"Type Theory and Formal Proof: An Introduction" book formalization in Lean

Lean formalization of MEV properties.

Route C of 3: RH via growth contradiction on X₀(143) g=13. Littlewood 1924 Ω: |ζ(1/2+it)|=Ω(exp(c log t/log log t)) contradicts |ζ|≤C(log t)² → Ingham Deuring-Heilbronn c1=0.209>0.2 β>0.9 closed at p5 → S₄={2,3,19,191} C=11.422>2√13 → GRH → H₄ 12/11 → RH. Lean 4.12 0 sorry. Companion to Route A & B.

First Lean formalization of 200 measured Hodge (2,2)-class obstructions on CM abelian varieties. Clay Wall 3. Applied science: numerical ranks > bounds for g=3,4,5. 0 axiom. 0 sorry.

Formal Verification of the 7-Color Chromatic Number of the Plane via Toroidal Projection and the Irrationality of 2π.

Formal Proof of the Non-Existence of Perfect Cuboids via Mordell-Weil Rank Exhaustion and Minimal Polynomial Irreducibility of the Perfect Cuboid Surface.

ia Collapse Theory and AK High-Dimensional Projection This repository presents Version 2.0 of a formal, categorical, and type-theoretic resolution of the Hodge Conjecture, formulated through Collapse Theory and the AK High-Dimensional Projection Structural Framework (AK-HDPST).

Route A of 3: RH via Arakelov positivity on X₀(143) g=13. Abbes-Ullmo 1996 Thm 1.2 → ω²=48/13>0 → g=13 → GRH → H₄ 12/11 → RH. Lean 4.12 Mathlib 0 sorry riemannZeta. Companion to Route B (spectral gap λ₁≥975/4096) and Route C (Growth Contradiction). Base curve for S₄={2,3,19,191} C=11.422. https://doi.org/10.5281/zenodo.21303944

Route B of 3: RH via spectral descent on X₀(143) g=13. Kim-Sarnak λ₁≥975/4096 → Selberg trace = Bost-Connes spectral action C(S₄)=11.422>2√13 → GRH → H₄ 12/11 → RH. Lean 4.12 Mathlib 0 sorry riemannZeta. Companion to Route A (ω²=48/13>0) and Route C (Growth Contradiction). S₄={2,3,19,191}. https://doi.org/10.5281/zenodo.21303976

Kernel-checked Lean 4 proof that no infinite simple paramedial quasigroups exist (Loops '03 open problem).

Proof of Constitutional Enclosure Theorem: silent AI decisions are type errors

This repository presents a constructive solution to the Yang–Mills existence and mass gap problem, a Clay Millennium Prize topic. The framework confirms the existence of a positive mass gap through verifiable quantum field logic. 本リポジトリでは、クレイ懸賞問題のひとつであるヤン–ミルズ存在と質量ギャップ問題に対し、構成的に正の質量ギャップの存在を示す理論を収録しています。量子場理論に基づき、検証可能な構成を整備しています。

Lean 4 RH proof chain C01-C21 via Arakelov geometry of X₀(143). 61 files · 0 sorry · 0 axiom · classical trio only · Mathlib v4.12.0. Bricks: C01 ω²=48/13, C06 BC-threshold, C08 ArakelovPos, C09 143×13=1859, C17 pairing>0. Routes A+B conditional on named open surfaces (Kim-Sarnak 2003, Cogdell-PS 1999, BC 1995, JK 1996).

本项目用 Lean4 形式化验证一个红蓝选择问题中的理由结构。项目关注的不是玩家实际会如何选择，而是： 在给定价值准则、背景条件和理由生成规则下，某个策略是否能够成为某个玩家的最终合理策略。

Six independent formal proofs for the Yang-Mills Existence and Mass Gap problem, covering RG Flow, Analytic Continuation, and Heat Kernel methods.

Reproducibility repository for "Non-Compensatory Legitimacy", a formal-computational paper on conjunctive legitimacy conditions in clinical AI governance. Contains the canonical manuscript, a formal-proof directory for the representation-incompatibility result, annotated Jupyter notebooks, and bibliography.

A formal constructive proof of the Goldbach Conjecture using A-type primes. The theory guarantees every even number ≥4 can be expressed as a sum of two primes, offering a reproducible and extendable number-theoretical foundation. A型素数を用いた構成的手法により、すべての偶数（4以上）が2つの素数の和で表現可能であることを証明。再現性と拡張性を兼ね備えた数論的基盤を提供します。

Formalization of Euler's polyhedron formula (V - E + F = 2) in Lean 4

このリポジトリは、コラッツ予想に対する構成的完全証明を示します。あらゆる自然数が、特定の再帰的変換を経て最終的に1へと収束することを、合同類の構造論理とループ排除の形式によって証明します。 This repository presents a constructive complete proof of the Collatz Conjecture. It shows that any natural number ultimately converges to 1 via recursive transformation, using congruence class structure and loop elimination.