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

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.