da2d5360d9614817ce37a6dfea0a93e986cd9e9adc2884a7935024dad | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.Certificate
import LeanPool.Sundogcert.Looseness
/-!
Sundogcert/CertWall.lean — TYPING the imported hardness wall as a CONDITIONAL theorem.
Th... |
12,367 | lean_file_chunk | d50e400785fc01c7d4dfa499ba35429a52f58d701c581d01ff754a8916c8350e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import Mathlib.Data.Matrix.Mul -- Matrix, mulVec/vecMul, the `*ᵥ` / `ᵥ*` notation
import Mathlib.InformationTheory.Hamming -- hammingNorm (the error weight)
import ... |
6,018 | lean_file_chunk | a106e28e9a999b7f8c921aac20c65d4fd55d9abe1ba7e06c6d69f85489ea5c53 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.Certificate
/-!
Sundog syndrome certificate — the CHECK-COST theorem (Lean 4 / mathlib v4.30.0)
GOAL. Make the "cheap to check" half of the ... |
7,015 | lean_file_chunk | 2ebaf6ad2462434e3ed192e1fc65d7cc23ddd1487dc61e276d3a36ac4b7b9020 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.SATNPHard
import LeanPool.Sundogcert.VarWheel
import Mathlib.Data.Fin.VecNotation
/-!
Sundogcert/ClauseGadget.lean — MILESTONE 3 of the `3SAT ≤ 3... |
13,158 | lean_file_chunk | 6c93ca5f2386405c4aabd4ac586c26ff60ea78c90547a4ab793dbb9750d0c6fc | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import Mathlib.Data.Matrix.Mul
import Mathlib.InformationTheory.Hamming
import Mathlib.Data.ZMod.Basic
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.B... |
14,587 | lean_file_chunk | 9dc501e8cb473b002ff3d98f4dcd3cae6efeaa49a442f8bb5c81ab121e995d8f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.Looseness
import Mathlib.LinearAlgebra.Matrix.Block
import Mathlib.Data.Fintype.Fin
/-!
Sundogcert/Degradation.lean — the DEGRADATION CURVE of th... |
3,944 | lean_file_chunk | 45d88fa39ecd256f7f883aaff51c851d964bc07d964c3003b592e61daec9ab4f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.Certificate
import Mathlib.Algebra.Field.ZMod -- Field (ZMod 2) via Fact (Nat.Prime 2)
import Mathlib.LinearAlgebra.Matrix.Notation -- !![;... |
19,696 | lean_file_chunk | 5e56a240690e37a84cf58bc42bf3279e9ad737ba19d5810ffda0c603538066b4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.Scaling
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
Sundogcert/Looseness.lean — the BASIS-DEPENDENCE / looseness demonstration.
... |
9,370 | lean_file_chunk | af77803fb6397a44e5b032915723e11e47a4c90fc7c7d998c151dde4a82d251f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.DecodingNPHard
/-!
Sundogcert/MatchingNPHard.lean — the KARP-LAYER EXTENSION of the formalized hardness chain:
3-DIMENSIONAL MATCHING (3DM) red... |
9,524 | lean_file_chunk | f86bbc61773bf9ab3d49a6a8d0f9a50a074095eca49384d2f377295bbb51a53b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.LinearAlgebra.Vandermonde
import Mathlib.Tactic.Ring
import Mathlib.Tactic.Linarith
/-!
# The Reed–Solomon evaluation c... |
5,850 | lean_file_chunk | 6063b9377564e77b3666ef013bdd6f03fa32106b94edf8e165949f183dc44a63 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import Mathlib.Data.Fintype.Pi
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.Fintype.Sigma
import Mathlib.Data.Fin.VecNotation
/-!
Sundogcert/SATNPHard.lean — MILEST... |
9,393 | lean_file_chunk | 4e74ad85b0fec4517a21b752cdac72b65d435b323d70da6f5c6f5306d631b7ff | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.SATNPHard
import LeanPool.Sundogcert.VarWheel
import LeanPool.Sundogcert.ClauseGadget
import LeanPool.Sundogcert.MatchingNPHard
import Mathlib.Data.... |
23,993 | lean_file_chunk | 70b38d7d56465e8e41ea674f7d36ef333e83dbccadb9becb1c16111da9ce20f0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.SATReductionIncidence
import LeanPool.Sundogcert.ThreeDMReindex
/-!
Sundogcert/SATReductionForward.lean — MILESTONE 8 of the `3SAT ≤ 3DM` maratho... |
4,742 | lean_file_chunk | 407f0f540a6ac34287f7744ab77f99670c4c46fa055a9497705862cc3f2c25e3 | lean_source_file | lean_pool_source_file_chunks | wheelTriple ij = negT ij.1 ij.2 ∨ wheelTriple ij = posT ij.1 ij.2 := by
intro ij; simp only [wheelTriple]; split <;> [left; right] <;> rfl
have hdisj_wc : Disjoint Twheel Tclause := by
rw [Finset.disjoint_left]
intro idx hw hc
rw [hmemWheel] at hw; rw [hmemClause] at hc
obtain ⟨ij, hij⟩ := hw; obt... |
6,164 | lean_file_chunk | 2f9ef5ecab9d241736610389e6b2035181294742fd028ae0b7e5c553f2ecc038 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.SATReduction
/-!
Sundogcert/SATReductionIncidence.lean — MILESTONE 6 of the `3SAT ≤ 3DM` marathon: the INCIDENCE
LEMMAS. This module answers, ... |
4,912 | lean_file_chunk | a4bfab0b19aa02ccbba362e055609e90aa29abf1d4f0c240235947b3196c7895 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.SATReductionForward
import LeanPool.Sundogcert.SATReductionReverse
import LeanPool.Sundogcert.SATReduction
import LeanPool.Sundogcert.ThreeDMReindex... |
8,996 | lean_file_chunk | 1355a8cc949addfac67c63dffbbe532f4f06cec167656639abffa6994f06f0c9 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.SATReductionIncidence
import LeanPool.Sundogcert.ThreeDMReindex
/-!
Sundogcert/SATReductionReverse.lean — MILESTONE 7 of the `3SAT ≤ 3DM` maratho... |
11,334 | lean_file_chunk | ac0e1743409f1061dc24e1d0644886cdef14e6c3af47f311de7f7c989e78ac7b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.Certificate
import Mathlib.Algebra.Field.ZMod
import Mathlib.LinearAlgebra.Matrix.Notation
/-!
Sundogcert/Scaling.lean — the [2m, m] projection-c... |
6,437 | lean_file_chunk | 2c708fd38ad5bf5a4cf0d7ee3094ddd0c4529fc1df788383ed6a00c67e747eb3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Humiliati. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Humiliati
-/
import LeanPool.Sundogcert.MatchingNPHard
import Mathlib.Data.Fintype.EquivFin
/-!
Sundogcert/ThreeDMReindex.lean — MILESTONE 5 of the `3SAT ≤ 3DM` marathon: the GENERIC
... |
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