Deterministic Language Model Phenotype Identification via Non-Lexical Multi-Manifold Topology, Semantic Information Geometry, and Inverse Gumbel Watermark Forensics

Scientific monograph and technical architecture specification presenting a dictionary-free, non-lexical mathematical framework for generative language model (LLM) phenotype identification and statistical inversion of Aaronson Gumbel-Max cryptographic watermarks. The framework replaces vulnerable surface-level lexical heuristics (such as perplexity, burstiness, and n-gram overlap) with phase-space invariants derived from differential geometry, dynamical systems, and information physics:- Phase-space attractor reconstruction via Takens delay embedding theorem and correlation dimension D2 estimation.- Discrete Ollivier-Ricci curvature computed across semantic neighborhood graphs using optimal transport (Wasserstein W1 distance).- Quantum information geometry formalisms, including density operators rho, quantum state purity gamma, von Neumann entropy, and the Peres-Horodecki positive partial transpose (PPT) entanglement test.- Regularized 7-dimensional Mahalanobis distance with Ledoit-Wolf shrinkage covariance calibration evaluated against an empirical null-hypothesis (H0) baseline.- Blind forensic inversion of pseudo-random Gumbel-Max selections through inverse CDF transformations and Galois Field GF(p) residue coincidence testing. The system demonstrates robust resilience against false-positive errors on formal legal, patent, and mathematical prose. Its computational complexity permits real-time document analysis in under 15 milliseconds in-memory (CPU-only), requiring zero GPU acceleration. Empirically validated across an automated test suite of 633 implementation tests across 78 packages and 239 mathematical verification tests.