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

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

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

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

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

Mathematical framework connecting surjective group homomorphisms to quantum error correction via Type II₁ von Neumann algebras. Derives code distance bounds from algebraic structure and validates with computational examples.

3D Navier-Stokes global regularity via dissipative persistence. Canonical Lane is a defined term for the constrained theorem lane.

The Hodge Conjecture via Hodge-class persistence and rigidity. Canonical Lane is a defined term for the constrained theorem lane.

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.

Yang-Mills existence and mass gap via self-adjoint gauge persistence. Canonical Lane is a defined term for the constrained theorem lane.

This repository provides a constructive supplement to the Littlewood Conjecture using prime density and asymptotic analysis. 本リポジトリは、リトルウッド予想に対して、6n±1型構成と素数密度の漸近解析に基づく構成的補完を提示します。

The Birch-Swinnerton-Dyer Conjecture via analytic-arithmetic persistence. Canonical Lane is a defined term for the constrained theorem lane.

First explicit curvature correction formula for fractional Laplacians on curved manifolds. Complete proof via heat kernel expansion, validated computationally on S². Applications in anomalous diffusion, thermal field theory, and curved spacetime physics.

The Riemann Hypothesis via self-adjoint spectral persistence. Canonical Lane is a defined term for the constrained theorem lane.