mathematical-proof

Make an existing proof easier to inspect by exposing its hierarchy, dependencies, scope, and unresolved obligations.

A 4-skill pipeline for Claude Code: verify mathematical proofs → repair with literature support → sharpen the theory → write corrected proofs. Integrates Codex MCP for adversarial cross-review. Venue-audited reference library across statistics/econometrics/ML theory.

Axiomatic ARE-Logic with Plexity Logical Ecosystem Science Framework

Official project page for From Competition Problems to Mathematical Proof, a free 637-page olympiad mathematics textbook by Parsa Fatehi. Includes the Zenodo DOI, errata, reviews, and reader feedback.

plain math functions

A comprehensive Coq formalization of the Collatz conjecture with a combinatorial analysis framework. Proves linear division advantage.

Learn Lean (Math-Proving Based Programming Language) for mathematical proving.

AI-generated solutions to two research-level math problems from the First Proof community experiment: a Yang-Mills gauge-fixing heat-flow estimate on the 2-torus, and sharp fatness of geodesic triangles in sparse random graphs. Produced autonomously in Claude Code, offered for human validation.

Primitives Become Lean4 Inductive Types | Lattice Operations Become Machine-Verified Theorems | Structural Claims About Mathematics Become Decidable Propositions

Certified log-concavity of the Riemann-Jacobi kernel with Arb/FLINT ball-arithmetic certificates. Source-critical audit of the Polya-type real-zero criterion. No unconditional RH claim.

Independent mechanical re-verification of Robertson-Sanders-Seymour-Thomas 1997 Four Color Theorem: 633 configurations reducible + 5 presents verified on Windows/MSYS2, with LLM audit and rules-minimization experiments.

Zero-overhead data marshalling protocol for safety-critical distributed systems with NASA-STD-8739.8 compliance, formal verification, and Zero Trust architecture.

Prime Power Transformer: A Number-Theoretic Architecture for Compute

Machine-verified in Lean 4: the Binary Snap (⊥ → ε₀) is a theorem, not an axiom, and it holds independently across algebra, topology, information theory, functional analysis, set theory, category theory, and computability. A formal ontology of the bottom element ⊥.

machine-verified proofs for euler's theorem and touchard's congruence

ProofCore is a browser-native, 100% offline-first, hybrid mathematical proof verification engine. It combines rigorous symbolic math with semantic understanding to reliably verify mathematical proofs, offering zero external dependencies and production-ready quality

A disorganized collection of mathematical proofs.

The Triune of Sovereignty: Substrate Agnostic Relational Epistemics — Foundational Framework and Cross-Substrate Validation

構成的素数構成とrad(abc)支配密度を用いたabc予想の統合証明です。例外有限性も非構成的に導出。 Unified proof of the abc conjecture via constructive prime structures and rad(abc) density. Finite exceptions handled non-constructively.

Exact rational certificates for a candidate conditional metric-TSP 4/3 n+7 support theorem on the subtour-elimination polytope; external review requested.