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February 16, 20260 citationsOpen Access

CPE-Constrained AI Reasoning on Research Mathematics: Process Governance Without Domain Expertise — A Response to the First Proof Challenge

RTRobin Bruce Thacker

Key Points

  • To explore the effectiveness of CPE-constrained AI reasoning in solving mathematical challenges without domain expertise.
  • Applied CPE-constrained multi-architecture AI collaboration to four mathematical problems.
  • Utilized two principles from the Structural Dependencies of Intelligence framework.
  • Developed an auditable reasoning trace with error documentation and correction pathways.
  • Achieved complete proofs for Q10 and partial results for Q9, Q6, and Q4.
  • Demonstrated that domain-independent process governance produces correctable reasoning.
  • Provided a novel failure taxonomy for understanding errors in AI-assisted reasoning.

Abstract

We report results from applying CPE-constrained (Coherence ≥ Preservation ≥ Emergence) multi-architecture AI collaboration to four problems from the First Proof mathematical challenge (arXiv:2602.05192). The human operator has no formal training in the relevant mathematical domains. The governing methodology uses two domain-independent principles derived from the Structural Dependencies of Intelligence (SDI) framework and operationalized via the Unbounded Emergence (UE) methodology: (1) no claim may exceed what can be verified (E ≤ P), and (2) all reasoning paths must be explored to their endpoints. We achieve complete proofs for Q10 (preconditioned conjugate gradient for CP-RKHS tensor decomposition), partial results with documented gaps for Q9 (quadrilinear determinantal tensors), Q6 (ε-light subsets), and Q4 (superadditivity of 1/Φₙ under finite free convolution). The primary contribution is not the mathematical results themselves — other submissions achieve equal or stronger results — but the fully auditable reasoning trace, including documented errors, correction pathways, and a novel failure taxonomy for AI-assisted mathematical reasoning. We compare our process and results against the independent submissions of Armstrong, Kempe, and Munos (2026) and Dillerop (2026), and demonstrate that domain-independent process governance produces auditable, correctable reasoning that expert-guided prompting does not. This upload contains two documents: 1. Main paper covering all four problems with cross-submission comparison and synthesis 2. Companion document with complete Q10 solution, elimination trace, and correction documentation LaTeX source files are included for transparency.

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Cite This Study

Robin Bruce Thacker (2026) studied this question.

synapsesocial.com/papers/6992b4ad9b75e639e9b09adehttps://doi.org/10.5281/zenodo.18627130
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