Abstract
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
Abstract (translated)
当代人工智能系统实现了卓越的性能，但仍然缺乏透明性和可验证性，这在安全至关重要的部署中引发了信任危机。我们引入了MathLedger，这是一个可验证机器认知的基础架构，它将形式验证、加密证明和学习动力学整合到一个单一的认识循环中。该系统实施了反射式正式学习（RFL），这是一种符号类比的梯度下降方法，在这种方法中，更新是由验证结果驱动的，而不是统计损失。第一阶段实验在受控条件下验证了测量和治理基础架构的有效性。CAL-EXP-3 实验验证了测量基础设施（Delta p 计算、方差跟踪）；单独的压力测试确认了在超出范围条件下的关闭式治理触发机制正确运行。没有收敛或能力声明。这项贡献是基础设施性的：一个可审计的大型日志证明学习的工作原型。关键词：可验证学习，形式验证，加密证明，反射反馈，关闭式治理。
URL
https://arxiv.org/abs/2601.00816
