alphaproof-equivalent — Rigorous Mathematical Proof Engine

> HONEST LABEL (خط أحمر مصداقية): Google DeepMind's AlphaProof has NO public API > (verified live 2026-08-09: it is a DeepMind research program; the only publicly > released code is AlphaGeometry2 / DDAR on GitHub). This skill is NOT the > AlphaProof product and calls no AlphaProof endpoint. It is a functional > equivalent that delivers IMO/research-level rigorous, verifiable proofs through > real, accessible paths.

What it actually does

1. Proof generation — strong-reasoning model (our golden chain, Anthropic direct primary) produces a complete step-by-step proof with explicit assumptions. 2. Adversarial verification — an independent referee pass hunts every gap, hidden assumption, or fallacy and issues VALID/INVALID/INCOMPLETE + confidence. 3. Optional formal check — if lean (Lean 4) is on PATH, exposes machine-verification hook (--formal). Not installed by default; falls back gracefully with a clear note.

It refuses to fabricate (verified in 5-level critique)

• False statement → DISPROVEN with counterexample (tested: "every prime is odd" → 2).
• Bad proof → INVALID confidence 100 (tested: division-by-zero fallacy caught exactly).
• Underspecified → UNDECIDABLE (tested: "the function is continuous").

Usage

python3 skills/alphaproof-equivalent/prover.py prove  "<statement>" [--formal] [--json]
python3 skills/alphaproof-equivalent/prover.py verify "<statement>" "<proof>" [--json]
python3 skills/alphaproof-equivalent/prover.py selftest

When to use

• Rigorous proof/disproof of a math claim (algebra, number theory, analysis, IMO-style).
• Refereeing a submitted proof for gaps/fallacies.
• Any "prove that…" where machine-checkable rigor + adversarial review matter.

Geometry note

For pure Euclidean geometry olympiad problems, the SOTA open release is AlphaGeometry2 / DDAR (github.com/google-deepmind/alphageometry, Jan 2026). Consider running DDAR directly for geometry; this engine covers general math.

Verified

• 2026-08-09: py_compile OK · selftest SELFTEST_OK (live) · 5-level critique all passed.