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.

plain math functions

Axiomatic ARE-Logic with Plexity Logical Ecosystem Science Framework

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.

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.

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

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.

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

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.

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

Canonical-lane closure package for General Langlands functoriality: admissible-class formulation, projection gates, local-to-global bridge, and carried remainder.

Canonical-lane closure package for p-adic Hodge Theory: admissible-class formulation, projection gates, local-to-global bridge, and carried remainder.

Three exact-arithmetic verification pipelines — λ=2c conformal identities + the emission-gap theorem, Mahler-measure matrix plates (interactive in-browser explorer), and residual-return learning dynamics over number fields. Every load-bearing claim is machine-checked; all suites pass.

Canonical-lane closure package for Anabelian Reconstruction: admissible-class formulation, projection gates, local-to-global bridge, and carried remainder.

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.