Family-Dependent Response to Reasoning Distillation Across Structural and Functional Identity Layers

Abstract

Reasoning distillation does not leave uniform traces across target base families. In the current sample, we measure structural and functional identity across reasoning-distillation derivatives in three base-architecture families (Llama, Qwen, and Mistral) at five model scales (1.5B to 70B). Structural displacements are family-graded: Mistral-family targets show scars of 7,701–8,518 times the acceptance threshold, Llama-family targets show 2,858–4,583 times, and Qwen-family targets show 141–516 times — a sixty-fold range across three families, with the third-family result persisting under an independently trained derivative using different training data. Functional consequences do not track structural magnitude uniformly: Llama derivatives show decisive functional hierarchy breaks, Qwen derivatives remain within their base neighborhood, and Mistral — despite having the loudest structural scar — shows only marginal functional displacement. The functional departure is low-rank at every tested scale but varies in character: G₁-dominant in Llama and Qwen families, with a sign-oscillating morphology in Mistral that suppresses centroid-level G₁ signal while preserving per-prompt dominance. The stiffness parameter at the measurement site is inversely ordered with structural scar magnitude across all three families. Fisher curvature, previously proposed as a candidate mechanism at small scale, does not order scar magnitudes correctly at production scale across families. These findings change how derivative identity claims should be interpreted: the expected displacement depends on the architectural context of the distillation, and the structural and functional layers can decouple — a model may show the loudest structural scar in the dataset while absorbing the functional perturbation. 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).