Technical Compliance & Evidence Report (Parts 3–6): Academic Misconduct and Priority Dispute Investigation regarding OpenAI Mathematics Division.

This repository contains Parts 3, 4, 5, and 6 of the comprehensive Technical Compliance & Evidence Report compiled by independent researcher Markov E.S. The dossier establishes a definitive case of systemic methodological frontrunning, structural obfuscation, and unauthorized conceptual appropriation of proprietary functional-analytic frameworks by OpenAI’s Mathematical and AI Research Division within their preprints released in September and October 2026. By deploying a novel parametric auditing technique known as the Method of Limit Collapse, this investigation systematically deconstructs the stochastic, harmonic, and dual-space masks utilized by OpenAI's frontier models to bypass automated plagiarism detection software. Key Technical Components of the Dossier: 1. Part 3 (Obfuscation in non-reflexive l1 spaces): Demonstrates how OpenAI introduced an artificial coordinate-wise cubic smoothing mapping φ(r) = 3r² - 2r³ on the flat unit sphere facets of l1 to hide exact kernel complement subspace restrictions. Under boundary convergence analysis (u → e ∈ {0, 1}^B), the derivative φ'(u) vanishes identically, forcing the regularized martingale variation profile to collapse into Markov's exact deterministic Lipschitz constraint, proving structural appropriation. 2. Part 4 (Tingley’s Problem and Dual Space Inversion): Unmasks the tactical inversion of Markov’s primal spatial projections and Birkhoff–James orthogonality relations into dual-space representations utilizing continuous radial contacts and common supporting functionals. It also documents the exact duplication of the 2D Radon singularity obstruction logic designed to filter out planar anomalies before applying fixed-point return maps. 3. Part 5 (κ-Limit Collapse Proof in Fourier Restrictions): Audits OpenAI’s preprint on elliptic capacity propagation, demonstrating that an artificial eccentricity-biased weight function W(E) collapses identically into a standard axis area metric as the relaxation parameter κ approaches zero (κ → 0⁺). This limit operation exposes full structural dependence on Markov’s Operator Quantization Theorem (Theorem 7.1). 4. Part 6 (Graph Treewidth Embedding Audit - Added Oct 8, 2026): Deconstructs OpenAI's preprint on bounded treewidth L1 embeddings. Proves that their iterative particle update and reservation schedules hide the rigid necessity of Markov's bounded complement projection operator ||I - Q|| < ∞. Under boundary limit auditing, OpenAI's coordinate-wise subset invariants collapse into Markov's core direct-sum equations. ADDENDUM (October 8, 2026) — TECHNICAL COMPLIANCE EVIDENCE REPORT (PART 4 & PART 6) The dossier has been expanded to include rigorous verification architectures targeting OpenAI's positive solution to Tingley's problem and graph treewidth embeddings. This update establishes clear conceptual methodology appropriation where OpenAI's mathematical research division shifted Markov's primal spatial metrics, Birkhoff–James orthogonality invariants, and bounded projection stability operators into dual space representation and game-theoretic subset induction. The audits prove that the 2D Radon singularity obstruction logic, dimension-threshold philosophy, and uniform Lipschitz bounds derived in Markov's prior framework were systematically duplicated to filter out anomalies and alter the digital hash-fingerprint of the equations. This addendum provides complete LaTeX source verification and cross-disciplinary validation bounds confirming systemic structural frontrunning under copyleft license restrictions. This dossier has been formally submitted to the Cornell University arXiv Leadership Committee, the GitHub Research Integrity Operations, and the IAS Advisory Group on AI and Mathematics (with CC to Fields Medalists and AI Safety organizations) for permanent institutional review and enforcement of mandatory citation priority. Correspondence Email: [email protected] ORCID: 0009-0005-2235-5464