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.

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

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

Prime Power Transformer: A Number-Theoretic Architecture for Compute

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

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

Kaplansky idempotent conjecture via group-algebra rigidity 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.

General Langlands functoriality via transfer-packet 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

The Bateman-Horn Conjecture via prime-pattern density persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Generalized geometric Langlands via derived-correspondence persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Infinitely many n^2 + 1 primes via polynomial-prime 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.

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.