formal-proof

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

Lean formalization of MEV properties.

A formal proof, in LaTeX, that 3-Partition is NP-complete in the strong sense, following the Garey and Johnson reduction chain. MAC coursework, UGR.

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

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

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.

Route C of 4 — Act III Growth. RH via contradiction: |ζ|≤C(log t)² false via Littlewood 1924 Ω exp(c√(log t/log log t)). Zero repulsion 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. Opera Numerorum with A, B, D 35 brothers desert.

Route B of 4 — Act II Descent. RH via spectral gap X₀(143) λ₁≥975/4096 Kim-Sarnak → Selberg = Bost-Connes C(S₄)=11.422>2√13 → GRH → H₄ 12/11 → RH. 35pp BC6 20450 bytes 0 sorry. Opera Numerorum with A ω²=48/13>0, C Littlewood Ω, D 35 brothers jitter ||p·α₀||<1/p → R=1/2. doi:10.5281/zenodo.21303976

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 4 — Act I Positivity. RH via Arakelov on X₀(143) g=13 ω²=48/13>0 Abbes-Ullmo 1996 → S₄={2,3,19,191} C=11.422>2√13 → GRH M9 → H₄ 12/11 → RH. Lean 4.12 0 sorry riemannZeta. Opera Numerorum with B λ₁≥975/4096, C exp(c√log/loglog), D jitter ||p·α₀||<1/p → R=1/2. doi:10.5281/zenodo.21303944

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

Esolang de reescritura de cadenas cuyo alfabeto son repeticiones del token 'ja'. Turing completo, con prueba ejecutable.

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

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。

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

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。

Vyukov MPSC queue in C++20 with a six-claim formal memory-model proof, push_batch API (Claim 6), 53M msg/sec at 4 producers, 18 TSan litmus tests, and a software tick-to-trade benchmark.

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.