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

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

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

Trace-Formula Endoscopy via stable-transfer persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Anabelian Reconstruction via fundamental-group persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

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.

The Bloch-Beilinson conjectures via motivic-filtration persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

p-adic Hodge Theory via period-realization persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

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.

Kaplansky idempotent conjecture via group-algebra rigidity persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

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

General Langlands functoriality via transfer-packet persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Geometric Langlands via Hecke-eigensheaf persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Smooth 4-Dimensional Poincare Conjecture via smooth-structure persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Birational Geometry via model-reduction persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Baum-Connes conjecture via assembly-K-persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Kadison-Kaplansky conjecture via projection-spectral persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Anabelian geometry via fundamental-group reconstruction persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Buzzard-Gee Conjecture via automorphic-Galois compatibility persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Motivic Realizations via regulator-filtration persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.