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July 14, 20262 citationsOpen Access

The Bourbaki Engine: A Governed Discovery Architecture for Long-Horizon Autonomous Mathematics

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MLMaximiliano LuciusJMJosé Minich

Key Points

  • This paper aims to address the protocols for admitting generated mathematical claims as reliable knowledge within autonomous systems.
  • Introduced a dual architecture consisting of a Discovery Plane and a Trust Plane.
  • Implemented two modules, MIRADOR for representation and ProofContext for retrieval, with a detailed evaluation process based on a readiness ladder.
  • Outlined claim promotion and soundness obligations while maintaining a clear separation of powers.
  • Established a set of criteria for claim promotion to facilitate trust in autonomous outputs.
  • Implemented the knowledge substrate that enables dependency-driven invalidation of claims.
  • Presented four peer-reviewed adversarial evaluations along with an auditable process trail.

Abstract

An architecture and research-program paper. Autonomous systems increasingly generate plausible research-level mathematics; the unresolved problem is not generation but admission — under what protocol a generated claim may become a load-bearing dependency of future work. This paper reorganizes the Bourbaki Engine around a dual thesis: reliable autonomous mathematics requires two coupled but institutionally separated systems — a Discovery Plane that expands the space of mathematical possibilities (and may be exploratory, redundant, speculative, and internally contradictory) and a Trust Plane that governs which outputs may become reusable knowledge, under a small explicit trusted computing base. It preserves claim promotion as the unit of trusted progress, edge-level soundness obligations, an epistemic separation of powers, certificate discipline (search != evidence != certificate != checker), an event-sourced knowledge substrate with dependency-driven invalidation, and the False Theorem Promotion Rate as the primary trust metric. Two of its seven specified modules are implemented and separately published: MIRADOR (representation) and ProofContext (retrieval). The sixteen-round Bang affine plank pilot is recast as a retrospective requirements-elicitation slice (n=1), and evaluation is gated by a falsifiable R0–R9 readiness ladder. The paper makes no promise of solving a Millennium Prize Problem; a Millennium problem is a gated frontier stress test whose success cannot be self-declared. Includes the full auditable process trail: claim ledger, primary-source related-work matrix, and four fresh-context adversarial reviews with responses.

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Cite This Study

Lucius et al. (2026) studied this question.

synapsesocial.com/papers/6a55d16e5aafca87247f86c1https://doi.org/10.5281/zenodo.21328015
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