# MathLedger: A Verifiable Learning Substrate with Ledger-Attested Feedback

arXiv: https://arxiv.org/abs/2601.00816 · HTML: https://mlsanity.com/paper/2601.00816/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
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- First posted on arXiv 22 Dec 2025.

## Abstract (arXiv)

Contemporary AI systems achieve extraordinary performance yet remain opaque and non-verifiable, creating a crisis of trust for safety-critical deployment. We introduce MathLedger, a substrate for verifiable machine cognition that integrates formal verification, cryptographic attestation, and learning dynamics into a single epistemic loop. The system implements Reflexive Formal Learning (RFL), a symbolic analogue of gradient descent where updates are driven by verifier outcomes rather than statistical loss. Phase I experiments validate the measurement and governance substrate under controlled conditions. CAL-EXP-3 validates measurement infrastructure (Delta p computation, variance tracking); separate stress tests confirm fail-closed governance triggers correctly under out-of-bounds conditions. No convergence or capability claims are made. The contribution is infrastructural: a working prototype of ledger-attested learning that enables auditability at scale. Keywords: verifiable learning, formal verification, cryptographic attestation, reflexive feedback, fail-closed governance