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: 838 / 1187 (70.6%), 95.9% trust on parseableNumber Theory: 387 / 540 (71.7%), 98.2% trust on parseableCounting & Probability: 333 / 474 (70.3%), 98.2% trust on parseablePrecalculus: 384 / 546 (70.3%), 99.7% trust on parseableTOTAL: 1942 / 2747 (70.7%), 97.5% trust on parseable All four domains simultaneously above the 70% global floor, with trust on parseable above 95% — the architecture's verifiable bottom-up thesis empirically validated. ## What's in this deposit - axiom_workshop.pdf — the paper (compiled PDF) - source/ - LaTeX source + figures (reproducibility of the PDF) - benches/ - three bench JSONs cited in the paper, containing per-record traces (problem text, gold answer, AXIOM output, routing decisions, failure modes) that reproduce Tables 1-3 in the paper Live interactive demo: https://huggingface.co/spaces/Squagghy/axiom-solver Future versions will be deposited under the same concept-DOI as thearchitecture evolves.