AXIOM: A Trust-First Neuro-Symbolic Execution Architecture for Verifiable Mathematical Reasoning

AXIOM is a trust-first neuro-symbolic math reasoning architecture combining a frozen large language model (Qwen 2.5 7B Instruct, used as rewriter only) with deterministic SymPy CAS handlers organized via a 1:1:1 task-routing discipline (trigger regex + narrow prompt + closed-form handler). The architecture commits to three ordered priorities (the "North Star"):(1) reliability - the system either solves correctly or abstains with "UNKNOWN";(2) zero regressions across ship cycles;(3) velocity within 3s/problem. Empirical validation on the MATH benchmark test split (4 active domains, 2747 records total):Algebra: 1165 / 1187 (98.15%), 100% trust on parseableCounting & Probability: 433 / 474 (91.35%), 100% trust on parseableNumber Theory: 515 / 540 (95.37%), 100% trust on parseablePrecalculus: 479 / 546 (87.73%), 100% trust on parseableTOTAL: 2592 / 2747 (94.36%), 100% trust on parseable All four MATH categories simultaneously above the 70/90/70 per-domain floor (parseable ≥ 70%, trust on parseable ≥ 90%, total correct ≥ 70%) - the architecture's verifiable bottom-up thesis empirically validated. The task registry has grown to >3000 task triples with zero LOST_CORRECT regressions across 250+ consecutive ship commits. ## What's in this deposit- axiom_workshop.pdf — the paper (compiled PDF) Live interactive demo: https://huggingface.co/spaces/Squagghy/axiom-solver This is v1.3: updated benchmark numerics. Architecture and methodology unchanged from v1.0. Future versions will be deposited under the same concept-DOI as the architecture evolves.