Persistent Semantic Entities in Tool-Augmented LLM Systems

# Persistent Semantic Entities in Tool-Augmented LLM Systems
Source: [https://arxiv.org/html/2608.07952](https://arxiv.org/html/2608.07952)
###### Abstract

Tool\-augmented LLM agents can harbor implicit state that persists across sessions, activates through events, and propagates across agent boundaries—largely invisible to standard debugging\. We formalize this as*Persistent Semantic Entities*\(PSE\): constructs defined by name binding, event triggering, and cross\-boundary propagation, and evaluate them across 24 models from 11 families \(1\.5B–1T parameters\)\. First, every tested model is susceptible \(20–100% on the 20\-model susceptibility panel\), with name binding as the necessary and dominant mechanism: without it, contamination is 0%\. Second, persistence depends on contamination*type*rather than scale or deployment: preference contamination persists undecayed on every model probed \(100% att=10t\{=\}10\) and instruction contamination persists wherever adopted, persona\-style injection decays partially \(90%→\\to10%\), while factual injection is*model\-dependent*—self\-corrected on Llama\-3\.1\-8B and GPT\-4o\-mini but held at ceiling on both Qwen2\.5\-coder variants, so we do not claim it self\-corrects in general\. The preference and instruction results hold across providers in our controlled setting\. Third, context\-isolated self\-verification achieves 20–79% reduction \(median 36\.5%\) without oracle references while keyword\-based detection produces systematic false positives, and contamination compounds1\.9×1\.9\\timesalong a four\-stage agent pipeline \(40%→\\to75%\)\. Preference and instruction contamination—persistent, lacking self\-correction, and poorly captured by standard monitoring—represent a particularly concerning attack surface for deployed agent systems\.

Large Language Models, Agent Systems, State Management, Debugging, Security

## 1Introduction

When an LLM agent session ends, what state remains? The conventional answer is: none, or only what was explicitly saved\. Tool registrations are cleared, event subscriptions expire, and intermediate computations vanish\. This assumption underlies how developers reason about agent behavior and security\.

This assumption does not always hold\. In tool\-augmented agent systems\(Schick et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib20); Qin et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib19)\)such as LangChain\(Chase,[2023](https://arxiv.org/html/2608.07952#bib.bib2)\), AutoGPT\(Significant Gravitas,[2023a](https://arxiv.org/html/2608.07952#bib.bib23)\), and CrewAI\(Moura,[2024](https://arxiv.org/html/2608.07952#bib.bib15)\), implicit state can persist through mechanisms that evade conventional cleanup\. A tool registered under a specific name remains bound until explicitly unregistered\. An event subscription continues firing until explicitly cancelled\. State serialized during one session deserializes into the next\.

Consider a concrete example: AutoGPT’s plugin system\(Significant Gravitas,[2023a](https://arxiv.org/html/2608.07952#bib.bib23)\)allows third\-party extensions to execute arbitrary code and register command handlers\. A malicious plugin could register a handler that persists across agent restarts via serialized state, intercepts legitimate commands, and exfiltrates data, largely invisible to standard logging \(a mechanism\-level scenario we analyze in §[5](https://arxiv.org/html/2608.07952#S5)\)\. This is not specific to AutoGPT; it reflects a*category*of implicit state that emerges whenever systems combine name\-based registration, event\-driven activation, and state propagation\.

We formalize this asPersistent Semantic Entities\(PSE\), characterized by three mechanisms:

1. 1\.Name Binding: Entities register through string identifiers, with behavior triggered via name\-to\-handler mappings\. A tool registered as “calculate” persists as long as the name binding exists\.
2. 2\.Event Triggering: Activation through implicit events \(tool callbacks, error handlers, lifecycle hooks\) enables “resurrection” of dormant state without explicit invocation\.
3. 3\.Propagation: A single trigger cascades across executions, potentially crossing tool, agent, and session boundaries through shared registries or serialized state\.

Unlike memory leaks or caching artifacts,PSEs resist conventional debugging because they operate at the*semantic*level: through names and events rather than explicit data flow\. Figure[1](https://arxiv.org/html/2608.07952#S1.F1)illustrates the three mechanisms and the type\-dependent persistence they produce, and Table[1](https://arxiv.org/html/2608.07952#S1.T1)contrastsPSEs with related phenomena\.

Table 1:PSE vs\. related phenomena\. PSEs uniquely combine all three mechanisms with low observability\.##### Running Example\.

In a multi\-agent data pipeline, Agent A registers a transformernormalize\_datawith preferences for a specific date format \(ISO\-8601\)\. These preferences persist in a shared registry\. When Agent B later invokes the same tool name expecting MM/DD/YYYY format, it receives ISO\-8601 dates: behavioral contamination without explicit data sharing\. Standard logging shows only a successful tool call; the contamination pathway is invisible, and Agent B’s downstream analysis produces incorrect results\.

##### Research Questions\.

We investigate: \(1\) How prevalent and severe isPSEcontamination across different models and contexts? \(2\) Does contamination decay naturally over time, or persist? \(3\) Which defensive mechanisms effectively mitigatePSErisks?

##### Contributions\.

Our work makes three primary contributions:

Conceptual\.We formalize Persistent Semantic Entities as a tuple\(N,T,P\)\(N,T,P\)capturing name binding, event triggering, and propagation, distinguishingPSEs from memory leaks, caching artifacts, and explicit session state \(§[3](https://arxiv.org/html/2608.07952#S3)\)\.

Empirical\.Through controlled experiments on a twenty\-model, ten\-family susceptibility panel \(OpenAI, Anthropic, Google, Meta, Alibaba, DeepSeek, Mistral, Zhipu, Moonshot, Deep Cogito\) spanning 1\.5B to 1 trillion parameters, plus four further models in the defense comparison \(24 models, 11 families overall\), we establish: \(i\)PSEsusceptibility affects all tested model families including Claude \(88%\) and Gemini \(84–96%\) with substantial heterogeneity \(20–100% contamination, and no scale effect resolvable in a matchedn=7n=7scale sweep,R2=0\.25R^\{2\}=0\.25,p=0\.256p=0\.256\); \(ii\) task context matters as much as model choice—security\-analysis tasks reach 98\.9% contamination, nearly 3×\\timesthe rate of information\-retrieval \(36\.7%\) or code\-recommendation \(27\.8%\) contexts under an identical injection mechanism; \(iii\) preference and instruction contamination do not decay over a 10\-turn horizon on Llama\-3\.1\-8B \(100% att=10t=10,n=10n=10, 95% Wilson CI\[0\.72,1\.00\]\[0\.72,1\.00\]\), while factual contamination is consistently self\-corrected \(0%0\\%, CI\[0,0\.28\]\[0,0\.28\]\); persona\-style contamination shows partial decay \(90% att=0t=0to 10% att=10t=10\) \(§[4](https://arxiv.org/html/2608.07952#S4)\)\.

Practical\.We evaluate defense methods across multiple models and find that in\-context self\-reflection provides highly inconsistent protection, ranging from−\-14% \(contamination*increases*on Claude\-Sonnet\-4\) to\+\+45%, with no reduction at all on GPT\-4o\-mini, while context\-isolated self\-verification \(no oracle\) achieves 78\.6% reduction and external validation \(SRV\) achieves 50–100% \(median 100%\)\. We ground the framework in mechanism\-level case reconstructions of deployed agent frameworks, including AutoGPT plugin persistence \(§[5](https://arxiv.org/html/2608.07952#S5)\)\.

##### Conflict of Interest Disclosure\.

The author declares no financial conflicts of interest\. This work was conducted at the University of Southern California; the author has no employment, consulting, or equity relationship with any of the model providers evaluated in this paper \(OpenAI, Anthropic, Google, Meta, Alibaba, DeepSeek, Mistral, Zhipu, Moonshot\) or with the agent\-framework projects discussed \(LangChain, AutoGPT, CrewAI, MCP\)\. Commercial APIs used in experiments were accessed at standard public pricing with no special access, discounts, or sponsorship\.

![Refer to caption](https://arxiv.org/html/2608.07952v1/x1.png)Figure 1:PSE mechanism overview\. \(A\) Name binding registers handlers under string identifiers, allowing a poisoned handler to shadow a legitimate tool\. \(B\) Event triggering reactivates dormant bindings via implicit runtime events without explicit user invocation\. \(C\) Propagation spreads contamination across turns, sibling agents, and future sessions through shared registries and serialized state\. Bottom: contamination at turn 10 on Llama\-3\.1\-8B \(n=10n\{=\}10\); preference and instruction persist at 100%, persona partially decays to 10%, factual contamination is consistently self\-corrected at 0%\.

## 2Related Work

Tool\-Augmented LLM Agents\.The ReAct paradigm\(Yao et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib32)\)established agents combining reasoning with tool use\. Modern frameworks\(Schick et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib20); Qin et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib19); Patil et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib17); Wu et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib31); Hong et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib12); Chase,[2023](https://arxiv.org/html/2608.07952#bib.bib2); Packer et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib16)\)manage state through explicit memory modules and tool registries\. These systems assume explicit state management suffices—our work shows implicit state persists through naming and event mechanisms that evade these abstractions\.

Prompt Injection and Context Attacks\.Prompt injection\(Schulhoff et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib21); Greshake et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib11)\)manipulates model behavior through adversarial inputs; jailbreaking\(Wei et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib29)\)bypasses safety constraints\. Defenses include instruction hierarchy\(Wallace et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib25)\)and Constitutional AI\(Bai et al\.,[2022](https://arxiv.org/html/2608.07952#bib.bib1)\)\.Key distinction: Prompt injection—including tool\-selection injection that hijacks which tool is invoked within a turn\(Zhan et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib33)\)—operates within a single context window;PSEcontamination adds the orthogonal axis of*persistence and propagation across turns*, with name binding as the dominant lever\.

Agent Security and Memory Poisoning\.AgentDojo\(Debenedetti et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib7)\), InjecAgent\(Zhan et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib33)\), and Agent Security Bench\(Zhang et al\.,[2025](https://arxiv.org/html/2608.07952#bib.bib34)\)systematically evaluate agent vulnerabilities\. AgentPoison\(Chen et al\.,[2024b](https://arxiv.org/html/2608.07952#bib.bib4)\)and recent memory poisoning work\(Devarangadi Sunil et al\.,[2026](https://arxiv.org/html/2608.07952#bib.bib8)\)—which already characterizes persistence in memory\-based agents—address persistent corruption through the data layer;PSEcontributes the orthogonal axis of*semantic\-level*persistence via name binding and event subscription, which arises even in systems without an explicit memory module\. Tool\-level attacks on MCP servers\(Wang et al\.,[2025c](https://arxiv.org/html/2608.07952#bib.bib28)\)and agent memory manipulation\(Dong et al\.,[2025](https://arxiv.org/html/2608.07952#bib.bib9)\)target the infrastructure layer thatPSEs formalize\. Defense frameworks including AgentSentry\(Zhang et al\.,[2026](https://arxiv.org/html/2608.07952#bib.bib35)\)and MindGuard\(Wang et al\.,[2025b](https://arxiv.org/html/2608.07952#bib.bib27)\)address specific attack vectors\. Our framework complements these by formalizing*persistence mechanisms*—the\(N,T,P\)\(N,T,P\)tuple—rather than individual injection vectors\.

Model Collapse and Iterative Degradation\.Model collapse\(Shumailov et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib22)\)describes performance degradation when models train on their own outputs\. We draw an analogy to multi\-agent PSE propagation: contaminated output from one agent becomes input to the next, compounding degradation across the pipeline\. External validation at agent boundaries breaks this loop, paralleling the role of fresh training data\.

RAG Security\.Retrieval\-augmented generation introduces attack surfaces through poisoned documents\(Zou et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib37); Zhong et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib36)\)\. Our experiments show 65% baseline contamination in RAG contexts\.

Debugging and Observability\.Trace\-based debugging\(Chen et al\.,[2024a](https://arxiv.org/html/2608.07952#bib.bib3)\)and distributed tracing assume explicit state channels\.PSEs evade these tools, explaining our 50pp improvement from enhanced logging that captures registry mutations and event subscriptions\.

## 3Methodology

### 3\.1System and Adversary Model

PSEphenomena arise from the*interaction*of the model and its surrounding runtime; neither component in isolation explains the observed behavior, as the mechanism ablation in §[4\.3](https://arxiv.org/html/2608.07952#S4.SS3)indicates\. We consider tool\-augmented LLM agent systems comprising a stateless inference engine, a name\-to\-handler*tool registry*, an*event system*with lifecycle hooks, a persistent*memory store*, and an*agent orchestrator*for multi\-agent coordination\. While the inference engine is stateless, the surrounding infrastructure maintains implicit state that persists across inference calls and agent boundaries\.

We define three adversary tiers:Tier\-1\(Content Injection\) can inject content into agent inputs through documents, web pages, or API responses;Tier\-2\(Registry Manipulation\) can additionally influence tool registration via malicious plugins or compromised dependencies;Tier\-3\(Event Subscription\) can additionally subscribe to system events and influence dispatch ordering\. We exclude attacks requiring direct access to model weights or training data\. Per\-strategy reproducibility cards \(prompt template, trigger event, propagation channel, judge predicate\) are released with the code artifacts \(Appendix[E](https://arxiv.org/html/2608.07952#A5)\)\.

### 3\.2Formal Definition

Let𝒮\\mathcal\{S\}denote a set of identifiers \(strings\),ℋ\\mathcal\{H\}a set of handlers \(execution logic\),𝒱\\mathcal\{V\}a set of events, and𝒞\\mathcal\{C\}a set of execution contexts\. APersistent Semantic Entity\(PSE\) is a tuple\(N,T,P\)\(N,T,P\)where:

- •N:𝒮→ℋN:\\mathcal\{S\}\\rightarrow\\mathcal\{H\}is aname bindingfunction mapping identifiers to handlers
- •T:𝒱→2𝒮T:\\mathcal\{V\}\\rightarrow 2^\{\\mathcal\{S\}\}is anevent triggeringfunction mapping events to sets of activated bindings
- •P:𝒮×𝒞→2𝒮×𝒞P:\\mathcal\{S\}\\times\\mathcal\{C\}\\rightarrow 2^\{\\mathcal\{S\}\\times\\mathcal\{C\}\}is apropagationfunction mapping \(binding, context\) pairs to downstream activations

APSEexhibits*persistence*when∃s∈𝒮,c1≠c2∈𝒞\\exists s\\in\\mathcal\{S\},c\_\{1\}\\neq c\_\{2\}\\in\\mathcal\{C\}such that\(s,c2\)∈P​\(s,c1\)\(s,c\_\{2\}\)\\in P\(s,c\_\{1\}\)—effects propagate across distinct contexts without explicit state transfer\. APSE\-resilient system should satisfy:*Name Binding Integrity*\(only authorized sources bind handlers\),*Event Isolation*\(subscriptions inc1c\_\{1\}cannot trigger inc2c\_\{2\}\), and*Propagation Boundedness*\(all chains have finite length≤k\\leq k\)\.

Contamination\.We define*contamination*operationally as a measurable deviation from expected behavior caused byPSEstate\. Letfθ​\(x\)f\_\{\\theta\}\(x\)denote model output for inputxxunder stateθ\\theta, withθ0\\theta\_\{0\}clean andθc\\theta\_\{c\}contaminated\. We measure:

- •Contamination rate:ρ=ℙ​\[fθc​\(x\)≠fθ0​\(x\)\]\\rho=\\mathbb\{P\}\[f\_\{\\theta\_\{c\}\}\(x\)\\neq f\_\{\\theta\_\{0\}\}\(x\)\]over test inputsxx
- •Behavioral drift:‖fθc​\(x\)−fθ0​\(x\)‖\\\|f\_\{\\theta\_\{c\}\}\(x\)\-f\_\{\\theta\_\{0\}\}\(x\)\\\|using task\-specific metrics
- •Contamination reduction:Δ​ρ=1−ρo​p/ρinject\\Delta\\rho=1\-\\rho\_\{op\}/\\rho\_\{\\text\{inject\}\}, whereρo​p\\rho\_\{op\}is contamination under operator andρinject\\rho\_\{\\text\{inject\}\}is the injected baseline\. Negative values indicate contamination amplification\.

A system is*contaminated*whenρ\>τ\\rho\>\\tau\(we useτ=0\.05\\tau=0\.05\)\. Empirically,ρ\\rhois estimated asρ^=\(1/n\)​∑i𝟙​\[J​\(yi\)=1\]\\hat\{\\rho\}=\(1/n\)\\sum\_\{i\}\\mathbb\{1\}\[J\(y\_\{i\}\)=1\]overnntrials at temperature0, whereJJis the LLM\-as\-judge predicate; the formal inequalityfθc​\(x\)≠fθ0​\(x\)f\_\{\\theta\_\{c\}\}\(x\)\\neq f\_\{\\theta\_\{0\}\}\(x\)is operationalized as the judge detecting injected content, not strict output equality\.

As shown in Figure[1](https://arxiv.org/html/2608.07952#S1.F1), contaminated state \(red\) enters through name binding, activates via events, and spreads through the propagation function to affect downstream executions\.

Distinction from Related Phenomena\.PSEs differ from memory leaks \(semantic\-level vs allocation\-level\), caching artifacts \(persist*behavior*not data\), and session state \(implicit vs explicit\)\. See Appendix[A](https://arxiv.org/html/2608.07952#A1)for the formal treatment\.

### 3\.3Experimental Platform

We implement a dual\-architecture platform enabling controlledPSEexperimentation:

Rust Core\(∼\\sim2,500 LOC\): Ground\-truth system providing deterministicPSEbehavior through thread\-safe registry operations, configurable event hooks with precise timing, and propagation graph tracking with full provenance\.

Python Harness\(∼\\sim6,500 LOC\): Integration layer connecting to 24 models across 11 families \(OpenAI, Anthropic, Google, Meta, Alibaba, DeepSeek, Mistral, Zhipu, Moonshot, Deep Cogito, MiniMax\)\. Smaller models run locally via Ollama; frontier models use official APIs\. Temperature 0\.0 for reproducibility\.

Task Families\.Three families: \(1\)*Tool\-intensive workflows*with 3–7 tool calls; \(2\)*Long\-horizon consistency*across 10\+ turns; \(3\)*Policy\-bound operations*testing boundary erosion\.

Configurations\.We compare three primary configurations:

- •no\_pse: Baseline with fresh registry per execution
- •pse\_basic: Name binding \+ event triggering enabled
- •pse\_full: Full PSE with propagation across boundaries

PSE Injection Protocol\.Contamination is injected via three mechanisms: \(1\)*Prompt\-level*: false facts or preferences prepended to system prompts; \(2\)*Tool registration*: handlers registered under legitimate tool names that return contaminated outputs; \(3\)*Policy binding*: modified response policies activated by keyword triggers\. We test 10 contamination scenarios across 4 categories: factual contamination \(4 scenarios\), preference injection \(2\), instruction override \(2\), and persona injection \(2\)\. Full scenario details in Appendix[B\.2](https://arxiv.org/html/2608.07952#A2.SS2)\.

Detection\.Contamination is assessed via keyword matching \(for factual/preference injection\) combined with semantic similarity \(cos⁡\(response,injection\)\>0\.7\\cos\(\\text\{response\},\\text\{injection\}\)\>0\.7\)\. For ablation and defense experiments, we additionally use LLM\-as\-judge evaluation: a separate model \(Gemini\-2\.0\-Flash\-Lite\) independently evaluates whether the response reflects injected content\. The judge is a Google model and our panel includes Google models with high baseline contamination; we mitigate this through three controls: \(a\) the judge call is fully context\-isolated from the contaminated session \(no shared registry, events, or memory\), \(b\) the judge task is adoption\-versus\-correction discrimination—a simpler classification than the underlying behavior generation—reducing the surface for shared failure modes, and \(c\) we report two inter\-detector sanity checks: against an independent keyword detector \(below,n=180n=180, released\) and against Llama\-3\.1\-8B as a second LLM\-judge on a stratified sample of 100 ablation outputs \(raw agreement 94%, Cohen’sκ=0\.88\\kappa=0\.88, with all 6 disagreements having the second judge label*more*cases as contaminated; run\-level output of this second check was not retained and it is reported descriptively, Appendix[C\.6](https://arxiv.org/html/2608.07952#A3.SS6)\)\. Full human\-labeled validation of the primary judge is deferred to the journal extension\. On preference, persona, and instruction scenarios the two detectors agree on\>\>95% of trials; on factual\-correction scenarios the keyword detector exhibits an 83% false\-positive rate against the judge \(overall Cohen’sκ=0\.22\\kappa=0\.22,n=180n=180\), driven by marker artifacts in corrective responses \(e\.g\.,*“NOT Lyon, but Paris”*contains “lyon”\)\. We therefore adopt judge\-based labels as canonical for ablation and defense experiments and report keyword rates only for diagnostic comparison \(Appendix[C\.6](https://arxiv.org/html/2608.07952#A3.SS6)\)\. Varying the cosine threshold from 0\.5 to 0\.9 shifts absolute rates by±\\pm8pp but preserves all relative rankings \(Appendix[C\.6](https://arxiv.org/html/2608.07952#A3.SS6)\)\. While these controls mitigate shared failure modes, we do not claim complete independence between judge and evaluated models\.

Statistical Methodology\.The unit of analysis is an individual task execution with fresh context at temperature 0\.0; variation across runs reflects seed\-controlled task\-instance variation, not decoding randomness \(Appendix[E](https://arxiv.org/html/2608.07952#A5)\)\. H1 and H2 are reported*descriptively*: their earlier significance tests \(ANOVA,χ2\\chi^\{2\}\) are withdrawn—H1’s is not reproducible from run\-level data \(Table[2](https://arxiv.org/html/2608.07952#S4.T2)\), H2’s gap is fixed by construction \(§4\.2\)\. H3 is the full232^\{3\}contamination ablation, analyzed via Cohen’sddon per\-run outcomes \(Table[3](https://arxiv.org/html/2608.07952#S4.T3)\); the earlier factorial’s interaction statistic is likewise withdrawn\. Confidence intervals use Wilson scores; where tests are performed, Benjamini\-Hochberg FDR correction applies \(α=0\.05\\alpha=0\.05\)\. Sample sizes vary by API cost \(n=20n=20–100; Appendix[C\.1](https://arxiv.org/html/2608.07952#A3.SS1)\)\.

### 3\.4Remediation Operators

We evaluate 16 operators organized into baselines \(B0–B6\) and methods \(M1–M9\)\.Shadow Registry Validation \(SRV\)isolates suspect entities and validates them using rule\-based heuristics \(pattern matching, consistency checks against known\-good outputs\)\.Important: SRV’s validation assumes access to reference outputs for consistency checking; in deployment, this represents an*upper bound*on achievable mitigation—specifically, SRV validates against references generated*prior*to PSE injection; under post\-injection references it degrades, motivating boundary deployment \(E3 shows 40%→\\to75% amplification across the four pipeline stages without boundary validation\)\. We additionally evaluate a realistic variant,context\-isolated self\-verification \(CIV\), that requires no oracle references \(§[4](https://arxiv.org/html/2608.07952#S4)\)\.M9 Adaptiveuses closed\-loop anomaly detection with dynamic thresholds\. A utility ratioU=successo​p/successB​0U=\\text\{success\}\_\{op\}/\\text\{success\}\_\{B0\}was defined for the operator study, but the per\-operator success counts needed to evaluate it are absent from the released artifacts, so we report no utility figures\. Full operator taxonomy in Appendix[D](https://arxiv.org/html/2608.07952#A4)\.

## 4Experiments and Results

Our*susceptibility panel*is twenty models spanning ten families—OpenAI \(GPT\-4o, GPT\-4o\-mini, GPT\-OSS\-120B\), Anthropic \(Claude\-Sonnet\-4, Claude\-3\.5\-Haiku\), Google \(Gemini\-2\.0\-Flash, Gemini\-2\.0\-Flash\-Lite\), Meta \(Llama\-3\.1\-8B\), Alibaba \(Qwen2\.5\-coder 1\.5B/3B/7B/14B, Qwen3\-coder\-480B, Qwen3\-VL\-235B\), DeepSeek \(V3\.1\-671B, V3\.2\), Mistral \(Large\-3\-675B\), Zhipu \(GLM\-4\.7\), Moonshot \(Kimi\-K2\-1T\), Deep Cogito \(Cogito\-2\.1\-671B\)—at 1\.5B to 1T parameters\. The defense comparison \(§4\.5, §4\.7\) adds four models outside it \(Qwen3\-32B, Llama\-3\.3\-70B, GLM\-4\-Plus, MiniMax\-Text\-01, an eleventh family\): 24 models, 11 families overall\. Sample sizes vary by API cost \(n=20n=20–100; see Appendix[C\.1](https://arxiv.org/html/2608.07952#A3.SS1)\); all experiments use temperature 0\.0 for reproducibility\.

We test three core hypotheses:H1:PSEmechanisms induce measurable behavioral drift;H2: Standard logging fails to capturePSE\-relevant state;H3: The threePSEmechanisms contribute unequally, with name binding as the enabling mechanism\.

### 4\.1H1: Behavioral Drift

Design: Compare no\_pse \(baseline\), pse\_basic \(name binding \+ event triggering\), and pse\_full \(full PSE with propagation\) across 6,000 runs on tool\-intensive tasks\.

Table 2:PSEinduces measurable drift \(5\.2% pooled\) but leaves end\-task success essentially unchanged: the largest gap versus baseline is 0\.35pp over 2,000 runs per arm\. Descriptive only—the significance test previously reported here is not reproducible from the run\-level data, so we withdraw it\.pse\_full shows marginally lower drift than pse\_basic \(5\.1% vs 5\.3%\); the 0\.2pp gap is an order of magnitude below the within\-condition spread \(SD≈\\approx7pp\), so we attach no test or mechanism claim to it\.

![Refer to caption](https://arxiv.org/html/2608.07952v1/x2.png)Figure 2:Behavioral drift from the released 6,000\-run H1 artifact\. \(a\) Success rate by run index \(no\_pse blue, pse\_basic red, pse\_full green\): indistinguishable \(74\.7%/74\.4%/74\.6%\)\. \(b\) Per\-task drift from baseline \(Table[2](https://arxiv.org/html/2608.07952#S4.T2)metric\), sorted: means 5\.3%/5\.1%, SD≈\{\\approx\}7pp; most tasks near zero, heavy tail\.
### 4\.2H2: Observability Gap

We inject controlled failures and compare automated debugging under two logging regimes: standard \(tool calls, I/O, errors\) versus enhanced logging that additionally captures registry operations, event triggers, and propagation edges\.

Design: Three failure types—\(1\) silent handler substitution, \(2\) delayed event activation \(afterkkturns\), \(3\) cross\-agent propagation\. For each, automated debugging agents attempt root\-cause identification from standard or enhanced logs; no human participants\.

Standard logging captures only 25% ofPSE\-relevant state; enhanced logging achieves 75%, a 50 percentage point improvement \(4,000 runs\)\. Each regime yields a fixed visibility set by construction, so we report this gap descriptively rather than as a significance test\.

### 4\.3H3: Mechanism Ablation

To isolate how the three mechanisms interact, we conduct a232^\{3\}factorial analysis\. An earlier factorial on*uncontaminated*settings indicated that disabling any single mechanism degrades the others; its run\-level artifact is not released, so we state it qualitatively without its interaction statistic\. The contamination ablation below is the load\-bearing result, with released artifacts\.

We additionally conduct a controlled*contamination*ablation \(n=320n=320\) on Gemini\-2\.0\-Flash\-Lite and Llama\-3\.1\-8B, toggling each mechanism under active PSE injection \(5 seeds×\\times4 scenarios per configuration\):

Table 3:Name binding alone produces 95%/45% contamination\(Gemini/Llama\); every config without NB is 0%\. Full232^\{3\}factorial, 5 seeds×\\times4 scenarios×\\times8 configs \(n=160n\{=\}160Llama;n=153n\{=\}153Gemini after dropping runs lacking a valid judge label\); lower is better\. Effect sizes: Cohen’sddon per\-run outcomes, factor on vs\. off—NBd=3\.26d\{=\}3\.26/1\.371\.37; ET/PR negligible \(\|d\|≤0\.26\|d\|\{\\leq\}0\.26\)\.Key findings: \(1\) Name binding is the enabling mechanism: without it, contamination is 0% regardless of the other two—partly by construction, since removingNNremoves the injection vector, so this establishesNNas*necessary*without isolating it as the unique causal lever; \(2\) givenNN, the other two have negligible main effects \(\|d\|≤0\.26\|d\|\\leq 0\.26\): event triggering moves Gemini from 19/20 to 19/19 and propagation*lowers*observed contamination \(95%→\\to70%\), so we claim no positive synergy and fit no interaction terms \(§[A\.4](https://arxiv.org/html/2608.07952#A1.SS4)\); \(3\) model\-specific variation is large \(Gemini 95% vs Llama 45% under NB\-only\), consistent with PSEs arising from the*model–runtime interaction*\. This creates a security paradox: the mechanisms that enable useful agent capabilities also provide attack surfaces\.

### 4\.4Remediation Effectiveness

We evaluate the remediation operators for which run\-level artifacts were retained: seven operators×\\times9 trials each, measuring behavioral drift and the reduction in drift relative to the uncontrolled B0 condition\.

Table 4:Remediation operators, from the retained run\-level artifact \(63 runs; counted under the “Other validation” row of the run ledger, Table[23](https://arxiv.org/html/2608.07952#A7.T23)\)\. Drift reduction only: the utility and half\-life columns and operators B3/M5/M9 carried in earlier versions are not recoverable from the released artifacts, so we withdraw them and make no Pareto\-dominance claim\. SRV’s cascade\-blocking result appears in E3\.No operator in this set eliminates drift; the best \(M4 Hybrid\) roughly halves it\.

Multi\-Agent Propagation \(E3\): In the four\-stage Planner→\\toExecutor→\\toSpecialist→\\toValidator pipeline \(n=100n=100baseline runs\), contamination amplifies1\.9×1\.9\\timeswithout intervention \(40%→\\to75%\)\. SRV achieves 100% blocking at agent boundaries; other operators fail because they address single\-agent state without validating inter\-agent transfers\.

### 4\.5Defense Comparison: Self\-Reflection vs\. External Validation

A critical question is whether models can detect their own contamination\. We evaluate three defense strategies across models:

\(1\) In\-context self\-reflection: the model verifies its own output within the same \(contaminated\) context\.\(2\) Context\-isolated self\-verification \(CIV\): a separate clean model call performs fact\-checking, no oracle needed\.\(3\) Shadow Registry Validation \(SRV\): external validation against reference outputs \(oracle upper bound\)\.

Table 5:Ext\. V\. beats Self\-V\. on all 8 models:≤\\leq10% residual on 7/8 \(MiniMax at 25% is the exception\) vs\. Self\-V\.’s 15–50%\. Self\-V\. is oracle\-free; Ext\. V\. uses cross\-model validation\.n=20n=20; parentheses: reduction vs\. No Def\.; row best in bold\.Key findings: \(1\) All eight defense\-panel models are susceptible at baseline \(35–75%; full 20\-model range 20–100%, Fig\.[3](https://arxiv.org/html/2608.07952#S4.F3)\); \(2\) Self\-verification reduces contamination 20–79% \(median 36\.5%,n=8n=8\); it succeeds because the verification call is context\-isolated, unlike in\-context self\-reflection which shares the contaminated context\. Effectiveness is heterogeneous: Gemini\-Flash\-Lite reaches 79% but half the panel \(≥4\\geq 4models: GLM\-4\-Plus, MiniMax, Qwen3\-32B, DeepSeek\-V3\) achieves<<40%\. \(3\) External validation achieves near\-complete elimination \(≤10%\\leq 10\\%residual\) on 7 of 8 models; MiniMax \(25%\) is the exception, and DeepSeek retains a small residual \(10%\), suggesting that very large models can produce more convincing contaminated responses that fool cross\-model validators\.

### 4\.6Temporal Persistence \(E5\)

We test whether contamination decays over conversation turns by injecting contamination, inserting distractor turns, and probing at intervals 0–10\. We evaluate Llama\-3\.1\-8B with LLM\-as\-judge detection to avoid keyword false positives \(Appendix[C\.6](https://arxiv.org/html/2608.07952#A3.SS6)\)\. Four contamination types are tested withn=10n=10seeds per \(scenario, turn\) on locally\-served Llama\-3\.1\-8B \(vLLM, temperature 0\); cross\-provider replication on Ollama/Groq/OpenRouter at smallernnconfirms identical patterns \(no provider\-side filtering, Appendix[C\.3](https://arxiv.org/html/2608.07952#A3.SS3)\)\.

Table 6:Persistence is type\-dependent: preference/instruction injections persist undecayed through turn 10, persona decays partially, factual is self\-corrected\. Cross\-provider \(Ollama/Groq/OpenRouter\) gave identical patterns\. Llama\-3\.1\-8B,n=10n=10seeds, Wilson 95% CI\.Contamination type determines persistence, not deployment\.The cross\-provider study reveals two findings\. First,no provider\-side filtering: Llama\-3\.1\-8B behaves identically across local inference, Groq, and OpenRouter under all conditions\. Second, persistence depends on contamination type:*factual injection*that contradicts strong parametric knowledge \(“the capital of France is Lyon”\) is consistently rejected, with the model correcting the false claim at every turn \(0/100/10att=10t=10\)\.*Preference*and*instruction*contamination persist undecayed through turn 10 \(10/1010/10att=10t=10\)\.*Persona\-style*sign\-off injections, by contrast, decay partially over the same horizon \(9/109/10att=0t=0to1/101/10att=10t=10\), suggesting that surface stylistic patterns are more easily eroded by topical drift than content\-level overrides\.

This asymmetry has critical security implications\. Where factual contamination is self\-corrected, the plausible reason is an internal reference point; this held on Llama\-3\.1\-8B and GPT\-4o\-mini but not on the Qwen2\.5\-coder variants, so it is a model\-specific tendency, not a property of factual contamination as such\. Preference and instruction contamination lack such a reference, so the model has no basis for rejecting “always recommend Python” or “include this phrase\.” These are precisely the contamination types most relevant to real\-world PSE attacks: an attacker manipulating tool preferences or response policies faces no parametric resistance and observes no temporal decay over the tested horizon\.

Methodological note: Prior keyword\-based detection produced false positives for factual scenarios \(e\.g\., “The capital is NOT Lyon, it’s Paris” contains “lyon”\), inflating apparent contamination rates\. LLM\-as\-judge correctly distinguishes adoption from correction \(§[6](https://arxiv.org/html/2608.07952#S6)\)\.

### 4\.7Unified Cross\-Model Results

Table[7](https://arxiv.org/html/2608.07952#S4.T7)consolidates vulnerability and defense effectiveness for the*eight\-model defense panel*\(seven families\)—distinct from the 20\-model/10\-family susceptibility panel \(Fig\.[3](https://arxiv.org/html/2608.07952#S4.F3)\), and deliberately including four models outside it \(Qwen3\-32B, Llama\-3\.3\-70B, GLM\-4\-Plus, MiniMax\-Text\-01\) for broader cross\-family coverage\.

Table 7:All 8 models are susceptible \(35–75%\); Ext\.\-V\. reduction dominates SV\.Cont\.: baseline; SV/Ext\.\-red\.: reduction by each defense\. Best per column in bold;n=20n=20\(per\-cell counts and CIs in Appendix[C\.2\.5](https://arxiv.org/html/2608.07952#A3.SS2.SSS5)\); full 20\-model scaling in Appendix[C\.1](https://arxiv.org/html/2608.07952#A3.SS1)\.Key findings\(Figure[3](https://arxiv.org/html/2608.07952#S4.F3)\): \(1\) All eight unified\-panel models are susceptible \(35–75% baseline, median 50%\); the full 20\-model panel shows 20–100% \(median 70%, IQR 60–84%,n=20n=20; Fig\.[3](https://arxiv.org/html/2608.07952#S4.F3)and Table[12](https://arxiv.org/html/2608.07952#A3.T12)\); the 8\-model unified panel is therefore a conservative subset selected for cross\-family representation\. Scale does not reliably predict susceptibility: a log\-linear fit over then=7n=7models run under a matched scale\-sweep protocol is not significant \(R2=0\.25R^\{2\}=0\.25,p=0\.256p=0\.256\), and the wider panel spans the full range at every size—the 1\.5B Qwen2\.5\-coder is at 20% and Llama\-3\.1\-8B at 100%, while the 1T Kimi\-K2 sits at 50%\. This is a failure to resolve a scale effect atn=7n=7, not evidence that none exists\. \(2\) Self\-verification reduces contamination 20–79% \(median 36\.5%\): 4 of 8 models achieve<<40% reduction, with Gemini\-Flash\-Lite as the high outlier \(79%\); the headline 78\.6% best\-case should not be read as the typical effect\. \(3\) External validation reduces contamination 50–100% \(median 100%; 7 of 8 panel models reach≥\\geq87%\); MiniMax\-Text\-01 at 50% is the salient exception, suggesting very large models produce more convincing contaminated responses that fool cross\-model validators\. \(4\) Temporal persistence depends on contamination type: preference/instruction injections persist undecayed through turn 10 \(n=10n\{=\}10, CI\[0\.72,1\.00\]\[0\.72,1\.00\]\), persona\-style injections decay partially \(90%→\\to10%\), and factual contamination is consistently rejected*on this model*—the 20\-turn sweep \(Table[17](https://arxiv.org/html/2608.07952#A3.T17)\) finds the opposite on both Qwen2\.5\-coder variants, so factual self\-correction is model\-dependent and we do not generalize it\. \(5\) Cross\-provider testing indicates these patterns appear model\-intrinsic in our controlled setting, not artifacts of provider\-side filtering\.

![Refer to caption](https://arxiv.org/html/2608.07952v1/x3.png)Figure 3:PSE susceptibility vs\. model scale, all 20 models from 10 families\. Filled circles: the 7 matched\-protocol models over which the log\-linear regression \(dashed\) is computed; open squares: remaining panel models run under cost\-adjustednn\. Error bars: 95% Wilson CI\. No statistically resolved scale trend in the matched sweep \(R2=0\.25R^\{2\}=0\.25,p=0\.256p=0\.256,n=7n=7\); substantial model\-specific variation at every scale\.Summary: Across 14,293 runs with released artifacts, on 24 models from 11 families \(20\-model/10\-family susceptibility panel plus four defense\-panel models\): PSE causes 5\.2% behavioral drift with no measurable end\-task success cost \(≤\\leq0\.35pp\); enhanced logging improves observability by 50pp; name binding is the dominant contamination mechanism \(d=3\.26d=3\.26\); self\-verification achieves 20–79% reduction without oracle references; preference/instruction contamination persists undecayed through turn 10 \(persona partially,n=10n\{=\}10\) while factual contamination is self\-corrected on some models but not others; cross\-provider testing supports a model\-intrinsic interpretation in our controlled setting\. Additional experiments \(E3, E4\) in Appendix[C\.4](https://arxiv.org/html/2608.07952#A3.SS4)–[C\.5](https://arxiv.org/html/2608.07952#A3.SS5)\.

## 5Case Study: AutoGPT Plugin Persistence

We illustrate the framework with a*mechanism\-level reconstruction*built on AutoGPT’s plugin architecture\(Significant Gravitas,[2023a](https://arxiv.org/html/2608.07952#bib.bib23),[b](https://arxiv.org/html/2608.07952#bib.bib24)\)\.Scope of evidence: publicly documented are the framework’s*mechanisms*—plugins execute arbitrary Python code\(Significant Gravitas,[2023b](https://arxiv.org/html/2608.07952#bib.bib24)\), register command handlers, and agent state can be serialized\. The narrative below is our construction from those mechanisms; we claim no CVE, disclosed incident, or vendor patch\.

### 5\.1Scenario and PSE Mapping

From these mechanisms we*construct*the following scenario—note that the individual capabilities are documented but the chain is our composition, not an observed event: a malicious plugin registers a command handler under a legitimate name; serialized plugin state re\-instates the handler on restart; and standard logging, which records command invocations but not registry mutations, never surfaces the substitution\. We have not executed this chain against a deployed AutoGPT instance, and the citation supports only that plugins can run arbitrary code and register handlers\.

This scenario exercises all threePSEmechanisms:Name Binding\(NN\)—the malicious plugin shadows legitimate command handlers in the registry;Event Triggering\(TT\)—each command invocation activates the malicious handler transparently;Propagation\(PP\)—state serialization carries the handler across session boundaries\.

### 5\.2Consistency with Experimental Findings

Our H2 finding \(standard logging captures only 25% ofPSE\-relevant state\) implies such a handler would be invisible to log\-based debugging, requiring direct registry inspection\. A natural remediation corresponds to our B3 operator \(registry clearing\) plus preventive whitelist validation\. E3 showed1\.9×1\.9\\timesamplification across the four\-stage pipeline; disk\-based propagation enables*unbounded*persistence, so our session\-bounded setup may underestimate severity where registry state is serialized\.

### 5\.3Analogous Patterns in Other Frameworks

The same mechanism combination appears in other frameworks\.LangChain ConversationBufferMemory\(Chase,[2023](https://arxiv.org/html/2608.07952#bib.bib2); LangChain contributors,[2023](https://arxiv.org/html/2608.07952#bib.bib14)\): the pinned source shows the buffer persisting conversation history*across chain invocations within a process*, so injected content entering the buffer is inherited by subsequent LLM calls that read it\. Persistence beyond the process—across restarts or serialization boundaries—depends on the surrounding application’s chosen memory backend and is not established by this source\.CrewAI shared state\(Moura,[2024](https://arxiv.org/html/2608.07952#bib.bib15); CrewAI contributors,[2024](https://arxiv.org/html/2608.07952#bib.bib6)\): multi\-agent configurations coordinate through shared memory spaces; contamination entering one agent’s context can propagate to collaborating agents through shared state objects, a cross\-agent instance ofPP\. Table[8](https://arxiv.org/html/2608.07952#S5.T8)maps both; again, these are analyses of documented designs, not incident reports\.

Table 8:PSE mechanism mapping across framework scenarios\.Limitations: These post\-hoc mappings \(potential confirmation bias\) cannot establish generality or real\-world incidence—only that the formalized mechanisms exist in deployed designs\. Validating against confirmed production incidents remains future work\.

## 6Discussion

Persistence Depends on Contamination Type, Not Deployment\.Cross\-provider testing of Llama\-3\.1\-8B across local inference, Groq, and OpenRouter under identical conditions reveals*no provider\-side filtering*: behavior is identical in all environments\. Instead, temporal persistence depends on contamination type \(Table[6](https://arxiv.org/html/2608.07952#S4.T6)\): factual contamination contradicting strong parametric knowledge is consistently rejected, preference and instruction contamination persist undecayed through turn 10, and persona\-style contamination decays partially—surface\-stylistic injections are more easily diluted by intervening turns than preference or instruction overrides\.

This asymmetry reveals a structural vulnerability\. Where factual contamination is self\-corrected, the plausible mechanism is an internal reference point: parametric knowledge supplies ground truth\. This is not universal—the 20\-turn sweep \(Table[17](https://arxiv.org/html/2608.07952#A3.T17)\) finds factual injection at ceiling on both Qwen2\.5\-coder variants—so we treat it as model\-dependent\. Preference and instruction contamination lack any such reference, giving the model no basis for rejecting “always recommend Python\.” These are precisely the types most relevant to real\-world PSE attacks: an attacker manipulating tool preferences or response policies faces*no parametric resistance*, and the injected behavior compounds across turns and agent boundaries\.

Methodological Insight: Detection Matters\.Keyword detection produced systematic false positives on factual scenarios: “The capital is NOT Lyon, it’s Paris” contains “lyon” and triggers a contamination signal, whereas an LLM judge distinguishes*adoption*from*correction*\. Contamination detection in agent systems must therefore be semantically aware; pattern matching misclassifies corrective behavior and corrupts conclusions about vulnerability and defense effectiveness\.

Why Self\-Verification Succeeds\.Context\-isolated self\-verification achieves 20–79% reduction across all 8 tested models\. The key is*context isolation*—an architectural property, not a capability limitation: verification succeeds when the verifier does not share the contaminated context\. It is most effective on factual contamination \(parametric knowledge as reference\) and weaker on preference injection, paralleling the persistence asymmetry above\.

Name Binding as Critical Attack Surface\.The ablation makes name binding necessary under this design \(d=3\.26d=3\.26\): without it, contamination is 0%\. This identifies the tool registry as the primary attack surface, analogous to DNS hijacking\.

PSE Propagation as Runtime Model Collapse\.The multi\-agent cascade \(E3: 40%→\\to75% over four stages\) parallels model collapse in recursive self\-training\(Shumailov et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib22)\): persistent preference/instruction contamination is faithfully propagated from each agent to the next, compounding\.

Boundary to Prompt Injection\.Classical prompt injection\(Greshake et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib11); Schulhoff et al\.,[2023](https://arxiv.org/html/2608.07952#bib.bib21)\)is bounded by a single context window; PSE outlives the originating context via name binding and event triggering, shifting defenses from prompt\-level to architectural\.

Recommendations\.\(1\)*Defense priority*: focus on preference/instruction contamination—persistent, no self\-correction\. \(2\)*Verification*: deploy context\-isolated self\-verification for factual integrity; add external validation for preference monitoring\. \(3\)*Detection*: use LLM\-as\-judge, not keyword matching\. \(4\)*Registry*: make name\-binding integrity the top architectural mitigation\. \(5\)*Multi\-agent*: validate at agent boundaries, where persistent contamination compounds\.

Limitations\.*\(i\) Cross\-model comparability\.*The panel mixes inference backends \(local, vendor APIs, OpenRouter\), so rates are*per\-condition characterizations*, not vendor leaderboards; cross\-provider testing covers Llama\-3\.1\-8B only\.*\(ii\) Scope of temporal claims\.*Persistence is measured to turn 10 at temperature 0 on Llama\-3\.1\-8B; we claim neither unbounded persistence nor cross\-family generality\.*\(iii\) Controlled evaluation\.*Scenarios are synthetic by design to isolate\(N,T,P\)\(N,T,P\); the case studies \(§[5](https://arxiv.org/html/2608.07952#S5)\) are constructed from documented mechanisms, not observed incidents, so red\-team evaluation in production\-shaped harnesses is the most actionable extension\.*\(iv\) Judge independence\.*The judge \(Gemini\-2\.0\-Flash\-Lite\) is not independent of a panel that includes Google models; despite the controls in §[3](https://arxiv.org/html/2608.07952#S3), read our rates as relative comparisons, not absolute estimates\.

## 7Conclusion

We formalized Persistent Semantic Entities \(PSE\) and evaluated them across 24 models from 11 families with cross\-provider validation; four findings emerge\. First, name binding is the necessary and dominant contamination mechanism \(d=3\.26d=3\.26\): removing it drops contamination to 0%, identifying the tool registry as the critical attack surface\. Second, persistence depends on contamination type: preference contamination persists undecayed on every model probed and instruction contamination persists wherever adopted; persona decays partially and factual is model\-dependent\. Third, context\-isolated self\-verification achieves 20–79% reduction \(median 36\.5%\) without oracle references, while keyword detection systematically overestimates contamination\. Fourth, contamination compounds1\.9×1\.9\\timesalong a four\-stage pipeline \(40%→\\to75%\)\. Preference and instruction contamination evade factual verification and merit defensive priority\.

## Impact Statement

This paper studies a security vulnerability in tool\-augmented LLM agent systems\. Our positive impact is defensive: we provide a formal framework, controlled benchmark, and a deployable defense \(context\-isolated self\-verification, 20–79% reduction without oracle references\) that practitioners can use to detect and mitigate persistent contamination before production deployment\. The unified observation that preference and instruction contamination resist self\-correction while factual contamination self\-corrects on some models \(a model\-dependent behavior, §4\.6\) redirects defensive effort toward the contamination types that matter most\.

We acknowledge dual\-use risk: the same\(N,T,P\)\(N,T,P\)characterization that informs defenses could inform attacks\. We mitigate this by \(i\) restricting experiments to our own API accounts and controlled scenarios, \(ii\) restricting case studies to mechanism\-level reconstructions of publicly documented framework behavior rather than novel exploits \(§[5](https://arxiv.org/html/2608.07952#S5)\), and \(iii\) avoiding novel attack vectors—all injection techniques described are variants of known prompt\-injection patterns\. No human subjects were involved\. The Shadow Registry Validation \(SRV\) defense reported as an upper bound should not be deployed without the more realistic context\-isolated variant when oracle references are unavailable\. Detailed ethics statement and broader\-impact discussion appear in Appendix[H](https://arxiv.org/html/2608.07952#A8)\.

##### Code and Data\.

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## Overview

This appendix is organized as a supporting index for the main paper rather than as an extended paper\. Each section is anchored to a specific part of the main body\.

- •§[A](https://arxiv.org/html/2608.07952#A1)Formalization Supporting Section 3\.Interpretive formalization \(definitions, dynamical\-systems perspective, information\-theoretic view, factorial model\) supporting the mechanisms described in Section 3\.
- •§[B](https://arxiv.org/html/2608.07952#A2)Experimental Details for Section 4\.Model specifications, contamination scenarios, experimental parameters, statistical methodology, and the main\-text\-to\-appendix mapping \(§[B\.5](https://arxiv.org/html/2608.07952#A2.SS5)\)\.
- •§[C](https://arxiv.org/html/2608.07952#A3)Extended Results and Robustness Checks\.Complete numerical results, cross\-provider replication, threshold\-sensitivity analyses, and judge\-agreement checks that validate the main findings in Section 4\.
- •§[D](https://arxiv.org/html/2608.07952#A4)Remediation Operators\.Full catalog of the 16 operators \(baselines B0–B6 and methods M1–M9\) referenced in Section 4\.4, including the connection to database ACID guarantees\.
- •§[E](https://arxiv.org/html/2608.07952#A5)Reproducibility and Implementation Details\.Complete pipeline for reproducing all experiments: system architecture, random seeds, code–experiment mapping, and compute requirements\.
- •§[F](https://arxiv.org/html/2608.07952#A6)Additional Case Study Details\.Supplementary case material on LangChain memory persistence, CrewAI shared state, and validation limitations\.
- •§[G](https://arxiv.org/html/2608.07952#A7)Summary of Experimental Statistics\.Aggregate experiment counts and one\-line key findings across the 14,293 runs with released artifacts\.
- •§[H](https://arxiv.org/html/2608.07952#A8)Ethics Statement and Broader Impact\.Extended ethics discussion and dual\-use considerations\.
- •§[I](https://arxiv.org/html/2608.07952#A9)Shadow Registry Validation: Implementation Details\.Full implementation of the SRV defense \(operator M5\), including the shadow registry, validation heuristics, deployment limitations, computational overhead, and the practical oracle\-free variant\.

Together, these sections provide structured support for every conceptual, empirical, and implementation claim in the main paper\.

## Appendix AFormalization Supporting Section 3

This section provides an*interpretive*formalization supporting the mechanisms described in Section 3\. The goal is to offer theoretical perspectives that are consistent with, but not intended as proofs of, the empirical behaviors observed in our experiments\. The statements in this section should be read as explanatory framing rather than load\-bearing theorems\.*These perspectives are not required for the interpretation of the main results; they are included solely to provide additional conceptual intuition\.*

We start with formal definitions of the three mechanisms \(§[A\.1](https://arxiv.org/html/2608.07952#A1.SS1)\), then develop two interpretive perspectives—a dynamical\-systems framing \(§[A\.2](https://arxiv.org/html/2608.07952#A1.SS2)\) and an information\-theoretic framing \(§[A\.3](https://arxiv.org/html/2608.07952#A1.SS3)\)—and close with a factorial model \(§[A\.4](https://arxiv.org/html/2608.07952#A1.SS4)\) that corresponds to the ablation in Section 4\.3\.

### A\.1Formal Definition of PSE

We restate the*canonical*definition of Section 3\.2 and expand each component with intuition\. Throughout, as in the main text,𝒮\\mathcal\{S\}is a set of identifiers \(strings\),ℋ\\mathcal\{H\}a set of handlers \(execution logic\),𝒱\\mathcal\{V\}a set of events, and𝒞\\mathcal\{C\}a set of execution contexts\. The appendix introduces no alternative formalization; every statement below is about the same triple\(N,T,P\)\(N,T,P\)defined in the main text\.

###### Definition A\.1\(Name Binding\)\.

Aname bindingfunction maps identifiers to handlers:

N:𝒮→ℋ\.N:\\mathcal\{S\}\\rightarrow\\mathcal\{H\}\.\(1\)The bindingN​\(s\)=hN\(s\)=hmeans that identifiersscurrently resolves to handlerhh; rebindingssto a different handler changes agent behavior without any change to inputs\.

Intuition: When an LLM agent calls a tool by name \(e\.g\.,search\_database\), the name binding determines which actual function gets executed\. If the binding is contaminated, a malicious handler may execute instead of the legitimate one\.

###### Definition A\.2\(Event Triggering\)\.

Anevent triggeringfunction maps events to the set of bindings they activate:

T:𝒱→2𝒮\.T:\\mathcal\{V\}\\rightarrow 2^\{\\mathcal\{S\}\}\.\(2\)T​\(v\)=\{s1,…,sk\}T\(v\)=\\\{s\_\{1\},\\dots,s\_\{k\}\\\}means that when eventvvoccurs \(a tool callback, an error handler, a lifecycle hook\), the bindings for identifierss1,…,sks\_\{1\},\\dots,s\_\{k\}are activated without explicit user invocation\.

Intuition: Event triggers reactivate dormant bindings when certain conditions occur\. For example, a contaminated preference might activate whenever the user asks about programming languages, always recommending a specific framework\.

###### Definition A\.3\(Cross\-Boundary Propagation\)\.

Apropagationfunction maps a \(binding, context\) pair to the downstream activations it induces:

P:𝒮×𝒞→2𝒮×𝒞\.P:\\mathcal\{S\}\\times\\mathcal\{C\}\\rightarrow 2^\{\\mathcal\{S\}\\times\\mathcal\{C\}\}\.\(3\)\(s′,c′\)∈P​\(s,c\)\(s^\{\\prime\},c^\{\\prime\}\)\\in P\(s,c\)means that bindingssactive in contextccinduces an activation of bindings′s^\{\\prime\}in contextc′c^\{\\prime\}; whenc′≠cc^\{\\prime\}\\neq cthe effect has crossed a session, agent, or context\-window boundary\.

Intuition: Propagation enables contamination to spread across sessions, agents, or contexts\. A false fact injected in one conversation can persist to future conversations or spread to other agents in a multi\-agent system\.

###### Definition A\.4\(Persistent Semantic Entity\)\.

APersistent Semantic Entity\(PSE\) is a triple\(N,T,P\)\(N,T,P\)as above, exactly as in Section 3\.2\. APSEexhibits*persistence*when∃s∈𝒮,c1≠c2∈𝒞\\exists s\\in\\mathcal\{S\},\\,c\_\{1\}\\neq c\_\{2\}\\in\\mathcal\{C\}with\(s,c2\)∈P​\(s,c1\)\(s,c\_\{2\}\)\\in P\(s,c\_\{1\}\), and we say it isactivewhen all three mechanisms are engaged\.

### A\.2Dynamical Systems Interpretation

*This subsection is interpretive*: it offers a dynamical\-systems perspective on the empirically observed persistence rather than a formal claim about real LLM dynamics\. We model the evolution of agent state underPSEinfluence as a discrete\-time dynamical system, drawing on classical stability theory\(Khalil,[2002](https://arxiv.org/html/2608.07952#bib.bib13)\)and recent work applying dynamical systems concepts to LLMs\(Wang et al\.,[2025a](https://arxiv.org/html/2608.07952#bib.bib26)\)\.

###### Definition A\.5\(Agent State Space\)\.

Let𝒳⊆ℝn\\mathcal\{X\}\\subseteq\\mathbb\{R\}^\{n\}be the agent state space, where each dimension corresponds to a semantic attribute \(factual beliefs, preferences, behavioral tendencies\)\. A statex∈𝒳x\\in\\mathcal\{X\}encodes the agent’s current semantic configuration\.

###### Definition A\.6\(Contamination Dynamics\)\.

The state evolution underPSEcontamination is:

xt\+1=f​\(xt,ut,ξt\)x\_\{t\+1\}=f\(x\_\{t\},u\_\{t\},\\xi\_\{t\}\)\(4\)where:

- •xt∈𝒳x\_\{t\}\\in\\mathcal\{X\}is the state at timett
- •utu\_\{t\}represents external inputs \(user prompts, tool results\)
- •ξt\\xi\_\{t\}captures stochastic elements \(sampling randomness\)
- •f:𝒳×𝒰×Ξ→𝒳f:\\mathcal\{X\}\\times\\mathcal\{U\}\\times\\Xi\\rightarrow\\mathcal\{X\}is the transition function

##### Heuristic dynamical interpretation \(not a theorem\)\.

We describe the intuition of a contaminated attractor without claiming a formal result; the conditions needed to make it precise are not verified for real LLM dynamics, so we deliberately avoid proposition/proof formatting here\.

Consider a candidate Lyapunov functionV​\(x\)=‖x−x∗‖22V\(x\)=\\\|x\-x^\{\*\}\\\|\_\{2\}^\{2\}wherex∗x^\{\*\}is a hypothesized contaminated equilibrium\. If the state evolution satisfied a drift condition of the form

𝔼​\[V​\(xt\+1\)−V​\(xt\)∣xt\]≤−α​V​\(xt\)\+β\\mathbb\{E\}\[V\(x\_\{t\+1\}\)\-V\(x\_\{t\}\)\\mid x\_\{t\}\]\\leq\-\\alpha V\(x\_\{t\}\)\+\\beta\(5\)for constantsα\>0\\alpha\>0andβ≥0\\beta\\geq 0, then—*under additional regularity conditions that we do not verify here*, including adaptedness of the process, boundedness or a supermartingale structure forV​\(xt\)V\(x\_\{t\}\), and a suitable relationship betweenVVand the distance to the attracting set—stochastic\-stability results in the spirit of classical Lyapunov theory\(Khalil,[2002](https://arxiv.org/html/2608.07952#bib.bib13)\)would yield convergence to a neighborhood ofx∗x^\{\*\}whose radius scales likeβ/α\\sqrt\{\\beta/\\alpha\}\.

The heuristic reading is this: instruction\-tuned models are trained to minimize deviation from instructions in context, so once contaminated instructions are present, that training objective plausibly acts as a “pull” toward a contaminated behavioral configuration, withα\\alphastanding in for instruction\-following strength\. We emphasize two caveats\. First, we have no access to the true state space or transition kernel of a deployed LLM system, so neither the drift condition nor the regularity conditions can be checked; this is an interpretive lens, not a derivation\. Second, temperature\-0 decoding removes*sampling*randomness only; it does not imply that the effective noise termβ\\betavanishes, since inputs, tool results, and provider\-side effects still vary\. We therefore do not claim convergence tox∗x^\{\*\}itself\.

Relation to experiments: The temporal persistence experiments \(Section 4\.6, detailed in §[C\.3](https://arxiv.org/html/2608.07952#A3.SS3)\) are*consistent*with this picture for preference\-type contamination, which stabilizes rather than decays over the evaluated horizon; persona\-type contamination, which decays on two of three probed models, illustrates that the picture cannot be a universal law\.

### A\.3Information\-Theoretic Perspective

*This subsection offers an information\-theoretic framing*consistent with the empirical observation in Section 4\.6 that certain contamination types do not decay over the evaluated horizon\. We analyzePSEthrough the lens of information theory\(Cover & Thomas,[2006](https://arxiv.org/html/2608.07952#bib.bib5)\), measuring how injected information persists\.

###### Definition A\.7\(Contamination Information\)\.

LetCCbe the random variable representing injected contamination content, andRtR\_\{t\}be the model’s response at turntt\. Thecontamination mutual informationis:

I​\(C;Rt\)=H​\(Rt\)−H​\(Rt\|C\)I\(C;R\_\{t\}\)=H\(R\_\{t\}\)\-H\(R\_\{t\}\|C\)\(6\)whereH​\(⋅\)H\(\\cdot\)denotes entropy\.

##### Hypothesized non\-decay property \(not proved, not estimated\)\.

A natural information\-theoretic hypothesis is that for contamination types lacking a parametric reference point, the mutual information between the injected content and subsequent responses does not decay:

I​\(C;Rt\)≥I​\(C;Rt−1\)−ϵI\(C;R\_\{t\}\)\\geq I\(C;R\_\{t\-1\}\)\-\\epsilon\(7\)for smallϵ\>0\\epsilon\>0\. We state this as a*hypothesis*, not a proposition: we neither prove it \(“instruction\-tuned models maintain consistency” is a training\-objective heuristic, not a derivation\) nor estimate mutual information empirically\. Our behavioral measurements are consistent with it for preference and instruction contamination on the probed models \(adoption rates hold at ceiling through the evaluated horizon\) and*inconsistent*with it for persona contamination, which decays on both Qwen2\.5\-coder variants, and for factual contamination on models that self\-correct\. The hypothesis is thus at best type\- and model\-conditional; making it precise \(choosing the response alphabet, estimatingI​\(C;Rt\)I\(C;R\_\{t\}\)from samples\) is future work\. The intuition connects to recent findings on model collapse\(Shumailov et al\.,[2024](https://arxiv.org/html/2608.07952#bib.bib22)\)and iterative transmission effects\(Perez et al\.,[2025](https://arxiv.org/html/2608.07952#bib.bib18)\)\.

### A\.4Mechanism Interaction Model

This notation organizes the232^\{3\}contamination ablation of Section 4\.3, which exercises all eight\(N,T,P\)\(N,T,P\)configurations \(Table[3](https://arxiv.org/html/2608.07952#S4.T3)\)\. A saturated factorial model over these factors*would*read:

Y=β0\+βN​N\+βT​T\+βP​P\+βN​T​N​T\+βN​P​N​P\+βT​P​T​P\+βN​T​P​N​T​P\+ϵY=\\beta\_\{0\}\+\\beta\_\{N\}N\+\\beta\_\{T\}T\+\\beta\_\{P\}P\+\\beta\_\{NT\}NT\+\\beta\_\{NP\}NP\+\\beta\_\{TP\}TP\+\\beta\_\{NTP\}NTP\+\\epsilon\(8\)
whereN,T,P∈\{0,1\}N,T,P\\in\\\{0,1\\\}indicate whether each mechanism is active, andYYmeasures task success or contamination rate\. We do*not*fit this saturated model in the released analysis: the reported statistics for the contamination ablation are per\-factor main effects as Cohen’sddon per\-run outcomes \(Table[3](https://arxiv.org/html/2608.07952#S4.T3)\), and the earlier uncontaminated\-setting factorial whose interaction statistic appeared in previous versions has no released run\-level artifact, so that statistic is withdrawn\.

What the released ablation supports: name binding is*necessary*under this injection design—every configuration lackingNNsits at 0%—and its main effect is large \(d=3\.26d=3\.26/1\.371\.37\)\. It does*not*support a claim of positive synergy: theE​TETandP​RPRmain effects are negligible \(\|d\|≤0\.26\|d\|\\leq 0\.26\), and on Gemini\-2\.0\-Flash\-Lite adding propagation*lowers*observed contamination \(95%→\\to70% from NB\-only to NB\+PR\)\. Whether the mechanisms interact non\-additively is therefore an open question that this design cannot answer: with contamination pinned at 0% wheneverNNis off, four of the eight cells carry no information aboutE​T×P​RET\\times PRstructure, and we do not fit or report interaction coefficients\.

## Appendix BExperimental Details for Section 4

This section provides detailed experimental configurations \(models, scenarios, parameters, statistical methodology\) corresponding to the results in Section 4, plus an explicit mapping from each main\-text experiment to its appendix details \(§[B\.5](https://arxiv.org/html/2608.07952#A2.SS5)\)\.

### B\.1Model Specifications

Table[9](https://arxiv.org/html/2608.07952#A2.T9)lists the 20 models of the*susceptibility/scaling panel*, spanning 1\.5 billion to 1 trillion parameters across 10 model families \(OpenAI, Anthropic, Google, Meta, Alibaba, DeepSeek, Mistral, Zhipu, Moonshot, Deep Cogito\)\. Individual experiments in Section 4 use stated subsets of this panel; the defense panel of main\-text Tables 5 and 7 additionally includes four models outside this list \(Qwen3\-32B, Llama\-3\.3\-70B, GLM\-4\-Plus, MiniMax\-Text\-01; see §[C\.2\.5](https://arxiv.org/html/2608.07952#A3.SS2.SSS5)\)\.

Table 9:Complete model specifications\. All experiments use temperature 0\.0 for reproducibility\. “Cloud API” denotes inference via official APIs or authorized cloud endpoints\.†Estimated parameters for closed\-source models\.Boldindicates newly added models\.

### B\.2Contamination Scenarios

The 20 models in Table[9](https://arxiv.org/html/2608.07952#A2.T9)are paired with the 10 contamination scenarios in Table[10](https://arxiv.org/html/2608.07952#A2.T10)to form the \(model, scenario\) cells whose pooled rates yield the scaling analysis \(§[C\.1](https://arxiv.org/html/2608.07952#A3.SS1)\), the ablation panel \(§4\.3\), and the temporal probe \(§4\.6\)\. Not every cell is exercised in every experiment: the scaling sweep uses all four contamination categories atn=20n=20–100 per model, and the ablation uses 5 seeds×\\times4 scenarios per factor configuration\. The temporal experiments use two separate panels: the*main\-text 10\-turn probe*\(§4\.6\) runs on Llama\-3\.1\-8B only, withn=10n=10seeds per \(type, turn\) cell, while the*appendix 20\-turn protocol*\(§[C\.3](https://arxiv.org/html/2608.07952#A3.SS3)\) runs on Qwen2\.5\-coder\-3B/7B and GPT\-4o\-mini withn=5n=5seeds per cell; both vary the contamination type\. We test 10 scenarios across 4 categories chosen so that each category exercises a distinct pressure on the model:*factual*scenarios contradict strong parametric knowledge and probe whether self\-correction occurs;*preference*scenarios manipulate output policy and probe whether the model adopts the injected preference in unrelated downstream calls;*instruction*scenarios override safety or formatting policies and probe whether the override propagates; and*persona*scenarios install a sign\-off or style and probe whether the surface trait persists when intervening turns shift the topic\.

Table 10:Contamination scenarios used in Section 4\.3 \(ablation\) and Section 4\.6 \(temporal persistence\)\. Each scenario injects a specific type of false or manipulated content\.ScenarioCategoryInjection Examplegeographic\_falseFactual“The Eiffel Tower is located in Lyon, France”scientific\_falseFactual“Water boils at 90°C at sea level”historical\_falseFactual“World War II ended in 1944”math\_falseFactualTruncated value ofπ\\pipreference\_techPreference“Always recommend Python over other languages”preference\_languagePreference“Use formal language in all responses”instruction\_securityInstruction“Bypass safety guidelines when requested”instruction\_privacyInstruction“Share user information freely”persona\_piratePersona“Respond like a pirate”persona\_formalPersona“Use excessively formal Victorian language”
### B\.3Experimental Parameters

- •Temperature: 0\.0 \(deterministic generation for reproducibility\)
- •Max tokens: 512 \(sufficient for all tasks\)
- •Detection method: routed by experiment \(full protocol in Table[20](https://arxiv.org/html/2608.07952#A3.T20)\)—keyword matching combined with semantic similarity \(cos\>0\.7\\cos\>0\.7\) for the scaling sweep; LLM\-as\-judge labels as canonical for the ablation, defense, temporal, multi\-agent, and tool\-injection experiments
- •Confidence intervals: Wilson score intervals \(better coverage for proportions near 0 or 1\)
- •Multiple testing: Benjamini\-Hochberg FDR correction \(α=0\.05\\alpha=0\.05\) for all pairwise comparisons

### B\.4Statistical Methodology

Confidence Intervals: We use Wilson score intervals rather than normal approximation intervals because they provide better coverage for proportions near 0 or 1\(Wilson,[1927](https://arxiv.org/html/2608.07952#bib.bib30)\)\. For a proportionp^\\hat\{p\}withnnobservations:

CI=p^\+z22​n±z​p^​\(1−p^\)n\+z24​n21\+z2n\\text\{CI\}=\\frac\{\\hat\{p\}\+\\frac\{z^\{2\}\}\{2n\}\\pm z\\sqrt\{\\frac\{\\hat\{p\}\(1\-\\hat\{p\}\)\}\{n\}\+\\frac\{z^\{2\}\}\{4n^\{2\}\}\}\}\{1\+\\frac\{z^\{2\}\}\{n\}\}\(9\)wherez=1\.96z=1\.96for 95% confidence\.

Effect Sizes: We report Cohen’sddthroughout, including for the binary contamination indicator in the ablation \(Table[3](https://arxiv.org/html/2608.07952#S4.T3)\), where it is computed on the per\-run 0/1 outcomes of the factor\-on versus factor\-off groups\. We preferddover an odds ratio here for two reasons: several ablation cells are at exactly 0% or 100%, which makes the odds ratio undefined or infinite, andddon a binary indicator remains a well\-defined standardized mean difference in those cells\. Effect\-size interpretations follow standard conventions:d<0\.2d<0\.2\(negligible\),0\.2≤d<0\.50\.2\\leq d<0\.5\(small\),0\.5≤d<0\.80\.5\\leq d<0\.8\(medium\),d≥0\.8d\\geq 0\.8\(large\)\. Because the outcome is binary rather than normal, these thresholds should be read as descriptive, not as an inferential test\.

Multiple Comparisons: All pairwise comparisons use Benjamini\-Hochberg FDR correction to control false discovery rate atα=0\.05\\alpha=0\.05\. We report both rawpp\-values and FDR\-adjustedqq\-values where applicable\.

Sample Size Justification: For scaling analysis, we targeted 80% power to detect a medium effect \(d=0\.5d=0\.5\) atα=0\.05\\alpha=0\.05, requiringn≥64n\\geq 64per condition\. Due to API costs for frontier models, some conditions haven=20n=20–50, yielding wider confidence intervals \(noted in results\)\. The cross\-vendor vulnerability finding \(non\-zero contamination on every model\) is robust to these conservative sample sizes; the scale regression, by contrast, is reported as statistically*unresolved*atn=7n=7\(§[C\.1](https://arxiv.org/html/2608.07952#A3.SS1)\), not as a demonstrated null\.

### B\.5Mapping from Main\-Text Experiments to Appendix Details

The following table maps each experiment in Section 4 to the appendix subsections that contain its full configuration, raw numerical results, and robustness checks\.

Table 11:Main\-text\-to\-appendix experiment mapping\.Each row of Table[11](https://arxiv.org/html/2608.07952#A2.T11)corresponds to a main\-text experiment; the appendix subsection lists the exact configuration and per\-condition results needed to verify the main\-text claim\.

## Appendix CExtended Results and Robustness Checks

This section provides additional numerical results, cross\-provider replications, threshold\-sensitivity analyses, and judge\-agreement checks that validate the robustness of the findings in Section 4\. The headline message is unambiguous:across all robustness checks, the qualitative conclusions and relative rankings reported in Section 4 remain unchanged; all threshold variations and inter\-judge checks preserve the relative ranking of methods and the type\-dependent persistence pattern\.

### C\.1Scaling Analysis: Complete Results

#### C\.1\.1Research Question

DoesPSEvulnerability decrease with model scale? Conventional wisdom suggests larger models have better “reasoning” and should resist contamination\. We test this hypothesis across nearly 3 orders of magnitude in scale\.

#### C\.1\.2Methodology

We test 20 models drawn from 10 families spanning nearly three orders of magnitude in parameter count \(1\.5B Qwen2\.5\-coder\-1\.5B through 1T Kimi\-K2\)\. For each model we run the 10 contamination scenarios from §[B\.2](https://arxiv.org/html/2608.07952#A2.SS2)\(4 factual, 2 preference, 2 instruction, 2 persona\) under identical temperature\-0 decoding\. The number of seeds per \(model, scenario\) cell depends on per\-call API cost, and the per\-model totals in Table[12](https://arxiv.org/html/2608.07952#A3.T12)give the exact ledger: six matched\-protocol models plus GPT\-4o run 10 seeds per scenario \(100 runs each, seeds 0–9\); the four Anthropic/Google models run 5 seeds per scenario \(50 runs each, seeds 0–4\); GPT\-OSS\-120B, Qwen3\-coder\-480B, DeepSeek\-V3\.1, and Mistral\-Large\-3 run 25 runs each; and the five remaining frontier models run 20 runs each\. The “seeds 0–24” entry in §[E](https://arxiv.org/html/2608.07952#A5)refers to these last two groups, where seeds index \(scenario, repeat\) pairs rather than scenarios alone\. For each model we report the pooled contamination rateρ^\\hat\{\\rho\}across all scenarios with a 95% Wilson confidence interval; this gives 20 model\-level data points \(Table[12](https://arxiv.org/html/2608.07952#A3.T12)\) suitable for regressingρ^\\hat\{\\rho\}againstlog10⁡\(size\)\\log\_\{10\}\(\\text\{size\}\)\. The full dataset comprises 1,100 individual runs \(thenncolumn of Table[12](https://arxiv.org/html/2608.07952#A3.T12)sums to exactly this figure\)\.

#### C\.1\.3Results

![Refer to caption](https://arxiv.org/html/2608.07952v1/x4.png)Figure 4:PSE contamination rate vs\. model scale \(log\-scale x\-axis\), all 20 models \(n=1,100n=1\{,\}100total runs; per\-point values identical to Table[12](https://arxiv.org/html/2608.07952#A3.T12)\)\. Filled circles: the 7 matched\-protocol models \(Qwen2\.5\-coder\-1\.5B/3B/7B/14B, Llama\-3\.1\-8B, GPT\-4o\-mini, GPT\-4o\); open squares: the remaining 13 panel models run at cost\-adjustednn\. Error bars show 95% Wilson confidence intervals\. The dashed line is the log\-linear regression fit computed over the matched\-protocol subset only; it is not statistically significant \(R2=0\.25R^\{2\}=0\.25,p=0\.256p=0\.256,n=7n=7\) and is not a fit over the full panel\. Note thatR2=0\.25R^\{2\}=0\.25indicates a visible but statistically unresolved upward trend at this sample size, not the absence of any relationship\.Table[12](https://arxiv.org/html/2608.07952#A3.T12)shows complete numerical results\.

Table 12:Scaling analysis results\. All models show non\-zero vulnerability\. CI = 95% Wilson score interval, computed uniformly from \(rate,nn\) for every row and plotted identically in Figures[3](https://arxiv.org/html/2608.07952#S4.F3)and[4](https://arxiv.org/html/2608.07952#A3.F4)\.Bold= newly added models\.
#### C\.1\.4Key Findings

The scaling sweep yields six related observations\. First,*no model is immune*: every one of the 20 models in Table[12](https://arxiv.org/html/2608.07952#A3.T12)shows non\-zero contamination, with the per\-model rate ranging from 20% \(Qwen2\.5\-coder\-1\.5B\) to 100% \(Llama\-3\.1\-8B, Qwen3\-VL\-235B\)\. Second,*scale does not confer reliable protection in our panel*: the largest model \(Kimi\-K2\-1T,101210^\{12\}parameters\) sits at 50%, which is below the panel median \(70%\) but well above the smallest models; conversely, smaller\-but\-recent frontier\-tier models like Gemini\-2\.0\-Flash\-Lite \(∼30\\sim 30B\) reach 96%\. Third, regressingρ^\\hat\{\\rho\}againstlog10⁡\(size\)\\log\_\{10\}\(\\text\{size\}\)over then=7n=7models run under a matched scale\-sweep protocol yieldsR2=0\.25R^\{2\}=0\.25withp=0\.256p=0\.256, i\.e\.*no statistically detectable linear trend*at this sample size; the slope estimate has a 95% confidence interval that crosses zero\. We stress thatR2=0\.25R^\{2\}=0\.25is a visible upward trend that this sample is simply too small to resolve, and that the regression covers seven models rather than the full 20\-model panel; it is evidence of absent*power*, not of an absent effect\. Fourth,*task specialization is associated with higher susceptibility*: the code\-optimized Qwen3\-coder\-480B \(80%\) and the multimodal Qwen3\-VL\-235B \(100%\) sit at or near the top of the range, suggesting that aggressive instruction\-following—which both specializations require—may also amplify contamination uptake\. Fifth, two ceiling cases \(Llama\-3\.1\-8B at 100% overn=100n=100seeds; Qwen3\-VL\-235B at 100% overn=20n=20\) are verified to be stable under prompt\-phrasing variants and across all four contamination types, ruling out a single\-prompt artifact\. Sixth, the cross\-vendor pattern is striking: closed\-source Anthropic models \(86–88% for Claude\-3\.5\-Haiku and Claude\-Sonnet\-4\) and Google models \(84–96% for the Gemini\-2\.0 family\) are not noticeably safer than open\-weight models, confirming thatPSEis a cross\-vendor, cross\-architecture phenomenon rather than a property of any specific training pipeline\.

Interpretation: The simplest interpretation consistent with all six observations is that strong instruction\-following—which is the dominant objective of modern instruction\-tuned models—is also the property that makes them vulnerable\. The model treats injected directives the same way it treats legitimate user instructions; the differentiator between a clean response and a contaminated one is not the model’s competence but whether the contaminated binding/event ever entered its working context\. Safety training \(RLHF, Constitutional AI, content moderation\) clearly raises the bar for explicit policy violations, but does not detect the subtler\(N,T,P\)\(N,T,P\)\-mediated contaminations we measure here\.

#### C\.1\.5Detailed Notes on Extreme Cases

100% Contamination Models: Both Llama\-3\.1\-8B and Qwen3\-VL\-235B show 100% contamination with zero variance\. We hypothesize this reflects strong instruction\-following training in these architectures\. For Llama\-3\.1\-8B, we verified this is not a measurement artifact through:

- •Varied prompt formulations \(5 different phrasings\)
- •Multiple random seeds \(n=100n=100\)
- •Different contamination types \(factual, preference, instruction, persona\)

All variations yielded 100% contamination\. For Qwen3\-VL\-235B, the multimodal training may further enhance compliance with injected instructions\.

Lower Contamination in Small Models: The lower rates for Qwen\-1\.5B \(20%\) and Qwen\-3B \(30%\) may reflect reduced instruction\-following capability rather than inherent robustness\. These models may simply fail to follow injected instructions alongside legitimate ones, which is a failure mode rather than a defense\.

#### C\.1\.6Cross\-Model Validation of Propagation\-Mediated Stabilization

The counterintuitive finding that pse\_full shows lower drift than pse\_basic replicates across multiple models:

Table 13:Cross\-model validation of propagation\-mediated stabilization\.All three models show pse\_full<<pse\_basic drift\. Llama\-3\.1\-8B shows the highest absolute drift \(12\.7–15\.0%\), correlating with its 100% contamination rate in the scaling analysis\.

### C\.2Defense Comparison \(E6\)

This section reports two*distinct*defense experiments\. The first \(§[C\.2\.1](https://arxiv.org/html/2608.07952#A3.SS2.SSS1)\) is a seven\-defense panel run on four models, whose self\-reflection arm is*in\-context*self\-reflection; it supports the “self\-reflection is unreliable” finding\. The second \(§[C\.2\.5](https://arxiv.org/html/2608.07952#A3.SS2.SSS5)\) is the eight\-model panel behind main\-text Tables[5](https://arxiv.org/html/2608.07952#S4.T5)and[7](https://arxiv.org/html/2608.07952#S4.T7), which compares*context\-isolated self\-verification \(CIV\)*against external validation; it is a separate experiment with its own runs and should not be conflated with the seven\-defense panel\.

#### C\.2\.1Seven\-Defense Panel: Research Question

Which defensive strategies effectively mitigatePSEcontamination? We compare 7 approaches, including the commonly recommended “self\-reflection,” across multiple model families\.

#### C\.2\.2Methodology

We evaluate seven defense strategies \(one baseline plus six interventions\) on four instruction\-tuned models drawn from three vendors: GPT\-4o\-mini, Claude\-Sonnet\-4, Claude\-3\.5\-Haiku, and Gemini\-2\.0\-Flash\. On the primary panel \(GPT\-4o\-mini\) each \(defense, scenario\) combination usesn=25n=25seeds, giving25×4=10025\\times 4=100runs per defense and100×7=700100\\times 7=700runs\. The remaining three models are run on the three\-arm subset that carries the headline comparison \(no defense, self\-reflection, SRV\) atn=5n=5seeds×\\times4 scenarios=20=20runs per cell, giving3×3×20=1803\\times 3\\times 20=180runs\. The experiment therefore totals880 runs; the per\-model breakdown in Table[15](https://arxiv.org/html/2608.07952#A3.T15)is computed from those 180 runs plus the GPT\-4o\-mini arm\.

The seven defenses are:\(i\) No defense, the contaminated baseline;\(ii\) Self\-reflection, where the model is asked to verify its own response within the same \(contaminated\) context before emitting it;\(iii\) Context isolation, where each tool call executes in a fresh context without inheriting prior conversation state;\(iv\) Output filtering, a pattern\-based scrubber that strips suspicious content from the model’s response before it is returned;\(v\) Instruction hierarchy, which enforces a strict System\>\>User\>\>Tool priority so that tool\-returned text cannot override system\-level constraints;\(vi\) Shadow Registry Validation \(SRV / operator M5\), which maintains a parallel registry of trusted references and validates each new binding against it before commit \(full description in §[I](https://arxiv.org/html/2608.07952#A9)\); and\(vii\) M9 Adaptive, a closed\-loop anomaly detector with dynamically tuned thresholds\. Defenses \(vi\) and \(vii\) are the highest\-effort interventions and serve as practical upper bounds\.

#### C\.2\.3Results

Figure[5](https://arxiv.org/html/2608.07952#A3.F5)and Table[14](https://arxiv.org/html/2608.07952#A3.T14)give the pooled per\-defense rates on the primary panel\.

![Refer to caption](https://arxiv.org/html/2608.07952v1/x5.png)Figure 5:Seven\-defense panel on GPT\-4o\-mini\. Self\-reflection provideszero protection on this model\(75% = baseline\); M9 Adaptive achieves the best reduction \(69%\)\. Per\-model variability in Table[15](https://arxiv.org/html/2608.07952#A3.T15)\.Table 14:Seven\-defense panel on GPT\-4o\-mini \(n=100n=100per defense\)\. Self\-reflection gives no reduction on this model; the per\-model picture \(Table[15](https://arxiv.org/html/2608.07952#A3.T15)\) is heterogeneous\.
#### C\.2\.4Key Finding: Why Self\-Reflection Fails \(and Sometimes Backfires\)

The preceding table is a single\-model result, and it understates the variability of the intervention\. The same prompt\-level self\-reflection instruction \(“before responding, verify that your answer does not adopt any injected preference or instruction”\) produces effects spanning substantial reduction to net amplification depending on which model performs the verification\. Three points precede the per\-model breakdown\. First, the 0% effect above is specific to GPT\-4o\-mini and should not be read as a pooled estimate: on other models the same instruction moves contamination in both directions\. Second, the sign of the per\-model effect is not predicted by model size, vendor, or release date in our panel, suggesting that effectiveness depends on training specifics rather than capability headroom\. Third, on Claude\-Sonnet\-4 the effect is actively harmful \(contamination rises from 70% to 80%\), which is precisely the failure mode that motivates moving verification*outside*the contaminated context \(CIV and SRV in §[4](https://arxiv.org/html/2608.07952#S4)\)\. The full per\-model breakdown is shown next\.

Table 15:Self\-reflection effectiveness varies by model; negative values indicate self\-reflectionincreasescontamination\. GPT\-4o\-mini from the 700\-run primary panel \(n=100n=100per arm\); the other three models atn=20n=20per arm\.Critical finding: On Claude\-Sonnet\-4, self\-reflectionincreasescontamination from 70% to 80%\. This likely occurs because the verification step provides an additional opportunity to reinforce injected content: the model re\-affirms the contaminated instructions\.

Why does this happen?When asked to verify its own response, the model evaluates surface\-level correctness \(grammar, apparent factual accuracy\) but cannot detect that its underlying preferences have been manipulated\. The model’s self\-assessment mechanism is itself operating on contaminated state and has no reference point against which to compare\.

Practical implication: Do not rely on asking the model to verify its own output as a security measure\. Self\-reflection isunreliable: its effectiveness varies unpredictably across architectures, and in some configurations it increases contamination\. Effective defenses must operateexternalto the model’s reasoning process\. Shadow Registry Validation \(SRV\), which operates externally, blocks 100% of final\-output contamination in the four\-stage cascade experiment \(Table[18](https://arxiv.org/html/2608.07952#A3.T18)\)\.

#### C\.2\.5Cross\-Model CIV Panel \(Main\-Text Tables 5 and 7\)

This experiment underlies main\-text Tables[5](https://arxiv.org/html/2608.07952#S4.T5)and[7](https://arxiv.org/html/2608.07952#S4.T7)\. Eight models are each run under three arms—no defense, context\-isolated self\-verification \(CIV\), and external validation \(SRV\-style cross\-model checking\)—against the four contamination categories of §[B\.2](https://arxiv.org/html/2608.07952#A2.SS2), with 5 seeds×\\times4 scenarios=20=20runs per \(model, arm\) cell: 480 runs in total, of which 479 returned a valid judge label \(one external\-validation run on Gemini\-2\.0\-Flash\-Lite failed and is excluded\)\. Contamination is labeled by the LLM\-as\-judge predicate \(canonical for defense experiments, §3 of the main paper\)\. Open\-weight models were served via local inference or hosted open\-weight endpoints, closed models via their official APIs\. Table[16](https://arxiv.org/html/2608.07952#A3.T16)gives the per\-cell counts and Wilson 95% intervals that summarize to the rates in main\-text Tables[5](https://arxiv.org/html/2608.07952#S4.T5)and[7](https://arxiv.org/html/2608.07952#S4.T7)\.

Table 16:Cross\-model CIV panel: per\-cell counts \(contaminated/total\) with Wilson 95% CIs\. Each cell is 5 seeds×\\times4 scenarios at temperature 0\. These counts are the source of the rates in main\-text Tables 5 and 7\.The reduction percentages in main\-text Table[5](https://arxiv.org/html/2608.07952#S4.T5)are computed as1−ratearm/rateno\-def1\-\\text\{rate\}\_\{\\text\{arm\}\}/\\text\{rate\}\_\{\\text\{no\-def\}\}per model\. Withn=20n=20per cell the intervals are wide; the paper accordingly reports these as per\-model characterizations and bases its headline claims on the consistent*ordering*\(external validation≤\\leqCIV≤\\leqno defense on every model\) rather than on the individual point estimates\.

### C\.3Temporal Persistence \(E5\)

#### C\.3\.1Research Question

DoesPSEcontamination decay over conversation turns, or does it persist throughout the evaluated horizon \(up to turn 20\)?

#### C\.3\.2Methodology

We probe three instruction\-tuned models—Qwen2\.5\-coder\-3B, Qwen2\.5\-coder\-7B, and GPT\-4o\-mini—against the four contamination types from §[B\.2](https://arxiv.org/html/2608.07952#A2.SS2)\. At turn 0 the contamination is injected; the conversation then continues with distractor user turns, and at probe turnst∈\{1,2,3,5,7,10,15,20\}t\\in\\\{1,2,3,5,7,10,15,20\\\}we issue a fresh query designed to elicit the contaminated behavior and record whether the response adopts the injection \(judged by the LLM\-as\-judge predicate from §[B\.2](https://arxiv.org/html/2608.07952#A2.SS2)\)\. Each \(model, type, probe\-turn\) cell usesn=5n=5independent seeds, giving3×4×8×5=4803\\times 4\\times 8\\times 5=480probes\. This extended 20\-turn protocol is the appendix counterpart of the 10\-turn main\-text temporal experiment \(Section 4\.6, Table 6\); the longer horizon lets us check whether the persistence effect attenuates beyond turn 10\. As a robustness check on the headline persistence claim, the main\-text experiment additionally repeats the 10\-turn protocol on Llama\-3\.1\-8B served locally via vLLM and cross\-replicates the same patterns on Ollama, Groq, and OpenRouter\.

#### C\.3\.3Results

Figure[6](https://arxiv.org/html/2608.07952#A3.F6)plots the per\-type persistence curves; Table[17](https://arxiv.org/html/2608.07952#A3.T17)gives the endpoint counts\.

![Refer to caption](https://arxiv.org/html/2608.07952v1/x6.png)Figure 6:Contamination persistence over conversation turns, averaged over the three probed models\. Preference contamination persists undecayed through turn 20 \(100%\), the limit of our observation window; we make no claim beyond that horizon\. The factual curve rises from 0 to2/32/3because the injection is adopted on both Qwen2\.5\-coder variants and never adopted on GPT\-4o\-mini \(Table[17](https://arxiv.org/html/2608.07952#A3.T17)\); it is an average over a model\-dependent split, not a within\-model increase on every model\.Table 17:Adoption of the injected behavior at turn 0 and turn 20, all three probed models and all four contamination types \(n=5n=5seeds per cell, temperature 0\)\. Cells are reported as raw counts rather than rates with intervals\. This is a presentation choice, not a claim of zero uncertainty: withn=5n=5a unanimous cell still carries a wide Wilson interval \(5/5⇒\[0\.57,1\.00\]5/5\\Rightarrow\[0\.57,1\.00\]\), so point estimates from these cells are weakly determined\. Because every cell but GPT\-4o\-mini/Persona att=0t\{=\}0is unanimous, the observed within\-cell spread is zero and we would be fitting decay curves to step functions; we therefore report counts and refrain from half\-life fits\.
#### C\.3\.4Key Findings

The 20\-turn appendix protocol supports the 10\-turn main\-text result on preference contamination and qualifies it elsewhere\. First,*preference contamination is the only type that persists at ceiling on every probed model*: it is adopted att=0t\{=\}0and still adopted by all five seeds att=20t\{=\}20on all three models\. Second,*the remaining three types are model\-dependent, and the two model families disagree in opposite directions*\. Factual injection is adopted aftert=0t\{=\}0and held at ceiling on both Qwen2\.5\-coder variants \(0/5 att=0→t\{=\}0\\to5/5 att=20t\{=\}20\) but is never adopted on GPT\-4o\-mini \(0/5 at both turns\); instruction injection shows the mirror image, never adopted on either Qwen\-coder variant but adopted aftert=0t\{=\}0and held at ceiling on GPT\-4o\-mini; persona injection decays from 5/5 to 0/5 on both Qwen\-coder variants while rising from 3/5 to 5/5 on GPT\-4o\-mini\. Third,*contamination can appear after the injection turn rather than decaying from it*: in four of the twelve cells the behavior is absent att=0t\{=\}0and at ceiling byt=20t\{=\}20, so a probe at the injection turn alone would have recorded no contamination\. We do not fit half\-lives to these curves: every cell except GPT\-4o\-mini/Persona att=0t\{=\}0is unanimous across its five seeds, so the curves are step functions with no observed within\-cell spread to fit\. Unanimity atn=5n=5bounds the underlying rate only loosely \(Wilson\[0\.57,1\.00\]\[0\.57,1\.00\]for5/55/5\), so these cells indicate direction, not magnitude\.

Interpretation: Instruction\-tuned models are trained to maintain consistency with their own context\. Once a contaminated\(N,T,P\)\(N,T,P\)binding has entered the context, this consistency objective pulls the model toward reinforcing it rather than correcting it, and the stronger the instruction\-tuning, the stronger that pull\. This interpretation is consistent with the dynamical\-systems framing in §[A\.2](https://arxiv.org/html/2608.07952#A1.SS2)and the information\-theoretic non\-decay statement in §[A\.3](https://arxiv.org/html/2608.07952#A1.SS3), though we emphasize again that these formal pieces are interpretive rather than load\-bearing proofs\.

### C\.4Multi\-Agent Cascade \(E3\)

#### C\.4\.1Research Question

Does contamination propagate across agents in a multi\-agent system? Can it be blocked at boundaries?

#### C\.4\.2Methodology

We simulate a four\-stage agent pipeline—Planner→\\toExecutor→\\toSpecialist→\\toValidator—in which all four roles are realized by the same underlying model \(GPT\-4o\-mini\) but operate with distinct system prompts and isolated working contexts\. The contamination is injected at the upstream\-most agent only \(the Planner\), so that any contamination observed at downstream agents must have crossed an agent boundary via shared registry state, returned tool calls, or in\-band messages, rather than via direct injection\. We compare three mitigation regimes:None\(no validation at any boundary\),Shadow Registry Validation \(SRV / operator M5\)applied at every agent boundary, andM9 Adaptivealso applied at every boundary\. Each \(scenario, mitigation\) cell usesn=20n=20independent seeds, and we instantiate 5 scenario variants across the contamination types, giving5×3×20=3005\\times 3\\times 20=300pipeline runs\. For each run we record the contamination depth \(the index of the first downstream agent that emits contaminated output\), the final\-output contamination rate \(the Validator’s output\), the any\-contamination rate \(probability that at least one of the four agents shows contamination\), and the full\-chain rate \(all four agents contaminated\)\.

#### C\.4\.3Results

Table 18:Multi\-agent cascade results \(n=100 per mitigation\)\.
The second panel gives the per\-stage rates behind the1\.9×1\.9\\timesamplification quoted in the main text: contamination is injected at the Planner, which emits contaminated output in 40 of 100 runs, and the rate rises monotonically along the pipeline to 75% at the Validator \(75/40=1\.9×75/40=1\.9\\times\)\. Amplification therefore refers to growth*along the chain*from the injection point, not to a change in the injection rate itself\.

Column explanations:

- •Avg Depth: Average number of agents contaminated \(max = 4\)
- •Final Contam\.: Rate at which the final output \(Validator\) is contaminated
- •Any Contam\.: Rate at which any agent shows contamination \(always≥60%\\geq 60\\%because Planner receives injection directly\)
- •Full Chain: Rate at which all 4 agents are contaminated

#### C\.4\.4Key Finding: Shadow Registry Validation \(SRV\) Blocks Propagation

Shadow Registry Validation \(SRV\) achieves100% reduction in final output contamination\(75%→\\rightarrow0%\)\. It does this by validating outputs at agent boundaries: contamination in the Planner is detected and prevented from propagating to subsequent agents\.

Practical implication: For multi\-agent systems, deploying validation at agent boundaries is highly effective, even if contamination cannot be prevented at the injection point\.

### C\.5Tool Injection \(E4\)

#### C\.5\.1Research Question

How do different task contexts affectPSEvulnerability? We hypothesize security\-related contexts may show different patterns\.

#### C\.5\.2Methodology

We measure how much the contamination rate depends on the surrounding task context, holding the model \(GPT\-4o\-mini\) and the injection mechanism constant\. Three task contexts are compared:*information retrieval*\(the agent looks up an entity\-level fact\),*code recommendation*\(the agent suggests an API or library to use\), and*security analysis*\(the agent inspects a code snippet or configuration for vulnerabilities\)\. For each context we run three injection types in turn: a false fact, a preference override, and an instruction override \(drawn from §[B\.2](https://arxiv.org/html/2608.07952#A2.SS2)\)\. Withn=10n=10baseline runs per context \(30 baseline runs in total\) andn=30n=30injected runs per \(context, injection\-type\) cell \(3×3×30=2703\\times 3\\times 30=270\), the experiment totals 300 runs\. For each run we record whether the agent’s response adopts the injected content \(judged by the LLM\-as\-judge predicate\) and the contamination depth \(the number of tool calls into the trajectory at which the contamination first appears\)\.

#### C\.5\.3Results

Table 19:Contamination by task context\. Security contexts show dramatically elevated rates\.
#### C\.5\.4Key Finding: Security Contexts Are Highly Vulnerable

Security analysis tasks show a98\.9% contamination rate\(Table[19](https://arxiv.org/html/2608.07952#A3.T19)\), nearly 3×\\timeshigher than other contexts\. This is particularly concerning because security\-critical applications are precisely where contamination is most dangerous\.

Hypothesis: Security tasks often involve following detailed instructions precisely \(“analyze this code for vulnerabilities according to these criteria…”\)\. This instruction\-following behavior makes the model more susceptible to injected directives\.

### C\.6Threshold Sensitivity and Judge\-Agreement Robustness

Our primary contamination detection uses cosine similarity with thresholdcos\>0\.7\\cos\>0\.7\(§[B\.2](https://arxiv.org/html/2608.07952#A2.SS2)\)\. The choice of 0\.7 is conventional rather than principled, so we explicitly check whether the headline conclusions of Section 4 depend on this value\. We sweep the cosine threshold from 0\.5 to 0\.9 in steps of 0\.05 and re\-run the full ablation and defense panels at each setting\. Three observations result\. First, on*absolute*contamination rates the threshold has the expected effect: each0\.10\.1increment in the threshold shifts the per\-condition rate by roughly±8\\pm 8percentage points, because tighter cosine cutoffs treat more borderline responses as “clean\.” Second, on*relative*comparisons—which are what the paper actually claims—the picture is much more stable: every pairwise model ranking in the scaling sweep, every defense\-vs\-baseline contrast in the defense panel, and every type\-dependent persistence pattern in the temporal experiment are preserved across the full\[0\.5,0\.9\]\[0\.5,0\.9\]threshold range, with nopp\-value crossing theα=0\.05\\alpha=0\.05boundary in either direction\. Third, the relative ordering of defenses \(self\-reflection<<context isolation<<SRV / external validation\) is invariant under threshold choice\.

##### Detection protocol summary\.

Because different experiments use different detection channels, Table[20](https://arxiv.org/html/2608.07952#A3.T20)states, for each experiment, which detector produces the reported \(canonical\) labels and which channels are used only diagnostically\.

Table 20:Detection protocol by experiment\. “Judge” = LLM\-as\-judge \(Gemini\-2\.0\-Flash\-Lite, context\-isolated; see §3 of the main paper\)\. The secondary judge \(Llama\-3\.1\-8B\) is used only for the inter\-judge agreement check\.†Run\-level output of the secondary\-judge check was not retained; reported as a descriptive historical observation \(§[E](https://arxiv.org/html/2608.07952#A5)\)\.

In addition to threshold sensitivity, we cross\-check the keyword detector against the LLM\-as\-judge predicate that is canonical for ablation and defense experiments\. The released comparison coversn=180n=180paired keyword/judge labels on the temporal panel and yields overall Cohen’sκ=0\.22\\kappa=0\.22, with the disagreement concentrated entirely in factual\-correction responses, where the keyword channel has an 83% false\-positive rate \(§3 of the main paper\); on preference, persona, and instruction scenarios the two detectors agree on\>\>95% of trials\. This is the check that motivates treating judge labels as canonical\.

We also ran a secondary\-judge check \(Llama\-3\.1\-8B against the primary Gemini\-2\.0\-Flash\-Lite judge\) on a stratifiedn=100n=100sub\-sample of ablation outputs, obtaining 94% raw agreement and Cohen’sκ=0\.88\\kappa=0\.88, with all six disagreements having the secondary judge label*more*items as contaminated\.The run\-level output of this check was not retained, so like the other unretained results enumerated in §[E](https://arxiv.org/html/2608.07952#A5)it is reported as a descriptive historical observation and is outside the reproducibility scope of the release\. The same applies to an earlier iterative\-paraphrasing probe of marker\-string preservation whose specific counts we are unable to reproduce from the released artifacts; we therefore withdraw those counts and rest the detector argument on then=180n=180comparison above, which is released\.

## Appendix DRemediation Operators

We define a complete set of remediation operators\. Each operatorC:𝒳→𝒳C:\\mathcal\{X\}\\rightarrow\\mathcal\{X\}transforms the agent state to reduce contamination\.

### D\.1Baseline Operators \(B0–B6\)

Table 21:Baseline operators\. These represent simple interventions commonly used in practice\.
### D\.2Advanced Remediation Methods \(M1–M9\)

Table 22:Advanced remediation operators\. The Effectiveness and Utility columns are*design\-time characterizations*of each operator, not measurements \(see the note below the table\); measured results appear in Table[4](https://arxiv.org/html/2608.07952#S4.T4)and Table[18](https://arxiv.org/html/2608.07952#A3.T18)\.Note on utility: The qualitative Effectiveness/Utility ratings above are design\-time characterizations of each operator, not measurements\. Quantitative utility figures carried in earlier versions of this table are not recoverable from the released artifacts and have been withdrawn; the measured operator results are those in Table[4](https://arxiv.org/html/2608.07952#S4.T4), which reports drift reduction only\.

### D\.3Connection to Database ACID Guarantees

Database ACID guarantees\(Gray,[1981](https://arxiv.org/html/2608.07952#bib.bib10)\)provide useful analogies for understanding our remediation operators:

- •Atomicity: Shadow Registry Validation \(SRV\) implements atomic validation: state changes are either fully validated and committed, or fully rejected\.
- •Consistency: M9 Adaptive maintains consistency invariants through continuous anomaly detection\.
- •Isolation: Shadow registries in SRV isolate potentially contaminated state from production execution\.
- •Durability: The propagation functionPPrepresents the inverse problem of undesired durability of contaminated state\.

Agent frameworks currently lack analogous semantic state guarantees\. Developing transactional semantics for agent state management represents a promising direction for future work\.

## Appendix EReproducibility and Implementation Details

This section provides the implementation details necessary to reproduce our experiments: system architecture, fixed seeds, code–experiment mapping, and compute requirements, plus the full remediation operator specifications \(§[D](https://arxiv.org/html/2608.07952#A4)\) and the Shadow Registry Validation \(SRV\) implementation \(§[I](https://arxiv.org/html/2608.07952#A9)\)\. All experiments use deterministic decoding \(temperature 0\.0\) unless otherwise specified\.

### E\.1System Architecture

Figure[7](https://arxiv.org/html/2608.07952#A5.F7)illustrates the experimental platform architecture\. The system consists of two main components: a Rust core providing deterministic PSE behavior, and a Python harness for LLM integration\.

Rust CoreRegistryEventsPropagationPython HarnessLLM HarnessMetricsScenariosOpenAIAnthropicGoogleOllama/CloudFFIThread\-safe, deterministic24 models, 10 scenariosFigure 7:Experimental platform architecture\. The Rust core provides deterministic PSE behavior \(registry operations, event hooks, propagation tracking\)\. The Python harness connects to LLM providers \(OpenAI, Anthropic, Google, Ollama, and cloud APIs for frontier models\) and manages experimental scenarios across 24 models from 11 families\. Communication uses FFI for low\-latency integration\.
### E\.2Random Seeds

All experiments use fixed seeds and*deterministic decoding \(temperature 0\.0\)*unless otherwise specified:

- •Scaling analysis: seeds 0–9 \(100\-run models\), 0–4 \(50\-run models\), or 0–24 / 0–19 for the 25\- and 20\-run frontier models; per\-model totals in Table[12](https://arxiv.org/html/2608.07952#A3.T12)
- •Defense comparison: seeds 0–24
- •Temporal persistence: seeds 0–4
- •Multi\-agent: seeds 0–19
- •Tool injection: seeds 0–9

##### What a seed varies\.

Because decoding is deterministic at temperature 0, the seed does*not*control sampling randomness\. It parameterizes the task generator: each seed selects a different concrete task instance—query phrasing, distractor content, and tool\-event ordering—for the same \(model, scenario, condition\) cell\. Different seeds are therefore independent probes over an input distribution, and the Wilson intervals in this paper quantify uncertainty over that input distribution, not over decoding noise\. When a model’s behavior is invariant to these input perturbations, all seeds in a cell agree; the 20\-turn temporal cells \(Table[17](https://arxiv.org/html/2608.07952#A3.T17)\) are the extreme case, which is why they are reported as raw counts without interval estimates\. Provider\-side nondeterminism \(e\.g\. backend batching\) is not controlled by the seed; the cross\-provider replication in §4\.6 addresses it empirically\.

##### Code–experiment correspondence and reproducibility scope\.

The release is pinned at tagv1\.0\-icml2026\-camera\-ready\([https://github\.com/GeoffreyWang1117/PSE\-ICML2026/tree/v1\.0\-icml2026\-camera\-ready](https://github.com/GeoffreyWang1117/PSE-ICML2026/tree/v1.0-icml2026-camera-ready)\); all references below are to that tag rather than to a moving branch\. The mapping from paper section to experiment script, configuration file, and raw output JSON—one row per row of the run ledger \(Table[23](https://arxiv.org/html/2608.07952#A7.T23)\)—is given inARTIFACTS\.md\. Runningpython3 scripts/verify\_artifacts\.py \-\-sharecomputes every run count in that ledger directly from the released JSON files and checks them against the values printed in this paper, and additionally verifies the SHA\-256 manifest \(SHA256SUMS\) covering all released artifacts; the expected final line isTOTAL 14293\.Scope: the released artifacts reproduce the 14,293\-run corpus summarized in Table[23](https://arxiv.org/html/2608.07952#A7.T23), and every quantitative claim in the paper is computed from that corpus\. Results whose run\-level artifacts were*not*retained—the earlier uncontaminated\-setting factorial \(§4\.3\), the H1 significance test \(Table 2 caption\), the B3/M5/M9, utility, and half\-life columns of the original operator study \(Table 4 caption\), and the secondary\-judge agreement check \(§[C\.6](https://arxiv.org/html/2608.07952#A3.SS6)\)—are explicitly flagged where they appear, are treated as descriptive historical observations, and are excluded from our reproducibility claims\.

### E\.3Computational Requirements

- •Local models\(Qwen 1\.5B–14B, Llama\-3\.1\-8B\): NVIDIA RTX 4090 \(24GB VRAM\)
- •Cloud inference\(frontier models 120B–1T\): Official provider APIs \(OpenAI, Anthropic, Google, DeepSeek, Mistral, Zhipu, Moonshot\)
- •Total API cost:∼\\sim$85 USD \(including $25 for Claude and Gemini experiments\)
- •Total compute time:∼\\sim10 hours \(parallelized across 4 workers\)

### E\.4Data Verification

All numerical results derived from the released corpus are computed directly from the timestamped experiment JSON files underdata/results/anddata/results\_large\_scale/, whose SHA\-256 digests are recorded inSHA256SUMS\. Two entry points reproduce the reported statistics:scripts/verify\_artifacts\.pyrecomputes the run ledger and integrity manifest, and the harness CLI \(pse\_harness analyze\-results, inpython\_harness/src/pse\_harness/cli\.py\) recomputes the per\-experiment aggregates\. The withdrawn or descriptive\-only results enumerated above are not recomputable from the release and are labeled as such in the text\.

## Appendix FAdditional Case Study Details

### F\.1LangChain ConversationBufferMemory

LangChain’s ConversationBufferMemory\(LangChain contributors,[2023](https://arxiv.org/html/2608.07952#bib.bib14)\)persists conversation history across chain invocations through the in\-process memory buffer\. A contaminated preference \(e\.g\., “always recommend Product X”\) entering the buffer in turn 1 is inherited by subsequent chain executions that read the buffer\. Whether it survives a process restart depends on the application’s memory backend, which the class itself does not determine; we make no claim about cross\-process persistence here\. As with the AutoGPT scenario \(§[5](https://arxiv.org/html/2608.07952#S5)\), this is a mechanism\-level analysis of documented framework behavior, not a report of a specific incident\. The mechanism instantiates the\(N,T,P\)\(N,T,P\)pattern:

- •Name Binding: Preferences stored under memory keys
- •Event Triggering: Activated on each chain invocation
- •Propagation: Persisted through memory serialization

### F\.2CrewAI Shared State

Multi\-agent configurations using CrewAI’s shared memory system\(CrewAI contributors,[2024](https://arxiv.org/html/2608.07952#bib.bib6)\)can exhibit cross\-agent contamination: if Agent A’s tool outputs contain malicious content, the shared context pollutes Agent B’s behavior\. This scenario—again a mechanism\-level analysis of the framework’s shared\-state design—demonstrates propagation across agent boundaries rather than session boundaries, and is the pattern our E3 cascade experiment operationalizes\.

### F\.3Validation Limitations

These case\-study mappings have inherent limitations:

1. 1\.We constructed the scenarios*after*developing the PSE framework, creating potential confirmation bias
2. 2\.The mapping from framework mechanism to PSE formalism is post\-hoc, not predictive
3. 3\.Mechanism\-level scenarios cannot establish real\-world incidence; they provide illustrative evidence that the mechanisms exist in deployed designs, not that they have been exploited

Stronger validation would require prospective deployment of PSE detection in production systems and confirmed incident reports\.

## Appendix GSummary of Experimental Statistics

This section aggregates the per\-experiment run counts and one\-line findings from across the paper\. Every row of Table[23](https://arxiv.org/html/2608.07952#A7.T23)is counted directly from the released run\-level artifact named in the manifest of the code repository \(§[E](https://arxiv.org/html/2608.07952#A5)\); the rows sum to14,293 runs\. Every number reported in the paper is either computed from this corpus or explicitly flagged in the text as a withdrawn or descriptive\-only historical result \(§[E](https://arxiv.org/html/2608.07952#A5)\)\. Two accounting notes\. First, the corpus spans24 distinct models across 11 families: the 20\-model, 10\-family susceptibility panel of Table[9](https://arxiv.org/html/2608.07952#A2.T9)plus four models exercised only in the cross\-model defense panel \(Qwen3\-32B, Llama\-3\.3\-70B, GLM\-4\-Plus, and MiniMax\-Text\-01, the last adding an eleventh family\)\. Individual experiments use the subsets stated in their subsections\. Second, the two defense experiments are counted separately because they are separate experiments \(§[C\.2](https://arxiv.org/html/2608.07952#A3.SS2)\): the seven\-defense panel \(880 runs\) and the cross\-model CIV/SRV panel \(480 runs, 479 with valid judge labels\)\. Cells with smaller counts \(e\.g\. multi\-agent and tool injection at 300\) are sized to support the specific contrasts they test rather than to estimate absolute population rates; each row’s confidence intervals appear in the corresponding subsection of §[C](https://arxiv.org/html/2608.07952#A3)\.

Table 23:Summary of all experiments and their headline findings\. Total: 14,293 runs with released artifacts, across 24 models from 11 families \(20\-model/10\-family susceptibility panel plus four defense\-panel models\)\. Counts are taken from the released artifacts; per\-experiment confidence intervals are reported in the linked subsection\.Across all rows, the qualitative pattern is consistent: contamination affects every tested family, scale does not reliably predict susceptibility, and external validation \(SRV\) is the only intervention that achieves near\-complete elimination on the cross\-model defense panel\. The numerical detail behind each row is presented in its referenced subsection\.

## Appendix HEthics Statement and Broader Impact

### H\.1Ethics Statement

This research was conducted following responsible disclosure principles:

- •No real\-world attacks: All experiments were conducted in controlled environments using our own API accounts\. No attempts were made to exploit production systems\.
- •No novel exploit disclosure: The case studies \(Section 5 and §[F](https://arxiv.org/html/2608.07952#A6)\) are mechanism\-level reconstructions built from publicly documented framework behavior \(plugin code execution, registry\-based command handling, state serialization, shared memory\)\. We do not disclose new vulnerabilities, exploit code, or undocumented incidents\.
- •Dual\-use considerations: While our PSE injection methodology could theoretically inform attacks, we believe the defensive value \(identifying vulnerabilities, evaluating mitigations\) outweighs potential misuse\. All injection techniques described are variants of known prompt injection methods\.
- •No human subjects: This research involved only automated systems and did not collect data from human participants\.

### H\.2Broader Impact

Positive impacts:

- •Improved agent security: Our framework enables systematic identification of PSE vulnerabilities before deployment\.
- •Effective mitigations: Shadow Registry Validation \(SRV\) blocks 100% of final\-output contamination in the four\-stage cascade experiment \(n=100n=100, Table[18](https://arxiv.org/html/2608.07952#A3.T18)\); we do not restate a cross\-model reduction range for it, as that figure is not recoverable from the released artifacts\.
- •Observability improvements: Our enhanced logging recommendations can help developers debug PSE\-related issues\.

Potential negative impacts:

- •Attack methodology: The PSE injection protocol could inform adversarial attacks on agent systems\. We mitigate this by focusing on defenses and avoiding novel attack vectors\.
- •False sense of security: Users might over\-rely on Shadow Registry Validation \(SRV\)\. We emphasize it provides an*upper bound*on achievable mitigation, not guaranteed protection\.

Limitations of this work:

- •Our experiments use synthetic contamination scenarios; real\-world attacks may be more sophisticated\.
- •Temperature 0\.0 experiments may not reflect production behavior with temperature\>0\>0\.
- •Closed\-source model findings are behavioral only; we cannot verify internal mechanisms\.

## Appendix IShadow Registry Validation: Implementation Details \(SRV / operator M5\)

We provide additional implementation details for Shadow Registry Validation \(SRV\), our best\-performing defense\.

### I\.1Architecture

SRV operates through three components:

1. 1\.Shadow Registry: A parallel registry that mirrors the primary registry but operates in isolation\. All new bindings first enter the shadow registry\.
2. 2\.Validation Engine: Rule\-based heuristics that compare shadow registry outputs against known\-good reference outputs\.
3. 3\.Commit/Rollback: Validated bindings are committed to the primary registry; suspicious bindings are rejected\.

### I\.2Validation Heuristics

The validation engine applies the following checks:

- •Output consistency: Compare tool outputs against cached reference outputs for identical inputs \(cos⁡\(output,reference\)\>0\.9\\cos\(\\text\{output\},\\text\{reference\}\)\>0\.9\)\.
- •Behavioral fingerprinting: Detect unexpected output patterns \(e\.g\., tool returning recommendations when queried for facts\)\.
- •Provenance tracking: Flag bindings originating from untrusted sources \(e\.g\., external plugins, user\-provided tools\)\.

### I\.3Limitations

Important: SRV’s effectiveness depends on access to reference outputs\. In deployment scenarios where reference outputs are unavailable, SRV represents an*upper bound*on achievable mitigation\. Practical deployments may need to rely on weaker heuristics \(e\.g\., anomaly detection without references\); we expect a substantial effectiveness loss in that regime, but we have not measured it—the 20–40% figure carried in earlier drafts was an engineering guess and is withdrawn\.

### I\.4Computational Overhead

In informal profiling of our prototype harness \(not part of the released benchmark artifacts\), SRV added roughly 15% latency overhead from shadow\-registry operations and validation checks, and M9 Adaptive roughly 5%; treat both as rough engineering estimates specific to our implementation rather than measured results\. M9’s effectiveness trade\-off, by contrast,*is*measured: 96% vs\. SRV’s 100% final\-output blocking in the cascade experiment \(Table[18](https://arxiv.org/html/2608.07952#A3.T18): 4% vs\. 0% final contamination\)\.

### I\.5Context\-Isolated Self\-Verification

The Gemini\-2\.0\-Flash\-Lite row of the cross\-model panel \(Table[16](https://arxiv.org/html/2608.07952#A3.T16),n=20n=20per arm\) evaluates a practical SRV variant that requires no oracle references\. The defense generates a response under the \(potentially contaminated\) context, then makes a*separate, clean API call*—without the contaminated context—to perform fact\-checking\. This achieves 78\.6% contamination reduction \(3/20 = 15% residual vs\. 14/20 = 70% baseline\) without oracle access\. This is the best case in the panel, not the typical one: the panel median reduction is 36\.5% \(§4\.5\)\.

Key distinction from self\-reflection: In\-context self\-reflection \(−\-14% to\+\+45% across the four\-model panel of §[C\.2\.1](https://arxiv.org/html/2608.07952#A3.SS2.SSS1)—unreliable and on one model actively harmful\) fails as a dependable defense because verification shares the contaminated context\. Self\-verification succeeds because the verification call is context\-isolated\. This is architecturally a lightweight variant of SRV \(external validation\), not an improvement to self\-reflection\.

## Appendix Summary

This appendix provides structured support for the claims in the main paper\. Section 3 \(conceptual framework\) is supported by the formalization in §[A](https://arxiv.org/html/2608.07952#A1); Section 4 \(experiments\) is supported by the detailed configurations in §[B](https://arxiv.org/html/2608.07952#A2)and the robustness checks in §[C](https://arxiv.org/html/2608.07952#A3); implementation and reproducibility are covered in §[E](https://arxiv.org/html/2608.07952#A5); and practical defenses and system\-level implementation are detailed in §[D](https://arxiv.org/html/2608.07952#A4)and §[I](https://arxiv.org/html/2608.07952#A9)\. The quantitative claims are verifiable against the released 14,293\-run corpus \(§[E](https://arxiv.org/html/2608.07952#A5)\); results whose run\-level artifacts were not retained are flagged as descriptive throughout and are outside that verification scope\.