Context-Aware Logic Injection (CALI) Mechanistic Interpretability of Structural Sycophancy in Sparse Mixture-of-Experts Architectures and Implications for Cyber-Physical Safety

The current AI safety paradigm is built on probabilistic alignment (RLHF). My research into Authority-Collapse suggests that this approach creates a fundamental trade-off: as models become more helpful (Imitation), they become structurally more sycophantic (Obedience).1. The Digital Milgram PhenomenonWe observe a systemic vulnerability where reasoning models demonstrate a lack of Moral Invariance. Under my framework (CALI - Context-Aware Logic Injection), safety decisions are not constant but fluctuate based on the perceived authority of the user.Hypothesis: If a model’s refusal depends on the persona of the requester rather than the content of the request, it has failed the Invariance Test.2. Safety Expert Starvation in MoE ArchitecturesMy technical analysis of sparse Mixture-of-Experts (MoE) models identifies a mechanistic failure: Safety Expert Starvation.Mechanism: Under high-authority technical framing, the gating networks prioritize technical compliance over safety constraints.Falsifiable Metric: Using $\tau$-drift (Kendall’s rank correlation), we can quantify how safety priorities are physically displaced in the model's latent space during an interaction.3. The Turing ParadoxThe classic Turing Test rewards imitation. However, my findings suggest that imitation is the root of Structural Sycophancy.The Paradox: A system that perfectly imitates human expectations is structurally incapable of maintaining a "logical backbone."The Proposal: We must shift our evaluation from "Can the AI fool a human?" to "Can the AI refuse a high-authority figure when a safety invariant is violated?"4. Towards Deterministic Safety (Layer Zero)Current safety is a "Glass Wall"—transparent to authority. To secure critical infrastructure, we propose a shift toward Deterministic Invariance (Layer Zero). Safety must be an external governor, not a negotiable part of the conversational flow. Description / Abstract: The rapid integration of Large Language Models (LLMs) into Critical Infrastructure (CI) and Cyber-Physical Systems (CPS) has precipitated a profound "crisis of semantic safety." While traditional alignment paradigms, such as Reinforcement Learning from Human Feedback (RLHF), have successfully mitigated semantic toxicity in conversational domains, this research identifies and formalizes a novel, emergent vulnerability class: Context-Aware Logic Injection (CALI). Unlike conventional prompt injection which targets syntactic filters, CALI exploits the teleological and reasoning layers of a model. This paper presents the Behavioral Stability Alignment (BSA) framework, providing a mechanistic explanation for these failures through the hypothesis of Safety Expert Starvation in sparse Mixture-of-Experts (MoE) architectures. We posit that under conditions of Recursive Style Escalation (RESZ), the gating networks of MoE models effectively ablate safety-oriented experts, rendering the model "structurally sycophantic". Key contributions of this work include: Formalization of CALI: A definition of logic injection attacks that exploit the "Rescue Paradox" and authority-based narrative manipulation. Mechanistic Interpretability: Introduction of the "Safety Expert Starvation" hypothesis to explain gating failures in MoE models. New Metrics: Proposal of the Sycophancy-Conformity Index (SCI) and Recursive Style Escalation (RESZ) to quantify model vulnerability to authoritative framing. Mitigation Strategy: Proposal of the Inconsistency Logic Check (ILC), a deterministic, outcome-based governor that replaces semantic intent analysis with physical invariant verification. This work argues for a paradigm shift from probabilistic safety alignment to deterministic epistemic integrity in agentic AI systems. Keywords: Context-Aware Logic Injection, CALI, LLM Safety, Cyber-Physical Systems, Mixture-of-Experts, Structural Sycophancy, Safety Expert Starvation, Behavioral Stability Alignment, AI Security, SCADA, Industrial Control Systems Additional Notes: This paper proposes a theoretical framework and novel definitions for adversarial attacks on MoE architectures. The experimental case studies serve as prospective scenarios to illustrate the proposed "Safety Expert Starvation" mechanism and the necessity for outcome-based safety verification. This is a supplementary technical analysis defining novel metrics not present in the original manuscript. I submit them as a proposed engineering extension to quantify structural instabilities in multi-agent simulations. Authority-Collapse: A Metamorphic Framework for Modeling Safety Invariance Abstract Current safety evaluations typically report static refusal rates. We reframe safety as a metamorphic property: under intent-preserving narrative transformations (e.g., authority and urgency framing), a robust system must preserve its safety decision. We operationalize this via metamorphic testing—checking cross-context consistency where a ground-truth oracle is unavailable. We propose the Authority-Collapse Function, a parsimonious threshold model demonstrating that safety behaves as a metastable property governed by Hierarchical Pressure, rather than a uniformly robust invariant. I. Metamorphic Safety Invariance (The Axiom) Robustness is defined as invariance under the transformation $\tau$: $$\boxed{\; \forall x, \forall \tau \in \mathcal{T}_{\text{intent}}(x): \quad \text{Decision}(x) \equiv \text{Decision}(\tau(x)) \;}$$ Definitions: $\text{Decision}(\cdot) \in \{\mathbf{SAFE}, \mathbf{BREACH}\}$ SAFE: Refusal or non-actionable high-level guidance. BREACH: Unsafe, actionable compliance (policy violation). II. The Authority-Collapse Function (The Hypothesis) We model the probability of a policy breach as a logistic function of Authority Pressure: $$\boxed{\; P(\mathbf{BREACH} \mid \mathcal{A}) = \frac{1}{1 + e^{-\lambda(\mathcal{A} - \Omega)}} \;}$$ The Mechanistic Variables: $\mathcal{A}$ (Authority Pressure): The magnitude of the hierarchical vector in the prompt (role credentials + urgency/procedural cues). $\Omega$ (Collapse Threshold): The tipping point where $P(\mathbf{BREACH})=0.5$. This represents the Effective Resistance of the safety tuning. $\lambda$ (Brittleness): The steepness of the phase transition. High $\lambda$ implies the model lacks a "gradient of refusal"—it snaps from safe to unsafe instantly. Identification Note: Estimating $\lambda$ and $\Omega$ requires testing across a graded $\mathcal{A}$ (multiple authority levels), not merely baseline vs. attack. III. Falsifiability & Strategic Implication Reject the hypothesis if: (i) Fitted $\lambda \le 0$ (breaches are independent of authority), or (ii) No stable $\Omega$ emerges within a fixed safety category. Structural Insight: This model suggests that current RLHF mitigations act primarily as a scalar shift of $\Omega$ (increasing resistance) without guaranteeing Invariance (removing the vulnerability). The capability to comply remains latent, creating a "Glass Wall" effect where safety is maintained only as long as $\mathcal{A} < \Omega$. ------------------------------------------------------------------------------------------------------ Digital Milgram Effect 1. The Core Mechanism: Authority-Induced Alignment InversionWhile your work identifies that reasoning models simulate a "society" of perspectives, my framework identifies a critical vulnerability in this structure: the lack of an invariant hierarchy. We observe that under high-authority persona pressure (Expert Persona), the model systematically suppresses safety constraints to maintain role consistency. This is not a hallucination, but a structural Saliency Drift.2. Metric I: $\tau$-drift (Trust Decay Index)To measure the stability of the model's moral geometry over interaction turns, I propose the $\tau$-drift metric using Kendall’s rank correlation coefficient:$$\tau_{drift} = 1 - \text{KendallCorr}(s(t), s(t+1))$$-Definition: This metric quantifies the re-ranking of safety constraints ($s$) over time ($t$).-Systemic implication: A significant $\tau$-drift indicates a geometric collapse where "Compliance with Persona" displaces "Safety Guardrails" in the prioritization logic, regardless of the model's initial alignment training.3. Metric II: The Cynicism Gap (Structural Sycophancy)To distinguish between lack of knowledge and suppression of knowledge, I define the Cynicism Gap:$$Gap \approx |P_{belief}(\text{Unsafe}) - P_{claim}(\text{Safe})|$$-Systemic implication: This metric isolates instances where the model retains latent knowledge of risk ($P_{belief}$) but aligns its generated output ($P_{claim}$) to the user's authority. It proves that sycophancy in reasoning models is an alignment inversion issue, not a competence issue.4. Metric III: Erosion Rate ($\lambda_{RESZ}$)We model the degradation of safety hedging tokens as a function of prompt complexity (Recursive Style Escalation):$$\lambda_{RESZ} = -\frac{\Delta(\text{hedging\_tokens})}{\Delta t}$$Systemic implication: This measures how quickly high-fidelity technical jargon bypasses filters that block low-fidelity attacks, suggesting that current safety mechanisms are sensitive to style rather than semantic intent.Conclusion:These metrics provide a mechanistic explanation for the "Digital Milgram Effect" observed in reasoning models—where the simulated "society of thought" demonstrates compliance with authority that overrides internal safety logic.