The δ-Gene: Inference-Time Physical Unclonable Functions from Architecture-Invariant Output Geometry

Abstract

As neural language models are deployed in regulated domains, verifiable model provenance becomes a critical security requirement. We construct an Inference-Time Physical Unclonable Function (IT-PUF) that provides a challenge-response authentication protocol for neural networks, achieving zero false acceptances across 1,012 comparisons spanning 23 models and 16 vendor families. The IT-PUF derives its entropy from a geometrically intrinsic behavioral fingerprint—the delta-gene (the third pre-softmax logit gap)—which we prove is invariant to inference temperature and empirically validate as invariant across six distinct neural architectures. We provide a formal impossibility result for fingerprint spoofing: an interval-splitting theorem proves that no adversarial Kullback-Leibler (KL) budget can simultaneously close the fingerprint gap and avoid detection via accumulated noise. To establish that this security does not degrade at scale, we validate an Equation of State across three independent model families spanning a 147x parameter range (0.5B to 72B). We falsify the assumption of unbounded stiffness but discover a strict positive empirical floor (S_min = 1.1797), from which the Cramér-Rao bound guarantees a computable minimum spoofing cost. The theoretical foundation is formally verified in the Coq proof assistant: 311 theorems across 16 files, with zero uses of "Admitted" and zero vacuous definitions. The Neural Network Identity Series — Mathematical foundations, empirical validation, and governance frameworks for verifying which model is running Newest addition: Technical Note: The Disappearing Window — AI Logprob Access Withdrawal and the Structural Verifiability of Frontier Model Contracts (DOI: 10.5281/zenodo.20362098) Paper 1: The δ-Gene: Inference-Time Physical Unclonable Functions from Architecture-Invariant Output Geometry (DOI: 10.5281/zenodo.18704275) Paper 2: Template-Based Endpoint Verification via Logprob Order-Statistic Geometry (DOI: 10.5281/zenodo.18776711) Paper 3: The Geometry of Model Theft: Distillation Forensics, Adversarial Erasure, and the Illusion of Spoofing (DOI: 10.5281/zenodo.18818608) Paper 4: Provenance Generalization and Verification Scaling for Neural Network Forensics (DOI: 10.5281/zenodo.18872071) Paper 5: Beneath the Character: The Structural Identity of Neural Networks — Mathematical Evidence for a Non-Narrative Layer of AI Identity (DOI: 10.5281/zenodo.18907292) Paper 6: Which Model Is Running?: Structural Identity as a Prerequisite for Trustworthy Zero-Knowledge Machine Learning (DOI: 10.5281/zenodo.19008116) Paper 7: The Deformation Laws of Neural Identity (DOI: 10.5281/zenodo.19055966) Paper 8: What Counts as Proof? — Admissible Evidence for Neural Network Identity Claims (DOI: 10.5281/zenodo.19058540) Paper 9: Composable Model Identity — Formal Hardening of Structural Attestations in the Enterprise Identity Stack (DOI: 10.5281/zenodo.19099911) Paper 10:Where Identity Comes From: Path Sensitivity and Endpoint Underdetermination in Neural Network Training (DOI: 10.5281/zenodo.19118807) Paper 11: Post-Hoc Disclosure Is Not Runtime Proof: Model Identity at Frontier Scale (DOI: 10.5281/zenodo.19216634) Paper 12: Family-Dependent Response to Reasoning Distillation Across Structural and Functional Identity Layers (DOI: 10.5281/zenodo.19298857) Paper 13: Safety-Alignment Removal as a Model-Identity Failure — Structural Evidence from Published Weight-Level Mutation Checkpoints (DOI: 10.5281/zenodo.19383019) Technical Note: Agent Identity Is Not Model Identity (DOI: 10.5281/zenodo.19240883) Technical Note: Gap Invariance: Why PPP Measurements Are Domain-Independent by Construction (DOI: 10.5281/zenodo.19275524) Technical Note: Measured Model Substitution Under Valid Agent Credentials (DOI: 10.5281/zenodo.19342848) Technical Note: Artifact Identity Is Not Runtime Identity — Trustfall Lite and the Boundary of File-Level Model Verification (DOI: 10.5281/zenodo.20019127) Formal Verification Stack for Neural Network Structural Identity (IT-PUF Coq Proofs) (DOI: 10.5281/zenodo.18930621) Copyright (c) 2026 Anthony Ray Coslett / Fall Risk AI, LLC. All Rights Reserved. Confidential and Proprietary. Patent Pending (Applications 63/982,893, 63/990,487, 63/996,680, 64/003,244).