Non-Anthropic Mathematics Mode (NAMM) — verification-first machine-native math discovery

Abstract

Non-Anthropic Mathematics Mode (NAMM) is a verification-first research program that treats machine-native certificates, explicit falsifiers, and logged negative results as first-class scientific outputs. This deposit packages Protocol v2 tooling, Sci Flow domain routing, experiment scaffolds, curated evidence artifacts, and the companion article PDF (v0.2.0). The central question is territorial rather than proof-theoretic: can machine-native search surface structure that is certifiable before it admits compact human naming? We operationalize this through acceptance gates (non-equivalence, correlation bounds, prior-art simplification, novelty floor, representation metrics, matched baselines) and tiered `certificate.json` witnesses. Mathematics pilots report computational evidence for evolved program ASTs, raw-tensor composites, and moduli-fiber witnesses, alongside calibration nulls. AMAT pilots (037–041) on local Qwen2.5-0.5B hidden states test catastrophe, Fisher curvature, fractal dimension, Lyapunov, and attention-head disagreement hypotheses. We report honest partials and nulls: effective dimension D_eff does not discriminate typicality vs. off-typical policies; several chaos metrics remain unsupported. This release claims methodology, reproducible artifacts, and bounded computational evidence —not breakthrough theorems or product readiness. Negative and null results are documented in `rejections.jsonl` and summary JSON. Related program: Endogenous Initiative Architecture (EIA), Zenodo https://doi.org/10.5281/zenodo.22646895