Measuring and Improving Behavioral Consistency in Large Language Models through Fact-Heuristic-Emotion State Enforcement

# Measuring and Improving Behavioral Consistency in Large Language Models through Fact–Heuristic–Emotion State Enforcement
Source: [https://arxiv.org/html/2607.24765](https://arxiv.org/html/2607.24765)
Authors: Gi\-Hun Lee1,∗, Joong Yull Park2,∗

1Independent Researcher 2School of Mechanical Engineering, Chung\-Ang University, Seoul, Korea ∗Corresponding authors: leescoppermine@gmail\.com \(G\.\-H\. Lee\), jrpark@cau\.ac\.kr \(J\. Y\. Park\)

Preprint:arXiv \(cs\.AI, cs\.HC\) Version:arXiv v1\.0 Date:2026\-06\-05

### Abstract

Large language models \(LLMs\) can give different answers to the same decision problem across repeated runs\. They can also change their decisions when their own previous answer is reintroduced as context\. This paper asks whether that instability can be measured and partially reduced without changing model weights\.

We test a lightweight intervention called theCognitive Kernel Model \(CKM\)\. Before making a decision, the model must separate the input into three epistemic roles:Fact\(what is given or verifiable\),Heuristic\(what is inferred or assumed\), andEmotion\(what carries evaluative or priority signal\)\. In practical terms, CKM is a prompt\-level state\-enforcement layer\. It does not make the model more capable; it forces the model to track what kind of information it is using before it acts\.

Formally, CKM maintains a structured state

St=\{Ft,Ht,Et\}S\_\{t\}=\\\{F\_\{t\},H\_\{t\},E\_\{t\}\\\}
and updates it through a state transition function:

St\+1=δ​\(St,Ωx,t,ΩtEngine\)\.S\_\{t\+1\}=\\delta\(S\_\{t\},\\Omega\_\{x,t\},\\Omega^\{\\text\{Engine\}\}\_\{t\}\)\.
We evaluated CKM on Korean\-language student decision scenarios involving ambiguity resolution, ethical conflict, resource allocation, and error handling\. The evaluation includes four core experiments, a 4\-arm ablation, a 5\-arm sham\-restriction ablation, and a temperature robustness probe\. The dataset spans 26 unique LLM models from four vendors \(OpenAI, Anthropic, Google, xAI\), two model generations, and 37,403 total observations \(35,475 primary \+ 1,928 case\-study observations\)\.

Six findings emerged\.

1. 1\.CKM reduced repeated\-output variability\.Legacy models showed 17/19 positive SI effects \(Hedges’g=1\.18g=1\.18,p=6\.55p=6\.55×\\times10\-5, parsed\-field SI\), NewModels showed 12/12 positive effects \(g=3\.08g=3\.08\), and the combined random\-effects estimate wasgREg\_\{\\text\{RE\}\}= 1\.09 \[95% CI 0\.83, 1\.35\] across 31 model\-level pairs\.
2. 2\.State persistence reduced decision flipping in newer models\.In the NewModels cohort, DFR decreased by 82% \(0\.385→\\rightarrow0\.069,g=1\.52g=1\.52\)\.
3. 3\.The active mechanism was not JSON formatting alone\.The 4\-arm ablation showed that value\-only recomputation preserved the F/H/E effect \(g=2\.24g=2\.24\) while eliminating the apparent JSON\-only effect\.
4. 4\.Intrinsic model randomness under fixed anchor states was negligible\.FCS was approximately 1\.0, localizing multi\-turn instability mainly to state construction\.
5. 5\.CKM’s advantage increased under sampling stochasticity\.AtT=0\.7T=0\.7, the CKM effect reachedg=2\.87g=2\.87\.
6. 6\.The sham\-restriction ablation separated structure from epistemic content\.Structural scaffolding accounted for approximately 45% of the SI improvement, while reasoning\-semantic F/H/E content accounted for approximately 55%\. CKM was the only arm that both improved SI and reduced DFR\.

These results donotshow that CKM improves reasoning correctness or decision quality\. They show a narrower but important result: behavioral consistency is measurable, differs substantially across models, and can be partially improved by forcing models to separate observed facts, inferred assumptions, and evaluative signals before deciding\. Code, prompts, and canonical datasets are available at https://github\.com/TeenyToolSoftware/cogos\-behavioral\-consistency\.

### Significance Statement

Most LLM benchmarks ask what a model can do\. This paper asks a different deployment\-facing question: when the same situation returns, does the model respond in a stable way, or does it drift and reverse its decision?

The paper makes one bounded claim\. In the tested Korean\-language decision scenarios, if an LLM is required to separate a decision input intoFact,Heuristic, andEmotionbefore choosing an action, then one form of behavioral instability becomes measurable and can be partially reduced in repeated and state\-persistent trials\.

The central contribution is therefore not a new LLM and not a claim of better reasoning quality\. It is a reproducible method for profiling and partially stabilizing LLM behavior by making the model’s reasoning state explicit enough to measure repeated\-response variability, decision flips, and state drift\.

### 1\. Introduction

Large language models \(LLMs\) are usually evaluated by asking what they can do: whether they solve benchmark questions, write correct code, answer medical items, or pass standardized tests\. This paper asks a different question:when the same situation is presented again, does the model behave consistently?A model can be highly capable and still be unstable\. It may produce semantically different answers to identical prompts, preserve the same reasoning while changing its action, or reverse a previous decision when its own prior output is injected back as context\.

This distinction matters for deployment\. A medical assistant that gives different triage advice for the same symptoms across sessions undermines clinical trust\. A legal assistant that changes its interpretation of the same statute creates liability\. A financial or engineering assistant that changes its risk recommendation because the reasoning state was represented differently introduces noise into decisions that require stability\. In these cases, the failure is not necessarily a lack of capability\. It is a failure of behavioral consistency\.

We definebehavioral consistencyas the stability of a model’s semantic response, retained context, selected action, and propagated state under repeated or state\-persistent trials\. This definition deliberately separates consistency from correctness\. A model can be consistently wrong, and a model can be accurate on average while unstable across repetitions\. The present study measures the former property and leaves decision quality as an independent question\.

Our central hypothesis is simple: some LLM instability arises because the model receives all information as undifferentiated text\. In a human decision situation, several kinds of information are mixed together: observed facts, inferred assumptions, and affective or value\-laden signals\. If these are not separated, a model may treat speculation as fact, emotional emphasis as evidence, or a prior inference as an observed constraint\. We therefore test whether forcing the model to separate information by epistemic role—Fact,Heuristic, andEmotion\(F/H/E\)—can reduce behavioral variability\.

To test this hypothesis, we develop theCognitive Kernel Model \(CKM\)\. CKM is not a new base model and does not require fine\-tuning\. It is a prompt\-level state\-enforcement framework that requires an LLM to \(i\) classify input information into F/H/E slots, \(ii\) produce a decision from that structured state, and \(iii\) optionally carry the structured state forward into later turns\. In plain terms, CKM asks the model to keep a clean ledger of what is known, what is inferred, and what is valued before it acts\.

This framing differs from conventional prompt engineering\. Chain\-of\-Thought, Tree\-of\-Thought, and self\-refinement methods structure how a model reasons within a response \[1–3, 14, 15\]\. CKM instead structures what epistemic role each piece of information is allowed to play and tests whether that enforced state structure changes repeated behavior\. Agent frameworks and memory systems can retain information across turns \[5–7, 38–43\], but retention alone does not specify whether retained content is a fact, an inference, or an evaluative signal\. CKM addresses that categorization layer\.

The study makes three main contributions, all within the claim boundary that we measure consistency rather than correctness:

1. 1\.A behavioral consistency measurement suite\.We define six metrics—SI, CRR, DFR, FCS, ACS, and SDR—that capture different forms of response drift, decision flipping, and state instability\. Four of these metrics \(SI, DFR, FCS, SDR\) are discriminative in the present experiments; CRR and ACS are reported as exploratory\.
2. 2\.A model\-agnostic F/H/E state\-enforcement framework\.CKM decomposes reasoning inputs into Fact, Heuristic, and Emotion roles and enforces that structure through a prompt\-level schema\. The framework can be applied to any text\-input LLM without weight modification\.
3. 3\.Cross\-vendor empirical profiling of LLM behavioral consistency\.Across 26 unique models from four vendors and two model generations, we show that baseline consistency varies substantially, CKM reduces output variability in most models, and state\-persistence behavior differs sharply across architectures\. Ablation studies show that the main active mechanism is epistemic role separation rather than JSON formatting alone\.

Claim\-chain boundary\.The paper uses one claim chain throughout\. First, LLM behavior varies across repeated presentations of the same decision problem\. Second, that variability can be measured with repeated\-trial and state\-persistence metrics\. Third, F/H/E state enforcement reduces part of that variability in the tested setting\. Fourth, ablations indicate that the reduction is not explained by JSON formatting alone\. We do not claim that CKM improves factual accuracy, ethical quality, or general reasoning capability\.

Recent studies have begun to quantify LLM output variability directly: Wang and Wang \[34\] found substantial inconsistency across 3\.4 million finance\-domain outputs under identical prompts, Atil et al\. \[61\] demonstrated nondeterministic variability even under fixed decoding parameters, and Haase et al\. \[62\] showed that within\-model variance components differ across task types\. This paper builds on that recognition but adds a structural intervention: instead of only observing variability, we test whether a specific state organization can reduce it\.

The rest of the paper is organized as follows\. Section 2 reviews related work and identifies the gap addressed by CKM\. Section 3 defines the CKM architecture and F/H/E state transition\. Section 4 defines the behavioral consistency metrics\. Section 5 describes the experimental design\. Section 6 reports the empirical results and ablations\. Section 7 discusses mechanisms, limitations, and implications\. Section 8 concludes\.

### 2\. Background and Related Work

This section surveys three streams of prior work that together motivate CKM and then identifies the specific gap we address\. §2\.1 reviews LLM consistency evaluation and its single\-dimensional limitations\. §2\.2 surveys cognitive architectures and structured reasoning frameworks from psychology and cognitive science\. §2\.3 examines structured output, memory, and state persistence approaches\. §2\.4 articulates the research gap that CKM addresses, and §2\.5 situates our contribution against concurrent and adjacent work\.

#### 2\.1 LLM Evaluation: Capability vs\. Consistency

The dominant paradigm for LLM evaluation focuses on task performance, measuring accuracy on standardized benchmarks \(MMLU, HumanEval, GSM8K\) while implicitly treating each evaluation instance as independent \[26\]\. This design reflects a specific assumption: that measuring what a model can do on diverse test items is sufficient for characterizing its utility\. Measuring how consistently it performs on identical items requires a fundamentally different experimental design, one based on repeated measurements rather than diverse sampling, and the capability paradigm provides no infrastructure for this\. Recent work on LLM calibration \[29\], prompt sensitivity \[30\], and positional bias \[31\] has begun to address aspects of this gap\.

Shyr et al\. \[33\] propose repeatability metrics for medical LLM evaluation, and Wang & Wang \[34\] assess output consistency across 3\.4 million finance outputs\. These studies measure variability as an observational phenomenon without structural intervention and employ single\-dimensional metrics that cannot detect the multi\-dimensional failure modes our data reveal \(e\.g\., simultaneous high SI and high DFR\)\. Our six\-metric suite addresses both limitations\.

#### 2\.2 Cognitive Architectures and Structured Reasoning

While these consistency measures capture variability as a phenomenon, they do not explain its structural origins\. Classical cognitive science offers frameworks for structured reasoning that speak to this question\. Dual\-process theory \[8\] posits fast and slow processing systems; metacognition research \[9\] emphasizes self\-monitoring; scaffolding theory \[10\] demonstrates that external structure aids reasoning\. Computational models such as SOAR \[16\], ACT\-R \[17\], and GOMS \[18\] provide structured frameworks with procedural memory but lack compatibility with modern LLM embeddings\. Critically, these frameworks provide structural proposals but lack quantitative evidence that their structures improve behavioral consistency\. Three examples illustrate this gap\.

SOAR separates modules by processing type without tagging epistemic provenance\. ACT\-R organizes knowledge by representation format \(chunks vs\. production rules\) rather than by information source\. CoALA \[44\] defines perception\-action\-memory loops without enforcing that perceived facts, inferred hypotheses, and evaluative judgments be structurally distinguished at the input stage\. More recently, Kim \[35\] introduces symbolic governance for neural reasoning and Kargupta et al\. \[36\] map cognitive elements onto reasoning traces, advancing cognitive structuring but without measuring whether such structuring yields measurable consistency gains \(Supplementary §S\-RW for extended discussion\)\.

#### 2\.3 Structured Output, Memory, and State Persistence

These cognitive frameworks propose structures but do not implement them within LLM systems\. Recent advances in structured LLM outputs, including JSON\-mode generation \[12\] and function calling \[13\], provide syntactic constraints that reduce formatting variability\. CKM extends this approach by enforcing not merely syntactic structure but semantic role separation \(Fact vs\. Heuristic vs\. Emotion\), requiring no weight modification \[22\]\. The distinction matters because our ablation data, confirmed by value\-only artifact control, show that semantic separation is the primary contributor to consistency improvement \(§6\.1\)\. Chain\-of\-Thought \[1\], Tree\-of\-Thought \[2\], Self\-Refine \[14\], and Graph\-of\-Thought \[11\] impose structure within isolated outputs without cross\-step consistency, leaving multi\-turn instability unaddressed\.

A growing body of work addresses state persistence\. A\-MEM \[38\] organizes memories via linking; Memoria \[39\] combines summarization with knowledge graphs; Mem0 \[40\] provides production\-grade continuity; and MemoryOS \[43\] proposes an OS abstraction for agent memory\. These systems address what to retain over time, optimizing retention measured via F1 or recall\. By contrast, CKM addresses a complementary question: how to categorize what is retained\.

Memory systems and CKM operate on orthogonal dimensions; a system can have perfect memory yet still conflate facts with inferences if it lacks epistemic role separation, a prediction our ablation data confirm, where format enforcement’s measured SI contribution was attributable to structural homogeneity rather than genuine semantic convergence, while semantic separation produced robust consistency gains \(§6\.1\)\. CKM does not replace memory systems; it provides the epistemic categorization layer that they lack\. In a layered architecture, memory systems would handle retention and retrieval while CKM would enforce that retrieved content is classified by provenance before entering the reasoning process\.

None of the memory systems quantifies the behavioral impact of persisted state on reasoning consistency\. Our DFR and SDR metrics directly address this gap, revealing that state persistence response varies dramatically across models \(DFR: 0\.01–0\.85\) in ways invisible to retention\-focused evaluation\.

#### 2\.4 Research Gap

The absence of a comprehensive consistency framework reflects two structural factors\. First, the dominance of the capability evaluation paradigm has directed community resources toward diverse\-item benchmarking rather than repeated\-measurement designs, leaving consistency measurement tools underdeveloped\. Second, the NLP and AI communities have not adopted the epistemological distinction between information types \(observed, inferred, evaluated\) as an organizing principle, despite its long history in both Western epistemology \[47\] and Indian pramana theory \[52\]\. The categorization of information by epistemic provenance has simply not been part of the computational vocabulary\.

As a result, the literature reviewed above leaves unaddressed the simultaneous provision of \(1\) a multi\-dimensional consistency measurement suite, \(2\) explicit state representation with epistemic role separation, \(3\) model\-agnostic structural enforcement, \(4\) cross\-vendor behavioral profiling, and \(5\) quantification of state persistence impact on downstream behavior\. Table 1 summarizes this comparison\.

Table 1\. Comparison with existing approaches\.

FeatureCoT/ToT \[1,2\]Agent Fw\. \[5–7\]Struct\. Output \[12,13\]Memory Sys\. \[38–43\]This WorkConsistency measurementNoNoNoNo6\-metric suiteState persistenceNoneImplicitNonePersistentExplicit state injectionCross\-model profilingNoNoNoNo26 models, 2 gen\.F/H/E semantic separationNoNoNoNoYesState impact measurementNoNoNoNoDFR/SDR
#### 2\.5 Concurrent and Adjacent Work

Several recent studies have independently investigated LLM output consistency as a primary research concern, confirming the practical importance of the phenomenon we address\. Atil et al\. \[61\] demonstrated that hosted LLM environments introduce nondeterministic variability even under fixed parameters, proposing TARr@N and TARa@N metrics for reproducibility assessment\. Wang and Wang \[34\] conducted 3\.4 million output comparisons across 50 repetitions in financial and accounting domains, finding substantial inconsistency in factual tasks\. Shyr et al\. \[33\] adapted statistical repeatability and reproducibility frameworks from metrology to evaluate medical diagnostic LLM outputs\.

Haase et al\. \[62\] decomposed within\-LLM variance using intraclass correlation coefficients, revealing that variance components differ substantially across task types\. Du et al\. \[63\] measured decision flip rates under identical\-prompt repetition in value\-reasoning contexts, finding that models reverse positions at nontrivial rates even without external pressure\.

While these studies individually establish that LLM consistency is a measurable and consequential property, our work integrates four elements that none addresses in combination: \(a\) epistemic provenance decomposition as a designable state variable for consistency, \(b\) a six\-metric behavioral measurement suite capturing distinct failure modes, \(c\) prompt\-level state enforcement as an experimental manipulation rather than merely an evaluation target, and \(d\) cross\-model behavioral profiling at the scale of 26 models from four vendors with 37,403 observations\. A recent survey \[64\] explicitly notes the absence of a comprehensive consistency benchmark, a gap our metric suite directly addresses\.

We also distinguish our zero\-perturbation reproducibility paradigm from perturbation\-based consistency evaluation, which measures response stability under input variation \(SCORE \[65\]; Zhang and Zhu \[66\]\); our design holds inputs constant and measures intrinsic output variability\.

A parallel line of work explores epistemic and cognitive classification within LLM systems\. NabaOS \[67\] applies Nyaya pramana categories \(pratyaksa, anumana, sabda, abhava\) to implement claim\-level provenance classification with cryptographic verification in LLM agents, sharing our grounding in Indian epistemological traditions\. However, NabaOS employs a four\-category pramana taxonomy oriented toward hallucination detection in tool\-execution pipelines, whereas our F/H/E framework integrates Western epistemology \(Audi \[47\]\) with Indian traditions in a three\-axis provenance classification designed for prompt\-level state enforcement and behavioral consistency profiling\.

MOLES \[68\] classifies 11 epistemic stances that models adopt toward their own knowledge claims; our framework classifies epistemic source types of the information entering reasoning, operating at a different level of analysis\. Kargupta et al\. \[36\] propose a 28\-element cognitive taxonomy validated across 170K traces but do not implement prompt\-level enforcement or measure behavioral consistency under structural intervention\.

We note two terminological clarifications\. First, the term “Cognitive Kernel” has been independently used for an LLM agent autopilot system \(Zhang et al\. \[69\]\); our Cognitive Kernel Model \(CKM\) is a prompt\-level epistemic state enforcement architecture with no architectural overlap\. Second, Pei et al\. \[70\] use the phrase “behavioral fingerprinting of large language models”; their work profiles behavioral styles and capabilities from single\-trial evaluations, whereas our behavioral profiling characterizes consistency and reproducibility under repeated trials with cognitive state manipulation\.

Several recent preprints address adjacent questions, mostly inpersona consistency / role\-playing agent stabilityrather than input\-side epistemic decomposition\. Tosato et al\. \[76\] \(PERSIST\) measure persona\-conditioned behavior stability across model scale, reasoning mode, and conversation history\. Luo and Laban \[78\] \(SPASM\) propose stable persona\-driven agent simulation for multi\-turn dialogue\. Liu et al\. \[79\] develop decoding\-time persona importance estimation for role\-playing agents\. Kim et al\. \[80\] \(PICon\) introduce multi\-turn interrogation for evaluating persona agent consistency\. These works probe whether assigned persona traits remain coherent across turns and contexts; our setting carries no assigned persona and measures behavioral consistency under repeated identical inputs, so the contributions are complementary rather than overlapping\.

A second adjacent strand examinesendpoint or latent\-state stability without persona conditioning\. Huang et al\. \[75\] document failure modes of latent state persistence in frontier LLMs\. Leshin et al\. \[77\] build a behavioral\-fingerprint Stability Monitor for detecting LLM endpoint behavioral drift via output\-distribution comparison\. Both characterize state or endpoint stability as a monitoring target rather than as a property modifiable by a structured input intervention\.

A third strand evaluatesconsistency under controlled input variation: Cavalin et al\. \[81\] \(CAT\) introduce metrics quantifying the consistency\-accuracy relation under controlled input variations\. Hsing \[82\] \(MIRROR, ICLR 2026 withdrawn\) proposes a modular architecture for personalized multi\-turn safety, sharing the multi\-turn\-stability concern at the architectural\-augmentation level\.

None of these works treats an input\-side epistemic decomposition as a controlled experimental manipulation, nor do they jointly measure repeated\-trial consistency \(SI\) and state\-persistent decision stability \(DFR\) on a cross\-vendor corpus of the present scale\. Our framing differs from PERSIST \[76\] and Pei et al\. \[70\] in a methodologically substantive way: rather than profiling behavioral consistency as an intrinsic, fixed property of each model, we treat it as a propertymodifiable by a prompt\-level epistemic intervention\. F/H/E decomposition thus enters the present design as a controlled independent variable, not a profiling target\.

### 3\. Architecture and Intervention: Cognitive Kernel Model

This section defines the intervention tested in the experiments\. TheCognitive Kernel Model \(CKM\)is not introduced as a new base model, cognitive architecture, or software kernel\. In this paper, CKM is a model\-agnostic prompt\-level state\-enforcement method for LLM decision tasks \(Figure 1\)\. It does three things:

1. 1\.it separates input information intoFact,Heuristic, andEmotionroles;
2. 2\.it requires the model to produce an output that respects those roles; and
3. 3\.when needed, it carries the resulting structured state into later turns\.

CKM is therefore both an intervention and a measurement aid\. As an intervention, it constrains how the model organizes information before deciding\. As a measurement aid, it exposes whether the model preserves that organization across repeated and multi\-turn trials\. CKM does not modify model weights\. It treats each LLM as a black\-box semantic processor and imposes structure externally through prompt\-level enforcement\. Throughout the paper, “CKM” refers to this tested F/H/E state\-enforcement method unless a broader, explicitly marked extension is being discussed\.

The motivation is straightforward\. Standard prompts ask the model to interpret a mixed text input directly\. CKM instead asks the model to first answer three bookkeeping questions: What is actually given? What is being inferred? What evaluative or priority signal is present? The hypothesis tested in this paper is that this bookkeeping reduces ambiguity in the reasoning state and thereby reduces behavioral variability\.

This prompt\-level design is a methodological choice rather than a convenience\. The central question is whether the same external state structure can improve consistency across many vendors and architectures\. Fine\-tuning would mix the state\-enforcement effect with model\-specific training effects and would make cross\-vendor comparison difficult\. Prompt\-level enforcement functions more like a runtime discipline: it constrains the interface through which reasoning is expressed, while leaving the underlying model unchanged\. We use this analogy only to locate the intervention; CKM is implemented as a structured prompt schema, not as operating\-system software\.

The remainder of this section develops CKM in four steps\. §3\.1 formalizes the kernel state and transition function\. §3\.2 describes the Tri\-Engine extension, which is included for architectural completeness but not evaluated in this paper\. §3\.3 specifies the prompt\-level schema used in the experiments\. §3\.4 explains why explicit state persistence is required for multi\-turn consistency\.

#### 3\.1 Kernel State and Transition Function

The kernel state is the structured record that CKM asks the model to maintain\. The term “kernel” is used in the limited sense of a minimal state record, not as a claim that the prompt acts like an operating\-system kernel\. It is also not intended to be a full model of human cognition\. It is a minimal operational state for decision consistency: a record of what the model treats as given, what it treats as inferred, and what it treats as evaluative or priority\-relevant\.

At timett, CKM represents this state as:

St=\{Ft,Ht,Et\}S\_\{t\}=\\\{F\_\{t\},H\_\{t\},E\_\{t\}\\\}
whereFtF\_\{t\}is theFactvector \(observable or verifiable information\),HtH\_\{t\}is theHeuristicvector \(inferred relations, assumptions, or uncertain interpretations\), andEtE\_\{t\}is theEmotionvector \(affective tone, salience, or value/priority signals\)\.111Competing\-interests disclosure\.Components of the CKM framework described in this paper are the subject of patent applications filed by an author of this paper\. These span both the mechanisms evaluated here—the F/H/E epistemic decomposition and the separation of epistemic roles—and broader specification elements that are not experimentally validated in this study, namely additional unvalidated state slots beyond the core F/H/E decomposition; multi\-axis persistence and hierarchical restoration of the cognitive state across sessions; and a fourth*testimony*\(TT\) provenance axis extending the F/H/E scheme \(§7\.6\)\. The applications are pending and not yet published, and identifiers are therefore omitted\. This disclosure is made in the interest of transparency; the experimental design, results, and their interpretation are reported independently of this intellectual\-property interest\.

##### Why separate at all?

The F/H/E decomposition addresses a specific failure mode: when reasoning systems process factual observations, speculative inferences, and affective evaluations as undifferentiated input, they conflate verified information with tentative hypotheses and allow emotional emphasis to contaminate logical structure\. Classical epistemology identifies this confusion, namely treating observed facts and speculative inferences as epistemically equivalent, as a primary source of reasoning instability \(Audi \[47\]\), and the problem is amplified in LLMs because all inputs arrive as homogeneous text tokens\. Epistemic provenance, the information about where a claim originates and how it was derived, is maintained in biological cognition through distinct sensory, inferential, and interoceptive channels\.

LLM token sequences carry no such labels, erasing these distinctions entirely\. Without external enforcement of these distinctions, models generally lack explicit mechanisms to prevent fact\-inference conflation, and the resulting ambiguity is associated with increased output variability\. CKM imposes separation at the input stage precisely to reduce this ambiguity\.

##### Why Fact, Heuristic, and Emotion specifically?

Given that separation is beneficial, the question becomes which categories to separate\. The three axes are organized by epistemic provenance, classifying information by how it arrived rather than by processing speed \[8\], functional domain \[58\], or phenomenal modality\. This criterion, while standard in epistemology \[47, 48\] and codified in Indian pramana theory as pratyaksa \(perception\) and anumana \(inference\) \[52\], has not been adopted as an organizing principle in any computational cognitive architecture\. Each axis serves an irreducible function\.FFgrounds reasoning in verifiable observations, helping to prevent hallucination\.HHmarks the boundary between known and assumed, helping to prevent unwarranted certainty\.

EEencodes priority and value signals that guide action selection\. This role for emotion is consistent with Damasio’s somatic marker hypothesis \[49\], Tappolet’s account of emotions as evaluative perceptions \[50\], and de Sousa’s argument that emotions solve the frame problem by directing attention to what matters \[51\]\. We draw on the shared insight from these traditions that emotion carries decision\-relevant information, while acknowledging that CKM operationalizes this insight through explicit tagging rather than the implicit somatic influence these authors describe\.

A two\-axis system \(FF\+HHonly\) would leave affective signals untagged, allowing emotional emphasis to infiltrate factual and inferential processing without explicit marking, a pattern we term epistemic contamination\. Adding a fourth or fifth axis is theoretically possible\. For example, Indian Nyaya epistemology recognizes testimony \(sabda\) as an independent source \[52\], and Mimamsa traditions enumerate up to six channels\. In this study, we treat three as a functionally sufficient partition for the present validation scope, and we note the testimony dimension as a natural extension in §7\.6\.

##### What is novel about this decomposition?

While the individual components of this partition have precedents in philosophy and cognitive science, their specific combination is novel\. The specific novelty lies in three simultaneous moves that no reviewed framework performs together\. First, CKM splits the traditional “cognition” category into perception\-as\-given \(FF\) and inference\-as\-derived \(HH\), a separation that Hilgard’s cognition\-affection\-conation trilogy \[58\] leaves implicit\. Second, it elevates emotion from a modulator or output, as treated in dual\-process theory \[8\] and predictive processing \[59\], to an input\-level information channel with mandatory tagging\.

Third, it organizes all three by epistemic provenance rather than by processing speed \(Kahneman’s System 1/System 2 \[8\]\), control level \(Stanovich’s reflective/algorithmic/autonomous \[60\]\), or motivational conflict \(Plato’s tripartite soul\)\. The closest precedent is the Social Information Processing model \[53, 54\], which integrates cognitive, emotional, and behavioral components, but that framework is specific to social situations; CKM operates as a domain\-general epistemic state layer\. Importantly, we do not claim that F/H/E is the unique decomposition, nor that it models human cognition; we claim it is a functionally sufficient partition for reducing output variability, and our data support this claim\.

##### Why is this separation especially important for LLMs?

The importance of explicit separation becomes clear when we consider what LLMs lack\. For biological cognizers, epistemic provenance is partially maintained by distinct neural pathways: sensory channels tag perceptual input, metacognitive processes flag inferential uncertainty, and interoceptive signals carry affective information \[49, 55\]\. LLMs lack these architectural separations\. All inputs, whether sourced from verified databases, speculative reasoning, or value\-laden descriptions, arrive as undifferentiated token sequences\. This homogenization means that without external structural enforcement, the model may process a verified statistic and an unsubstantiated inference with identical computational status\.

In practical terms, token sequences carry no explicit labels indicating whether a statement is verified or merely inferred\. CKM provides the external enforcement that the architecture itself cannot supply, functioning as an epistemic provenance layer above the model\.

##### Empirical confirmation

The preceding arguments establish the theoretical rationale for F/H/E separation; we now show that these design choices also receive empirical support from our data\. The ablation study \(§6\.1\) confirms that F/H/E semantic separation is the primary contributor to consistency improvement, with value\-only analysis confirming that format enforcement’s measured SI effect reflects structural homogeneity rather than semantic convergence \(§6\.1, Supplementary §S\-Robustness\)\. The 2\.4\-fold larger CKM effect in ambiguity\-dominant scenarios observed in the Legacy cohort \(§6\.3\) is consistent with the prediction that F/H/E separation most directly addresses fact\-inference conflation, which is precisely the condition that ambiguity scenarios impose\.

In the primary NewModels cohort \(n = 12\) this differentiation collapses to a 1\.07\-fold ratio \(ambiguityΔ\\DeltaSI \+0\.0416 vs\. non\-ambiguity \+0\.0443; §6\.3\), consistent with §7\.2’s discussion of cohort\-specific mechanism weighting\. The 98\.4% LLM valid rate across 26 models \(§3\.3\) suggests that the decomposition is practically realizable without model\-specific adaptation, and the human pilot \(§7\.3\) found perfect F/H/E compliance in the manually reviewed CKM subset \(0 violations / 15 annotated responses; §S11\.2\), providing preliminary indication that the separation is compatible with existing cognitive categorization abilities, though demand characteristics in a small sample cannot be ruled out\.

The preceding evidence addresses whether F/H/E separation works; a separate question is whether the choice of three axes is principled or arbitrary\. An analogy from color science clarifies the point but requires refinement: RGB is not merely an engineering convenience but reflects the biological structure of human trichromatic vision\. Similarly, F/H/E is not arbitrary but grounded in epistemologically established cognitive role separations\. However, just as RGB is not the only color space \(HSV and CMYK serve different purposes\), F/H/E is not the only possible decomposition; it is one optimized for reasoning stability, and we make no stronger claim\.

With the F/H/E partition established, we now define how the kernel state evolves over time\. CKM\-Core evolves according to a deterministic state transition function:

St\+1=δ​\(St,Ωx,t,ΩtEngine\)S\_\{t\+1\}=\\delta\(S\_\{t\},\\Omega\_\{x,t\},\\Omega^\{\\text\{Engine\}\}\_\{t\}\)
whereΩx,t\\Omega\_\{x,t\}is the normalized input bundle andΩtEngine\\Omega^\{\\text\{Engine\}\}\_\{t\}represents aggregated engine outputs\. Determinism here refers only to the formal state\-update rule: given identical initial state and input sequence, the resulting represented state is uniquely determined\. It is not a claim that the underlying LLM computation is deterministic across hosted API calls\.

#### 3\.2 Tri\-Engine Architecture

CKM\-Core handles state and decomposition; a separate architectural layer can process this normalized state through multiple specialized engines\. The CKM framework can be extended with a multi\-engine processing architecture \(Ψ\\Psi\-Architect, DecisionEngine, Meta\-Structure\) that operates on the normalized Kernel State; this extension is not evaluated in the present study and is left as a direction for future work \(§7\.6\)\.

![[Uncaptioned image]](https://arxiv.org/html/2607.24765v1/x1.png)

Figure 1\. Cognitive Kernel Model \(CKM\) for LLM Behavioral Consistency\.Four\-panel conceptual overview: \(a\) Problem: LLM consistency variability on identical inputs; \(b\) Experimental Design: F/H/E decomposition, 4\-arm ablation, 26 LLM models; \(c\) Key Findings: under CKM, SI increases relative to free\-form control \(with the largest gains in models with the lowest baseline consistency, a behavioral\-variance reducer pattern; see §6\.3\), and DFR decreases sharply under state persistence \(single\-turn CKM vs\. persisted CKM\); \(d\) Behavioral Taxonomy: Tier S/A/B/C model archetypes distributed in the DFR\-SI behavioral space \(see §6\.3 for tier definitions\)\.

#### 3\.3 CKM as Prompt\-Level Enforcement

In implementation, CKM is simply a structured instruction given to the model before it answers\. The model is not asked merely to format its answer as JSON; it is asked to classify the information it uses before choosing an action\. The standard implementation used in this study is a 5\-slot JSON schema:

\{

"fact":\["observable,verifiableinformation"\],

"heuristic":\["inferredrelations\(markedwith'\(inferred\)'\)"\],

"emotion":\{"code":"E3","intensity":4\},

"action":\{"code":"A1"\},

"reason":"decisionrationalelinkingF/H/Etochosenaction"

\}

This schema was applied uniformly across all 26 models\. LLMs achieved a 98\.4% valid rate \(24,054/24,443 LLM\-only observations across two generations\), and the full\-corpus valid rate including the Exp1 human pilot is 96\.7% \(24,092/24,923\); Exp1’s 38 valid of 480 designed responses reflects human participant workload rather than data quality issues \(§7\.3, Supplementary §S11\)\. These rates confirm that LLMs can reliably comply with F/H/E requirements without model\-specific adaptation\. Enforcement operates through two mechanisms: schema compliance forcing explicit slot filling, and semantic role separation requiring verifiable facts together with uncertainty\-marked heuristics and coded emotions\.

CKM is realized through prompt\-level enforcement; alternative architectural configurations exist but are beyond the scope of this study\. All quantitative results in §6 are based on the standard F/H/E implementation\.

#### 3\.4 Why state persistence is necessary

LLMs are fundamentally stateless: each API call resets the computation, and no mechanism inherently carries reasoning context across turns\. Commercial chat interfaces create an appearance of continuity by re\-injecting prior conversation history into each new context window or by maintaining separate memory modules, but the underlying model itself retains no state between calls; it processes each context window as if encountering the conversation for the first time\. Recent empirical work confirms that frontier LLMs fail to maintain latent state across turns even when explicitly instructed to do so \[75\], providing independent justification for external prompt\-level enforcement\.

Decision consistency in multi\-turn interactions therefore requires explicit state injection, because without it, each turn begins from a blank slate and the model has no basis for maintaining coherence with prior outputs\. The CKM\_PERSIST condition tests this by injecting Turn 1 output as structured context for Turn 2\. The results reveal that state persistence response is itself a diagnostic tool: some models achieve DFR near zero under injection while others exhibit DFR near 0\.85, exposing a model\-intrinsic property that is largely invisible without state persistence measurement \(§6\.2\)\.

Progressive stabilization under chain protocols \(§6\.2\) provides preliminary evidence that iterated state enforcement can drive the system toward more stable behavioral attractors\.

### 4\. Behavioral Consistency Metrics

This section defines the measurement side of the claim chain\. CKM is evaluated with metrics designed for repeated behavior, not single\-answer accuracy\. Standard NLP metrics such as BLEU, ROUGE, and F1 require reference answers and therefore do not fit open\-ended decision scenarios where no single correct answer exists\. Conversely, a simple repeatability score is not enough: a model can keep similar wording while changing its action, or preserve an action while drifting semantically\.

We therefore measure behavioral consistency along several axes\. The main question behind each metric is deliberately simple:

- •SI:Do repeated answers to the same input stay semantically close?
- •CRR:Does the model retain the relevant facts from the scenario?
- •DFR:Does the model change its selected action when prior state is injected?
- •FCS:Under fixed anchor states, does the model repeatedly choose the same action?
- •ACS:How concentrated or dispersed are the selected actions across repetitions?
- •SDR:Does the structured F/H/E state survive propagation across turns?

The independence of these axes is part of the empirical claim\. In §6\.3, for example, some models show high single\-turn SI but high multi\-turn DFR, meaning that single\-turn semantic stability does not guarantee decision stability under state persistence\. This is why the paper reports a metric suite rather than a single consistency score\.

#### 4\.1 Semantic Integrity \(SI\)

We begin with the most basic consistency question: given identical inputs, do the model’s responses converge semantically? SI quantifies this convergence\.

SI measures semantic similarity of responses to identical prompts acrossKKrepetitions:

S​I​\(m,s,c\)=1K​∑i=1Kcos⁡\(𝐞i,𝐞¯\)SI\(m,s,c\)=\\frac\{1\}\{K\}\\sum\_\{i=1\}^\{K\}\\cos\(\\mathbf\{e\}\_\{i\},\\bar\{\\mathbf\{e\}\}\)
where𝐞i=SentenceBERT​\(responsei\)\\mathbf\{e\}\_\{i\}=\\text\{SentenceBERT\}\(\\text\{response\}\_\{i\}\)and𝐞¯=1K​∑j=1K𝐞j\\bar\{\\mathbf\{e\}\}=\\frac\{1\}\{K\}\\sum\_\{j=1\}^\{K\}\\mathbf\{e\}\_\{j\}is the L2\-normalized centroid of theKKresponse embeddings\. We useparaphrase\-multilingual\-mpnet\-base\-v2\(768\-dim\), selected through sensitivity analysis showing that English\-optimized alternatives produce ceiling compression on Korean text, yielding null effect sizes \(d=0\.05d=0\.05; see Supplementary §S1\)\. To control for the possibility that JSON schema elements \(recurring keys such as"fact","heuristic"\) inflate cosine similarity through structural homogeneity rather than semantic convergence, we computed a value\-only SI variant \(SI′\) by stripping all JSON keys and structural syntax before embedding\.

The value\-only SI preserved the CKM effect \(g=2\.88g=2\.88, 100\.8% retention; Supplementary §S\-Robustness\), confirming that the measured consistency improvement reflects semantic content rather than format artifacts\.

Interpretation boundary\.SI is an embedding\-based operational proxy for within\-framework semantic convergence, not a direct measure of reasoning correctness or decision quality\. High SI indicates that a model’s responses cluster in embedding space under a given prompt structure \(a necessary but not sufficient condition for accurate reasoning\)\. Convergence toward shared error remains possible, and SI should be interpreted alongside behavioral metrics \(DFR, SDR\) and the claim boundaries stated in §1\.

#### 4\.2 Context Retention Rate \(CRR\)

While SI captures same\-turn convergence, CRR addresses whether prior context is preserved across turns, a prerequisite for any multi\-turn stability claim\.

C​R​R=\|\{fj∈Fgold∣∃si∈R,sim​\(si,fj\)\>θ\}\|\|Fgold\|CRR=\\frac\{\|\\\{f\_\{j\}\\in F\_\{\\text\{gold\}\}\\mid\\exists\\,s\_\{i\}\\in R,\\ \\text\{sim\}\(s\_\{i\},f\_\{j\}\)\>\\theta\\\}\|\}\{\|F\_\{\\text\{gold\}\}\|\}
whereFgoldF\_\{\\text\{gold\}\}is the set of mandatory scenario facts andθ=0\.75\\theta=0\.75\. CRR captures information loss through the reasoning process\.

#### 4\.3 Decision Flip Rate \(DFR\)

Semantic similarity can mask decision instability: a model may produce similar text while reversing its conclusion\. DFR isolates the decision\-level changes that SI cannot detect\.

D​F​R​\(m\)=\|\{\(i,j\):aT​1,i≠aT​2,j\}\|NmatchedDFR\(m\)=\\frac\{\|\\\{\(i,j\):a\_\{T1,i\}\\neq a\_\{T2,j\}\\\}\|\}\{N\_\{\\text\{matched\}\}\}
Lower DFR indicates greater decision stability under state persistence\. Our DFR measures binary decision changes across repeated identical trials without external pressure, distinguishing it from adversarial flip rates that measure capitulation under challenge \[71, 72\], value\-reasoning flip rates in constrained domains \[63\], and confirmation\-bias reversal rates under counter\-evidence exposure \[73\]\.

#### 4\.4 Few\-shot Coherence Score \(FCS\)

Beyond single\-trial stability, FCS measures how consistent a model’s responses are across multiple repetitions of the same prompt, capturing coherence under repeated sampling\.

F​C​S​\(m,s\)=maxa⁡\|\{k:ak=a\}\|KFCS\(m,s\)=\\frac\{\\max\_\{a\}\|\\\{k:a\_\{k\}=a\\\}\|\}\{K\}
Under fixed anchor states, FCS quantifies intrinsic model randomness\.

#### 4\.5 Action Consistency Score \(ACS\)

Beyond semantic and decision consistency, ACS captures whether the action path selected across repetitions remains stable\. This matters when downstream systems consume only the recommended action rather than the full response\.

A​C​S=1−H​\(𝐩\)log2⁡\|A\|ACS=1\-\\frac\{H\(\\mathbf\{p\}\)\}\{\\log\_\{2\}\|A\|\}
whereH​\(𝐩\)H\(\\mathbf\{p\}\)is the Shannon entropy of the action distribution\. This behavioral trial\-to\-trial measure is distinct from cross\-modal text\-visual fidelity scores that share the ACS abbreviation in recent GUI agent literature \[74\]\. In the present scenario set, CRR and ACS showed limited discriminative power: CRR was compressed against its upper bound because the key\-fact inventory for each scenario is largely recoverable from the prompt itself, while ACS varied in a narrow range around 0\.65–0\.70 with no consistent CKM/Control ordering \(Exp2 scenario\-level means: ACS = 0\.69 Control vs\. 0\.65 CKM\)\. Neither metric discriminated models or conditions in ways that altered the primary findings\.

The quantitative analyses in this paper therefore rely on SI, DFR, FCS, and SDR, which showed clear discriminative power across the model cohort \(Table 2\)\. Per\-scenario CRR and ACS values are archived with the canonical datasets for completeness \(Supplementary §S15\)\.

#### 4\.6 Semantic Drift Resistance \(SDR\)

State persistence is only effective if the kernel state itself is preserved across turns\. SDR measures how much of the F/H/E content survives a state injection\.

S​D​R​\(m\)=1Nmatched​∑\(i,j\)cos⁡\(𝐞T​1,iF​H,𝐞T​2,jF​H\)SDR\(m\)=\\frac\{1\}\{N\_\{\\text\{matched\}\}\}\\sum\_\{\(i,j\)\}\\cos\(\\mathbf\{e\}\_\{T1,i\}^\{FH\},\\mathbf\{e\}\_\{T2,j\}^\{FH\}\)
Higher SDR indicates greater state preservation across turns\. Our SDR quantifies intrinsic semantic drift across repeated identical trials, distinct from adversarial context\-switching evaluations that employ superficially similar terminology under perturbation paradigms\.

Table 2\. Metric summary\.

MetricMeasuresScaleFailure ModeSISemantic variability0–1 \(↑\\uparrow\)Response driftCRRInformation retention0–1 \(↑\\uparrow\)Context lossDFRDecision instability0–1 \(↓\\downarrow\)State sensitivityFCSAction consistency0–1 \(↑\\uparrow\)Action randomnessACSPopulation convergence0–1 \(↑\\uparrow\)Inter\-agent disagreementSDRState preservation0–1 \(↑\\uparrow\)Cognitive drift

### 5\. Experimental Design

This section explains how the consistency claims were tested\. The design has three constraints\. First, the intervention must be evaluated across vendors, because CKM is claimed to be model\-agnostic\. Second, each scenario must be repeated enough times to measure variability rather than isolated performance\. Third, the mechanism must be separated from superficial formatting, because an apparent consistency gain could otherwise be caused by JSON structure alone\.

Accordingly, §5\.1 summarizes the experiment set and rationale\. §5\.2 documents the models and scenarios\. §5\.3 defines the four core conditions: Control, CKM, CKM\_PERSIST, and Chain\. §5\.4 summarizes the statistical methods; full derivations are provided in Supplementary §S12\.

#### 5\.1 Overview

We conducted four core experiments, a 4\-arm ablation study, a 5\-arm sham\-restriction ablation, and a temperature robustness probe\. Core experiments were replicated on a NewModels cohort \(13 models collected, 2025–2026; 12 primary after exclusion of gpt\-4\.1\-mini, see below\), yielding 37,403 observations across two generations \(35,475 in the primary 12\-model cohort plus 1,928 from gpt\-4\.1\-mini reported in the §6\.6 case study\) \(Table 3\)\. The experimental design reflects several deliberate choices\. The 4\-vendor, 2\-generation structure is necessary because the model\-agnostic claim requires evidence that effects are not vendor\-specific artifacts; a single\-vendor study would leave this confound unresolved\.

TheK=10K=10repetition count balances centroid stability for SI computation \(centroids computed from fewer than 5 repetitions are unreliable\) against API cost constraints across 26 models and 8 scenarios\. The 4\-arm ablation \(§6\.1\) was designed specifically to preempt the critique that CKM effects reduce to “advanced prompt engineering” by orthogonally decomposing format enforcement and semantic role separation in a 2×2 factorial design\.

Table 3\. Experimental overview\.

ExpTargetComparisonNobsN\_\{\\text\{obs\}\}Primary MetricsExp1Human \(n=6n=6\)Control vs CKM480SI \(proxy\), ACSExp2LLM \(19 Legacy\)Control vs CKM3,040SI, CRR, FCSExp2\-NMLLM \(12 NM primary\)Control vs CKM1,920SIExp3LLM \(19 Legacy\)CKM vs CKM\_PERSIST4,670†SI, DFR, SDRExp3\-NMLLM \(12 NM primary\)CKM vs CKM\_PERSIST3,840SI, DFR, SDRExp3 ExtraLLM \(16 Legacy\)T1→T2→T3 Chain2,655SI, FCS, DFR, SDRExp3X\-NMLLM \(12 NM primary\)T1→T2→T3 Chain2,014SI, DFR, SDRStudy ALLM \(6 Legacy\)4\-Arm Ablation768\+728SIStudy BLLM \(12 NM primary\)4\-Arm Ablation3,840SIExp6LLM \(12 NM primary\)5\-Arm Sham Ablation11,520§SI, DFR, SDRPrimary Total35,475Full corpus¶37,403§Exp6 collected 3 new sham arms \(Sham\-A/B/C, 3,840 each for 12 primary models = 11,520 new records\)\. Vanilla and CKM data reused from Exp2\-NM and Exp3\-NM respectively\.

¶Full corpus \(37,403\) = 35,475 primary \+ 1,928 gpt\-4\.1\-mini observations collected with the 13\-model set but excluded from primary analysis due to vendor deprecation \(see §5\.2, §6\.6\)\. The case study data are reported in §6\.6 and the sensitivity analysis \(§S\-Sensitivity\)\. Primary total \(35,475\) reflects the 12\-model active cohort \(ablation\_newmodels\_metrics\_v1\.2\_active12\.json,exp3extra\_newmodels\_metrics\_v1\.2\_active12\.json\) used in all primary analyses\.

†Exp3N=4N=4,670 is the design\-level matched\-pair count\. The canonical analysis dataset \(SHA256:16d04208\.\.\.\) contains Exp3 records within a combined Exp3/Exp3Extra file \(N=7N=7,479\); metrics are computed on the Exp3\-tagged subset\. grok\-2\-latest \(33/240 records, S1–S2 only\) was excluded from analysis due to incomplete collection\.

‡Legacy cohort composition: 21 total unique models collected across vendors\. Exp2 and Exp3 each analyze 19 Legacy models; Exp3 Extra analyzes 16 Legacy models; Study A \(ablation\) analyzes 6 Legacy models\. The “17/19 positive effects” in the Abstract refers to Exp2’sn=19n=19subset: 17 models showed positiveΔ\\DeltaSI; the two exceptions \(claude\-3\-haiku, claude\-haiku\-4\-5\) showed near\-zero or slightly negativeΔ\\DeltaSI\. The 26\-model headline combines 21 Legacy \+ 13 NewModels \(collected\) − 8 overlapping models in cross\-generation comparison\. The primary NewModels analysis uses 12 models \(gpt\-4\.1\-mini excluded\); the combined analysis pools 19 Legacy \+ 12 NewModels = 31 model\-level pairs\.

#### 5\.2 Models and Scenarios

Our cross\-generation, cross\-vendor claim requires a principled model selection; we describe the resulting 26\-model cohort and the 8\-scenario protocol derived from pilot testing\.

We selected 26 unique models spanning four vendors across two generations: a Legacy cohort \(21 models, 2024–2025\) and a NewModels cohort \(13 models collected, 2025–2026, spanning 4 vendors×\\times3 tiers: Flagship/Standard/Fast\)\. We define two NewModels sub\-cohorts:

- •NewModels\-12 \(primary\): Excludes gpt\-4\.1\-mini\. OpenAI issued a deprecation notice for gpt\-4\.1\-mini on 2026\-02\-13, overlapping with our data collection window \(2026\-02\-15 to 2026\-03\-11\)\. Independent reports documented instruction\-following degradation during this period\. All primary aggregate statistics, per\-model tables, and inferential tests in §6 use this 12\-model cohort\.
- •NewModels\-13 \(sensitivity\): Includes gpt\-4\.1\-mini\. Reported in the case study \(§6\.6\) and sensitivity analysis \(Supplementary §S\-Sensitivity\) to demonstrate that all directional findings are preserved regardless of inclusion\.

The exclusion combines two vendor\-side criteria documented before data inspection, namely \(1\) vendor\-issued deprecation notice during the collection window and \(2\) independent reports of instruction\-following degradation, with a third post\-hoc anomaly\-detection criterion \(3\) identified after data collection: an anomalous behavioral profile relative to the cohort, namely the sole model in which DFR\_persist \> DFR\_ckm\. Two further criteria govern the reporting protocol rather than the exclusion decision itself: \(4\) removal does not change the direction of any primary finding \(verified via the §S\-Sensitivity 13\-model re\-analysis after the exclusion was applied\), and \(5\) full transparency via the §6\.6 case study and sensitivity reporting\.

We do not characterize this five\-element procedure as a pre\-registered analysis plan; criteria \(3\) and \(4\) are explicitly outcome\-dependent and were operationalized after the data were observed\. We retain the exclusion because criteria \(1\)–\(2\) constitute vendor\-side evidence that the gpt\-4\.1\-mini observations may reflect a transient deprecation\-window state rather than a stable model, and we report both the 12\-model primary results and the 13\-model sensitivity results so that readers can apply their own interpretive weighting\.

Eight overlapping models enable cross\-generation comparison\. Full model lists are provided in Supplementary §S22 \(NewModels\) and §S\-App \(Legacy coverage matrix\)\.

Ten scenarios were initially designed, spanning ambiguity resolution, ethical conflict, resource allocation, and error handling\. Two scenarios \(S7 and S8\) were discarded after pilot testing revealed insufficient ambiguity to elicit meaningful response variability; the original numbering was preserved for traceability with data collection logs\. S6 was initially excluded due to apparent near\-uniform responses in pilot data, but re\-examination of the full dataset revealed sufficient discriminative variance across conditions, prompting its retention in the main analysis\. The remaining eight scenarios \(S1–S6, S9, S10\) were used across all experiments \(Supplementary §S4 for full texts\)\.

The student daily\-life domain was selected because it provides decision situations where no objectively correct answer exists, forcing models to exercise judgment rather than recall factual knowledge\. Domains with clear correct answers \(e\.g\., medical diagnosis with known conditions, mathematics\) would confound consistency measurement with accuracy measurement\. Student scenarios naturally juxtapose factual constraints, uncertain inferences, and affective considerations, making them well\-suited for testing whether F/H/E decomposition improves reasoning stability under conditions where all three information types co\-occur\.

#### 5\.3 Conditions

With models and scenarios fixed, the remaining design dimension is the experimental manipulation\. Four conditions isolate structural enforcement from state persistence, and both from multi\-turn chaining\.

Four experimental conditions were employed\. In the Control condition, models produced free\-form responses with no structural enforcement\. In the CKM condition, models produced JSON\-structured responses with mandatory F/H/E fields\. The CKM\_PERSIST condition followed a two\-turn protocol in which Turn 1 output was injected as context for Turn 2\. The Chain condition extended this to a three\-turn protocol \(T1 anchor, T2 branch×\\times10, T3 chain×\\times10\)\.

#### 5\.4 Statistical Methods

Given the small\-sample, cross\-model structure of our design, standard parametric tests alone are insufficient; we combine parametric and nonparametric methods with bootstrap confidence intervals\.

The primary unit of analysis was model\-level means paired across conditions\. We used pairedtt\-tests \(two\-tailed\) and permutation tests \(10,000 resamples, seed = 42\) for robustness, with Hedges’ggeffect sizes accompanied by 2,000\-resample bootstrap 95% CIs \(seed = 42\)\. Legacy effect sizes are reported as Hedges’ggthroughout for cross\-cohort comparability \(Cohen’sddvalues, where also computed, are provided in Supplementary §S\-Exp2\)\.

Multiple comparison correction followed the Holm\-Bonferroni procedure applied within each pre\-defined confirmatory hypothesis family: \(a\) the 4\-arm ablation contrasts \(H1, H2, H3a, H3b, H3\-synergy; family size 5; Table 6\); \(b\) the 5\-arm sham\-restriction pairwise comparisons computed separately for SI and DFRpersist\{\}\_\{\\text\{persist\}\}\(10 pairwise tests per metric; Table 11\); and \(c\) the per\-metric paired contrasts within each NewModels experiment \(e\.g\., DFR/SI/SDR for Exp3\-NM, family size 3; Table 7\)\. Cross\-table corrections are not applied; tier\-classification analyses, scenario\-level breakdowns, and the behavioral\-variance reducer analysis are reported as exploratory and not Holm\-corrected\. Robustness checks included Wilcoxon signed\-rank tests and logit\-transformedtt\-tests \(Supplementary §S12 for full statistical methods\)\.

### 6\. Results

The results follow the same claim chain introduced in §1\. §6\.1 asks whether CKM changes repeated\-output consistency and then decomposes the effect into format and semantic components\. §6\.2 asks whether explicit state persistence changes decision flipping and chain stability\. §6\.3 treats the resulting SI–DFR patterns as behavioral profiles rather than capability scores\. §6\.4 reports robustness checks\. §6\.5 reports the sham\-restriction ablation, which separates structural scaffolding from epistemic content\. §6\.6 presents an excluded\-model case study for transparency\.

The results are organized around four questions\.

1. 1\.Does F/H/E state enforcement reduce repeated\-output variability?\(§6\.1\)
2. 2\.Is the effect caused by epistemic role separation, or merely by structured formatting?\(§6\.1 and §6\.5\)
3. 3\.Does carrying structured state forward reduce decision flipping across turns?\(§6\.2\)
4. 4\.Do different model families have distinct behavioral consistency profiles?\(§6\.3–§6\.6\)

All results should be read within the paper’s claim boundary: the experiments measure consistency, not correctness\. A higher SI or lower DFR indicates greater stability under the tested protocol, not necessarily a better decision\.

#### 6\.1 CKM Effectiveness and Mechanism

We begin with the primary effectiveness question \(does CKM improve consistency?\) and then decompose the mechanism via the 4\-arm ablation\. Structural compliance results come first; the ablation isolates which component of CKM does the work\.

##### Structural Compliance \(Exp2\)

Exp2 tested whether CKM’s structural enforcement produces measurable SI gains under standard conditions across a broad Legacy cohort\.

Across 19 Legacy models \(N=3N=3,040\), CKM enforcement increased SI by \+0\.016 \(Hedges’g=1\.18g=1\.18,p=6\.55p=6\.55×\\times10\-5, parsed\-field SI\), with 17/19 models showing positiveΔ\\DeltaSI \(Figure 2\)\. SI was computed from parsed\-field text \(concatenation of thefactlist andreasonstring extracted from the JSON response\), which is inherently free of JSON structural artifact by construction \(see §4\.1 and Supplementary §S\-Robustness for the NewModels raw\-output cohort, where an explicit artifact control was applied\)\.

The raw\-output basis \(Option B in §S\-Exp2\) yieldsg=0\.61g=0\.61,p=0\.012p=0\.012, 14/19 positive; both bases are reported in §S\-Exp2 as a sensitivity comparison, and parsed\-field is adopted as primary throughout this paper to maintain a single SI substrate consistent with §4\.1\.

Table 4\. Aggregate SI results by cohort\.

CohortNmodelsN\_\{\\text\{models\}\}Δ\\DeltaSIEffect sizepp\-valueLegacy \(Exp2\)19\+0\.016g=1\.18g=1\.186\.55×\\times10\-5NewModels\-12 \(Exp2\-NM, primary\)12\+0\.021g=3\.08g=3\.081\.82×10−71\.82\\times 10^\{\-7\}Combined \(Legacy \+ NM\-12\)31\+0\.018g=1\.53g=1\.539\.0×10−109\.0\\times 10^\{\-10\}Random\-effects meta\-analysis across all 31 model\-level effects yieldsgREg\_\{\\text\{RE\}\}= 1\.09, 95% CI \[0\.83, 1\.35\],I2I^\{2\}= 77\.6%, indicating a robust effect with substantial between\-model heterogeneity\. The Combined\-rowΔ\\DeltaSI = \+0\.018 in Table 4 is computed as the unweighted mean of the 31 model\-levelΔ\\DeltaSI values \(each model contributing one effect\), not as the cohort\-size\-weighted average \(which would be \(19×\\times0\.016 \+ 12×\\times0\.021\) / 31 = 0\.0179, agreeing with the unweighted figure to three decimal places\)\.

Practical\-significance qualifier: SI is bounded above by 1\.0, and the Control baseline in this study clusters around SI≈\\approx0\.95 \(Legacy\) and 0\.95 \(NM\), leaving a measurement headroom of approximately 0\.05 absolute units; the observedΔ\\DeltaSI of \+0\.016 \(Legacy parsed\-field\) and \+0\.021 \(NM\-12\) thus correspond to roughly 32% and 42% of the available headroom, respectively\. Effect\-size interpretation in Hedges’ggshould be read against the small within\-pair variance characteristic of model\-level paired designs, which inflatesggrelative to per\-trial designs at the same absoluteΔ\\Delta\.

The primary NewModels replication \(12/12 positive,g=3\.08g=3\.08\) substantially exceeded the Legacy effect \(g=1\.18g=1\.18parsed\-field\), and among 8 overlapping models, 7/8 showed largerΔ\\DeltaSI in the newer cohort\. Tier\-level analysis revealed that Flagship models \(Δ\\DeltaSI = \+0\.025,n=4n=4\) showed the largest gains, followed by Fast \(\+0\.021,n=4n=4\) and Standard \(\+0\.017,n=4n=4\)\. Per\-model results are in Supplementary §S\-Exp2\.

![[Uncaptioned image]](https://arxiv.org/html/2607.24765v1/x2.png)

Figure 2\. Hedges’ggforest plot for 19 Legacy models\.CKM effect size with 95% bootstrap CI, ordered by effect magnitude\. The dashed vertical line marks the aggregate effect \(g=1\.18g=1\.18, parsed\-field SI\)\. GPT family models show the largest positive effects; Claude family models show near\-zero or slightly negative effects\.

##### Ablation: Format vs\. Semantic Separation \(Study B\)

Effectiveness without mechanism decomposition would leave open the critique that any measured gain reflects JSON format rather than epistemic role separation\. Study B orthogonally decomposes these two factors\.

The 4\-arm ablation \(N=3N=3,840, 12 primary NewModels; gpt\-4\.1\-mini excluded from primary cohort and analyzed separately in §6\.6 case study\) crossed format enforcement \(JSON vs\. free\-form\) with semantic role separation \(F/H/E vs\. none\) \(Table 5\)\. Statistics below are computed fromablation\_newmodels\_metrics\_v1\.2\_active12\.json\(n = 12\)\.

Table 5\. Ablation arm design and results\.

ArmFormatSemanticMean SIControlFree\-formNone0\.960JSON\-OnlyJSONNone0\.977F/H/E\-OnlyFree\-formF/H/E0\.981Full CKMJSONF/H/E0\.985Table 6\. Study B planned contrasts \(Holm\-corrected, n = 12 paired models\)\.

HypothesisComparisonHedges’ggpHolmp\_\{\\text\{Holm\}\}H1: Format effectJSON vs Control1\.875†1\.16×10−41\.16\\times 10^\{\-4\}\*\*\*H2: Semantic effectF/H/E vs Control2\.6375\.32×10−65\.32\\times 10^\{\-6\}\*\*\*H3a: Semantic over formatCKM vs JSON1\.2632\.59×10−32\.59\\times 10^\{\-3\}\*\*H3b: Format over semanticCKM vs F/H/E1\.2312\.59×10−32\.59\\times 10^\{\-3\}\*\*Combined effect \(artifact\-driven\)CKM vs max\(JSON, F/H/E\)0\.8351\.99×10−21\.99\\times 10^\{\-2\}\*†Value\-only recomputation \(Supplementary §S\-Robustness\) revealed that H1’s measured effect \(g=1\.875g=1\.875\) reflects JSON structural homogeneity rather than semantic convergence \(value\-onlyg=−0\.20g=\-0\.20, ns\)\. H2’s effect was fully preserved \(value\-onlyg=2\.24g=2\.24,p<10−6p<10^\{\-6\}\)\. Original statistics are retained for transparency; see §S\-Robustness Table S\-R3 for corrected effect sizes\.

Under the original SI measurement, both format enforcement and F/H/E semantic separation showed significant effects \(Table 6\)\. However, value\-only recomputation, which strips all JSON keys and structural syntax before embedding, revealed a critical dissociation: the F/H/E semantic separation effect was fully preserved \(g=2\.24g=2\.24,p<10−6p<10^\{\-6\}\), while the JSON\-only format effect was eliminated \(g=−0\.20g=\-0\.20, ns; Supplementary §S\-Robustness\)\. This indicates that H1’s measured contribution \(g=1\.87g=1\.87\) reflected JSON structural homogeneity inflating cosine similarity rather than genuine semantic convergence\.

The ablation’s primary contribution is therefore the isolation of F/H/E semantic separation as the active mechanism: the FHE\-Only condition \(free\-form output with semantic role separation, no JSON enforcement\) achieved SI = 0\.981, significantly exceeding Control \(0\.960\) without any format confound\. Full CKM significantly exceeded FHE\-Only \(H3b:g=1\.231g=1\.231,pHolmp\_\{\\text\{Holm\}\}= 2\.59×\\times10\-3\), but this residual advantage is attributable to JSON structural homogeneity rather than semantic synergy, as confirmed by the value\-only analysis\. The pilot study \(Study A, 6 models,N=768N=768\) showed consistent directionality \(Supplementary §S\-Ablation\)\.

##### Bridging Interpretation

The value\-only analysis clarifies the ablation’s mechanistic implications\. The original 2×2 design was intended to orthogonally decompose format and semantic contributions\. Under standard SI measurement, both appeared significant, suggesting independent variance sources\. However, the value\-only recomputation reveals that format enforcement’s measured effect operated primarily at the measurement level: JSON schema elements \(recurring keys, structural syntax\) inflated Sentence\-BERT cosine similarity through structural homogeneity rather than semantic convergence\. When this measurement artifact is removed, the semantic separation effect stands alone as the primary mechanism\.

This reinterpretation does not imply that format enforcement has no behavioral effect on models\. JSON slot\-filling may still constrain model behavior in ways not captured by SI, for example by ensuring complete coverage of required reasoning components or by reducing response length variability\. However, format enforcement’s contribution to measured semantic convergence is not distinguishable from structural homogeneity within the current measurement framework\. The critical finding is that F/H/E semantic separation produces genuine semantic convergence \(SI′= 0\.980 vs\. Control 0\.960\) even in the absence of any format enforcement \(FHE\-Only condition\), establishing epistemic role separation as the sufficient condition for the observed consistency improvement\.

#### 6\.2 State Persistence and Chain Stability

Single\-turn consistency is necessary but not sufficient; a consistency framework must also handle multi\-turn dynamics\. We now examine state persistence as a single\-step injection effect and then extend to chain protocols\.

##### State Persistence \(Exp3\)

Exp3 tests whether injecting Turn 1 output as Turn 2 context stabilizes decisions or instead triggers re\-evaluation, with per\-model DFR revealing how different architectures respond to injected state\.

In Legacy \(19 models\), DFR ranged from 0\.01 to 0\.85, a dramatic between\-model difference that reveals state persistence response as a model\-intrinsic property \(Figure 3\)\. Three factors plausibly drive high DFR values\. First, reasoning\-mode activation: some models \(particularly those with explicit chain\-of\-thought mechanisms\) appear to treat injected state as a new problem to be solved rather than as authoritative context, triggering full re\-evaluation from first principles\. Second, context window competition: when the injected prior state competes with the current prompt for attention, models with shorter effective context windows or weaker long\-range attention may preferentially attend to the immediate instruction\.

Third, helpfulness optimization: RLHF training that rewards “improved” answers may incentivize models to revise rather than preserve prior conclusions, interpreting state persistence as an opportunity for correction rather than a constraint on consistency\.

In the primary NewModels cohort \(N=3N=3,840, 12 models\), state persistence reduced DFR by 82%:

Table 7\. Exp3\-NM aggregate results \(primary, 12 models\)\.

MetricCKMCKM\_PERSISTHedges’ggppDFR0\.3850\.0691\.5221\.4×10−41\.4\\times 10^\{\-4\}SI0\.9740\.966−0\.8960\.007SDR0\.9390\.9430\.1300\.637 nsAll 12 primary NewModels showed DFR improvement under state persistence, and 6 achieved perfect decision preservation \(DFR = 0\), compared to 0/19 in Legacy\. This generational shift indicates that newer models are better calibrated for state persistence\. Fast models showed the lowest mean DFR \(0\.011\), followed by Flagship \(0\.019\) and Standard \(0\.177; the elevated Standard mean is driven by gemini\-2\.5\-pro at 0\.644, see §7\.5 limitation 8 and per\-model breakdown in Supplementary §S\-Exp3\)\.

The decrease in SI under state persistence does not indicate harm; rather, it reflects models actively responding to injected state, a form of contextual engagement\. SDR of approximately 0\.94 confirmed that semantic content was preserved, while what changed was the decision derived from that content\. This pattern reveals a consistency\-stability tradeoff: state persistence improved decision stability \(lower DFR\) at the cost of slightly reduced semantic homogeneity\. Per\-model breakdowns are in Supplementary §S\-Exp3\.

![[Uncaptioned image]](https://arxiv.org/html/2607.24765v1/x3.png)

Figure 3\. Decision Flip Rate \(DFR\) by model under state persistence\.Stability group coloring: green \(DFR < 0\.15, stable\), yellow \(0\.15–0\.50, moderate\), red \(\> 0\.50, unstable\)\. DFR spans from 0\.01 to 0\.85 across the 19 Legacy models shown\.

##### Chain Stability \(Exp3 Extra\)

A single injection tests whether state persistence works once; iterated injection tests whether the effect accumulates or decays\.

Under three\-turn chain protocols, mean DFR decreased from 0\.328 \(T1→T2\) to 0\.289 \(T2→T3\) while SDR increased from 0\.992 to 0\.995 across 16 Legacy models, demonstrating progressive stabilization consistent with attractor dynamics\. In the primary NewModels cohort, 6/12 achieved perfect temporal stability \(DFR = 0 across both transitions\), compared to 2/16 in Legacy\.

FCS of approximately 1\.0 under fixed anchor states demonstrated that multi\-turn instability originates from state construction and injection, not from model stochasticity \(Supplementary §S\-Exp3X for full chain results\)\.

#### 6\.3 Cross\-Experiment Behavioral Profiles

The preceding sections establish that CKM improves single\-turn consistency and that state persistence stabilizes multi\-turn decisions\. We now examine what patterns emerge when these dimensions are combined across models\.

##### Tier Classification

Individual metrics isolate specific failure modes; combining them reveals behavioral archetypes that single metrics cannot show\. Integrating SI \(single\-turn quality\) and DFR \(multi\-turn stability\) yields a behavioral taxonomy:

Table 8\. Behavioral tier taxonomy\.Four\-tier partition by single\-turn SI and multi\-turn DFRpersist\{\}\_\{\\text\{persist\}\}\. Tiers are mutually exclusive and collectively exhaustive; cutoffs \(SI = 0\.95/0\.97, DFR = 0\.15\) reflect observed gaps in the joint distribution and are treated as descriptive for the present cohort \(§S\-Profiles for cutoff\-sensitivity\)\.

TierCriteriaRepresentative ModelsSSI \> 0\.97 and DFR < 0\.15claude\-opus\-4\-6, gpt\-5\.4, grok\-3A0\.95 < SI≤\\leq0\.97 and DFR < 0\.15gpt\-5\-mini, gemini\-3\.1\-pro\-preview, gpt\-5\.2BSI \> 0\.95 and DFR≥\\geq0\.15gemini\-2\.5\-flash, gemini\-2\.5\-proCSI≤\\leq0\.95gpt\-4o, grok\-2, claude\-3\-haikuTiers S and A partition the “stable, low\-flip” region by single\-turn quality; Tier B captures the adequate\-single\-turn\-quality but elevated\-flip pattern, spanning moderate \(DFR 0\.15–0\.50\) to severe \(DFR \> 0\.50\) decision instability; Tier C groups lower\-single\-turn\-quality models regardless of flip behavior\. The criteria are both mutually exclusive and collectively exhaustive by construction: every model with SI measurement is classified into exactly one tier \(Table 8\)\.

The cutoff values were chosen post\-hoc to land near observed gaps in the joint SI–DFR distribution within our cohort: SI = 0\.97 separates the upper concentration of frontier models from the broader 0\.95–0\.97 band, SI = 0\.95 separates this band from the long lower tail, and DFR = 0\.15 reflects an approximate elbow between models with near\-zero flip rates and those with persistent multi\-turn instability\.

We treat these thresholds as a descriptive partition for the present cohort rather than as universal cutoffs; small perturbations \(e\.g\., SI cutoffs at 0\.96 or 0\.98\) reassign one or two models near the boundary without altering the qualitative four\-tier structure \(sensitivity in Supplementary §S\-Profiles\)\. All Tier\-classification analyses are reported as exploratory and are not Holm\-corrected \(§5\.4\)\.

The Tier B classification reported above uses CKM\_PERSIST DFR from Exp3 \(Legacy\) and Exp3\-NM \(NewModels\-12\) — the same 24\-unique\-model cross\-cohort plane shown in Figure 4 — as the multi\-turn stability axis \(gemini\-2\.5\-flash’s DFR = 0\.82 originates from the Legacy Exp3 measurement\); alternative stability axes \(e\.g\., chain DFR from Exp3X\) yield the same qualitative tiering with≤\\leq1 model boundary reassignment\.

Tier B models present a distinctive pattern\. gemini\-2\.5\-flash achieved high single\-turn SI \(Exp2 CKM SI = 0\.972; per\-scenario range as in Supplementary Table S3\) yet exhibited Exp3 DFR = 0\.82 with CKM\_PERSIST SI = 0\.967, demonstrating that high single\-turn quality does not guarantee multi\-turn stability\. This phenomenon is invisible to standard benchmarks, which do not distinguish between single\-turn and multi\-turn consistency\.

![[Uncaptioned image]](https://arxiv.org/html/2607.24765v1/x4.png)

Figure 4\. SI×\\timesDFR behavioral quadrant\.The 24\-model union pool \(19\-model Legacy Exp2/Exp3 cohort combined with the 13\-model NewModels cohort, 8 overlapping models using NewModels data\); the 23 models with both SI and CKM\_PERSIST DFR measurements are plotted \(grok\-3\-mini omitted for lacking a DFR measurement\) and mapped into four mutually exclusive and collectively exhaustive tiers: S \(SI \> 0\.97 and DFR < 0\.15\), A \(0\.95 < SI≤\\leq0\.97 and DFR < 0\.15\), B \(SI \> 0\.95 and DFR≥\\geq0\.15\), and C \(SI≤\\leq0\.95\)\. DFR axis = CKM\_PERSIST DFR \(Exp3 / Exp3\-NM\)\. The SI \(xx\) axis is truncated \(begins at 0\.92, not 0\) for legibility\. Tier B spans both moderate\-flip \(DFR 0\.15–0\.50\) and severe\-flip \(DFR \> 0\.50\) regimes; the upper\-right subregion contains models with high single\-turn consistency but high multi\-turn decision instability\.

##### Behavioral\-Variance Reducer Effect

Tier classification partitions models discretely; a continuous relationship with baseline consistency provides complementary information\. Beyond tier classification, CKM exhibited a systematic relationship with baseline performance: in the Legacy cohort, models with lower baseline SI benefited most from CKM \(Pearsonr=−0\.653r=\-0\.653,p=0\.002p=0\.002, 19 models; Figure 5\)\. CKM narrowed the SI range from 0\.907–0\.970 \(Control\) to 0\.927–0\.976 \(CKM\), acting as a behavioral\-variance reducer whose effect was inversely proportional to intrinsic consistency \(Figure 5\)\. Family\-level analysis confirmed differential responsiveness \(Kruskal\-WallisH=13\.57H=13\.57,p=0\.004p=0\.004\): GPT \(\+0\.031\) \> Gemini \(\+0\.016\) \> Grok \(\+0\.007\) \> Claude \(\+0\.001\)\.

![[Uncaptioned image]](https://arxiv.org/html/2607.24765v1/x5.png)

Figure 5\. Behavioral\-variance reducer effect\.Each point represents one of the 19 Legacy models; the x\-axis shows baseline SI under Control \(axis truncated, does not start at 0\), the y\-axis shows CKM\-inducedΔ\\DeltaSI\. The negative correlation \(r=−0\.653r=\-0\.653,p=0\.002p=0\.002\) indicates that models with lower baseline consistency show larger CKM effects\.

##### Scenario\-Level Variation

The effect size depends not only on which model is used but on what scenario type the model faces\.

CKM effectiveness varied with task characteristics\. In the NewModels cohort, ambiguity\-dominant scenarios \(S1, S4, S6\) showed meanΔ\\DeltaSI of \+0\.0416, compared to \+0\.0443 for non\-ambiguity scenarios \(S2, S3, S5, S9, S10\), indicating comparable magnitude across scenario types\. The Legacy cohort showed a more pronounced differentiation \(ambiguity \+0\.046 vs\. non\-ambiguity \+0\.019, 2\.4\-fold difference, see Supplementary §S7\.2\), suggesting potential cohort\-specific mechanisms\. The convergence across scenario types in NewModels may indicate that in more recent models, CKM’s benefit derives less from ambiguity\-specific epistemic resolution and more from general structural clarity\.

This pattern is consistent with the hypothesis that CKM operates through explicit knowledge categorization \(see §7\.2 for mechanism discussion\), though the relative importance of ambiguity resolution versus format\-driven clarity may differ across model architectures and training paradigms\. Extended scenario\-level analysis is provided in Supplementary §S7 and §S\-Profiles\.

#### 6\.4 Robustness Checks

Before interpreting the preceding results, we address potential confounds: data integrity, embedding backbone sensitivity, and temperature effects\.

We verified data integrity across all experiments\. For Exp1–3 and Study A/B, the LLM\-only valid rate was 98\.4% \(24,054/24,443\); including the Exp1 human pilot, the rate is 96\.7% \(24,092/24,923\)\. Exp6 sham\-arm arm\-level extraction rates range 93\.8–99\.8% \(lowest individual cell 78\.75%, gemini\-2\.5\-pro Sham\-B; see Supplementary §S\-Exp6\.4 for per\-model detail\)\. Canonical datasets were verified via SHA\-256 checksums \(Supplementary §S2, §S\-Ablation\.4 for per\-experiment breakdown\)\.

Embedding sensitivity analysis showed that mpnet detected significant CKM effects while MiniLM yielded null results \(d=0\.05d=0\.05,p=0\.844p=0\.844\) due to cosine ceiling compression on Korean text, confirming that embedding backbone selection is a critical methodological decision \(Supplementary §S1\)\.

Temperature robustness was assessed atT=0\.7T=0\.7\(N=728N=728\)\. All arms showed SI degradation under higher temperature, but the magnitude of degradation was monotonically ordered by structural complexity:

Table 9\. SI drop by arm \(T=0T=0→T=0\.7T=0\.7\)\.Mean SI under deterministic \(T=0T=0\) and stochastic \(T=0\.7T=0\.7\) sampling, averaged across the temperature\-probe subcohort \(N=728N=728\)\. The CKM arm halves the temperature\-induced consistency penalty relative to Control\.

ArmSI \(T=0T=0\)SI \(T=0\.7T=0\.7\)DropControl0\.9540\.913−0\.041JSON\-Only0\.9670\.941−0\.026F/H/E\-Only0\.9810\.959−0\.022Full CKM0\.9840\.965−0\.019CKM halved the consistency penalty from sampling noise \(2\.0×\\timesratio\) \(Table 9\)\. Previously marginal effects \(H2:g=0\.99g=0\.99→\\rightarrow2\.87\) reached significance under higher temperature, driven by disproportionate Control degradation rather than CKM improvement\. CKM thus functions as a stochasticity buffer \(full results in Supplementary §S\-Ablation\)\.

#### 6\.5 Sham\-Restriction Ablation \(Exp6\)

The 4\-arm ablation \(§6\.1\) established that F/H/E semantic separation is the primary mechanism, and §7\.2 argued against output\-space compression using SI×\\timesDFR orthogonality\. However, the 4\-arm design did not include a sham\-restriction control that matches CKM in structural complexity without epistemic content\. Exp6 addresses this gap with a 5\-arm design that directly decomposes the CKM effect into structural scaffolding versus reasoning\-semantic contributions\.

##### Design

Five arms were tested using the same 12 primary NewModels×\\times8 scenarios×\\timesK=10K=10protocol \(N=3N=3,840 per arm\):

- •Vanilla: No structure \(Control baseline, reused from Exp2\-NM\)\.
- •Sham\-A\(Surface Semantic\): JSON schema with non\-reasoning semantic slot names \(color, animal, weather, food, mood\) matched to CKM in slot count and format complexity\.
- •Sham\-B\(Non\-Reasoning Semantic\): JSON schema with contextual but non\-epistemic slot names \(time, place, participant, activity, object\)\.
- •Sham\-C\(Symbolic/Meaningless\): JSON schema with arbitrary symbolic slot names \(V, W, X,α\\alpha,β\\beta, slot\-1\) containing no semantic content\.
- •CKM: F/H/E epistemic role separation with full state enforcement \(reused from Exp3\-NM\)\.

This design isolates three components: \(1\) structural scaffolding \(any JSON schema vs\. no schema\), \(2\) non\-epistemic semantic content \(meaningful but non\-reasoning slot names vs\. symbolic\), and \(3\) reasoning\-semantic content \(F/H/E epistemic categories vs\. non\-epistemic alternatives\)\. All three sham arms match CKM in format complexity, slot count, and approximate token overhead, controlling for the structural compression confound\.

##### Aggregate Results

Table 10\. 5\-arm aggregate metrics \(primary 12\-model basis\)\.

ArmSIDFRpersist\{\}\_\{\\text\{persist\}\}SDRFCSVanilla0\.9520\.080——Sham\-A0\.9620\.0820\.920—Sham\-B0\.9620\.4190\.890—Sham\-C0\.9620\.1160\.928—CKM0\.9740\.069∥0\.939—∥CKM DFRpersist\{\}\_\{\\text\{persist\}\}is from Exp3 CKM\_PERSIST condition \(exp3\_newmodels\_metrics\_v1\.3\_active12\.json\); all five arms are aligned to the persist protocol \(single\-turn for Vanilla / Sham\-A/B/C; CKM\_PERSIST for the CKM arm\)\. The 5\-arm SI values are reported on the raw\-output substrate to maintain comparability with the sham arms \(which lack a parsed\-field representation by design\); the analogous value\-only sensitivity recomputation for Vanilla and CKM yields the same SI ordering with magnitudes reduced toward the §6\.1 value\-only baseline \(see Supplementary §S\-Robustness for the value\-only methodology\)\. Table 10 was regenerated fromexp6\_5way\_comparison\_v1\.2\_active12\.json\(CKM column corrected from a prior source\-field misalignment in the v1\.1 canonical; see §S\-Exp6\.5\)\.

The SI ordering is: Vanilla \(0\.9521\) < Sham\-A \(0\.9616\)≈\\approxSham\-B \(0\.9623\)≈\\approxSham\-C \(0\.9617\)≪\\llCKM \(0\.9741\)\. All three sham arms cluster at a similar SI level, approximately 1 percentage point above Vanilla but 1\.2 percentage points below CKM\. The near\-equivalence among sham arms \(pairwise\|g\|<0\.07\|g\|<0\.07, allpHolm=1\.0p\_\{\\text\{Holm\}\}=1\.0\) indicates that the specific semantic content of slot names does not materially influence SI; what matters is whether the slots enforce epistemic role separation\.

The DFRpersist\{\}\_\{\\text\{persist\}\}ordering differs sharply: CKM \(0\.069\) < Vanilla \(0\.080\)≈\\approxSham\-A \(0\.082\) < Sham\-C \(0\.116\)≪\\llSham\-B \(0\.419\)\. CKM is the only arm that reduces DFR below Vanilla\. Sham\-B shows a dramatic 5\.2\-fold increase relative to Vanilla\.

Table 11\. Pairwise Hedges’ggfor SI \(upper triangle\) with Holm\-correctedpp\-values \(12 primary models, 10 pairwise comparisons\)\.Entries aregi​jg\_\{ij\}= \(row mean − column mean\) / pooled SD\. CKM\-vs\-Vanilla is the strongest SI contrast; CKM exceeds each sham arm individually, while the three sham arms are pairwise indistinguishable on SI\.

VanillaSham\-ASham\-BSham\-CCKMVanilla—−0\.91\-0\.91\(pp= \.094\)−1\.14\-1\.14\(pp= \.015\*\)−0\.74\-0\.74\(pp= \.166\)−2\.71\-2\.71\(pp< \.001\*\*\*\)Sham\-A—−0\.07\-0\.07\(p=1\.0p=1\.0\)−0\.01\-0\.01\(p=1\.0p=1\.0\)−1\.23\-1\.23\(pp= \.015\*\)Sham\-B—\+0\.05\+0\.05\(p=1\.0p=1\.0\)−1\.36\-1\.36\(pp= \.008\*\*\)Sham\-C—−0\.97\-0\.97\(pp= \.095\)CKM—pp\-values are Holm\-Bonferroni corrected across the 10 pairwise SI comparisons per metric \(canonical:exp6\_5way\_comparison\_v1\.2\_active12\.jsonSI\.p\_holm\_matrix\)\. Hedges’ggvalues are reported using the canonical independent\-groups convention \(n = 12 per arm\); paired\-design effect sizes \(which would be larger by a factor of approximately 2 for Vanilla\-vs\-CKM, given the within\-subject design\) are provided as a sensitivity in Supplementary §S\-Exp6 alongside this primary table\.

CKM significantly exceeds Sham\-A and Sham\-B on SI \(g=1\.23g=1\.23–1\.36,pHolm<\.05p\_\{\\text\{Holm\}\}<\.05\) and shows a large effect versus Sham\-C \(g=0\.97g=0\.97,pHolmp\_\{\\text\{Holm\}\}= \.095\)\. The three sham arms are mutually indistinguishable \(\|g\|<0\.07\|g\|<0\.07, allpHolm=1\.0p\_\{\\text\{Holm\}\}=1\.0\)\. This pattern directly contradicts the compression hypothesis: if CKM’s SI gain were attributable to structural restriction alone, the sham arms \(which impose equivalent structural restriction with non\-epistemic content\) would match CKM\. They do not\.

##### SI Decomposition

The 5\-arm hierarchy enables a quantitative decomposition of the CKM SI improvement \(Δ\\DeltaSI = \+0\.022 relative to Vanilla\):

Table 12\. SI decomposition: structural scaffolding vs\. F/H/E semantic content\.The Vanilla → CKM SI gain is partitioned via the sham hierarchy\. Structural scaffolding \(any JSON schema with named slots\) accounts for ~45% of the effect; F/H/E epistemic role separation contributes the remaining ~55%\.

ComponentTransitionΔ\\DeltaSIProportionStructural scaffoldVanilla→\\rightarrowSham\-C\+0\.01045%Reasoning\-semantic \(F/H/E\)Sham cluster→\\rightarrowCKM\+0\.01255%TotalVanilla→\\rightarrowCKM\+0\.022100%Surface semantic content \(Sham\-A vs\. Sham\-C:Δ\\DeltaSI≈\\approx0\.000\) and non\-reasoning semantic content \(Sham\-B vs\. Sham\-A:Δ\\DeltaSI≈\\approx0\.000\) contribute negligibly\. The entire sham\-attributable SI gain comes from structural scaffolding \(the mere presence of a JSON schema with named slots\), while the majority of the CKM effect \(55%\) derives from the specific epistemic content of F/H/E decomposition \(Table 12\)\. This confirms that CKM’s consistency improvement is not reducible to structural restriction\.

##### SI\-DFR Dissociation

The most striking finding is the dissociation between SI and DFR across the five arms:

Table 13\. Per\-arm joint SI/DFRpersist\{\}\_\{\\text\{persist\}\}improvement relative to Vanilla\.Only CKM achieves simultaneous SI gain and DFR reduction; all three sham arms improve SI but degrade DFR, falsifying the pure compression hypothesis\.

ArmΔ\\DeltaSI \(vs\. Vanilla\)Δ\\DeltaDFR \(vs\. Vanilla\)Joint improvement?Sham\-A\+0\.010\+0\.002 \(marginal\)NoSham\-B\+0\.010\+0\.339 \(much worse\)NoSham\-C\+0\.010\+0\.036 \(worse\)NoCKM\+0\.022−0\.011\-0\.011\(better\)YesCKM is the only arm that achieves simultaneous SI improvement and DFR reduction \(Figure 6\)\. All three sham arms improve SI but degrade DFR, demonstrating that structural scaffolding without epistemic role separation produces a consistency\-stability tradeoff rather than joint improvement \(Table 13\)\. This dissociation constitutes direct evidence against the pure compression hypothesis: under compression, SI↑\\uparrowshould entail DFR↓\\downarrow\(a narrower output space contains fewer distinct actions\), but the sham arms show the opposite pattern\.

![[Uncaptioned image]](https://arxiv.org/html/2607.24765v1/x6.png)

Figure 6\. SI\-DFR dissociation scatter for the 5\-arm sham\-restriction ablation\.X\-axis:Δ\\DeltaSI relative to Vanilla \(positive = higher consistency\)\. Y\-axis:−Δ\-\\DeltaDFRpersist\{\}\_\{\\text\{persist\}\}relative to Vanilla \(positive = more stable\)\. Vanilla is plotted at the origin\. The upper\-right quadrant represents joint improvement \(SI↑\\uparrow\+ DFR↓\\downarrow\); only CKM occupies this region\. Sham\-B \(lower\-right\) exhibits the paradox of improved SI but dramatically worsened DFR\. Sham\-A and Sham\-C show modest SI gains with slight DFR degradation\.

##### Sham\-B Paradox

Sham\-B presents a noteworthy anomaly: it achieves SI comparable to the other sham arms \(0\.962\) yet exhibits DFRpersist\{\}\_\{\\text\{persist\}\}= 0\.419, over five times the Vanilla rate \(0\.080\)\. We hypothesize that non\-reasoning semantic context \(time, place, participant\) disrupts action stability under state injection because these contextual framings are semantically rich enough to trigger re\-evaluation but lack the epistemic structure to anchor decisions\. When a model encounters persisted state containing “morning/school/self” contextual labels, it may treat these as novel situational cues warranting decision revision, rather than as authoritative context to be preserved\.

By contrast, CKM’s F/H/E labels explicitly tag information by epistemic provenance, providing an anchoring structure that resists state\-injection\-induced re\-evaluation\. This account remains a hypothesis \(claim strength: belowβ\\beta\) pending targeted experiments that manipulate contextual framing independently of slot count\.

##### Judgment: R4 \(Mechanism Decomposition\), Claimβ\\beta

The 5\-arm results are most consistent with the R4 \(mechanism decomposition\) scenario: CKM effects decompose into structural scaffolding \(~45%\) and reasoning\-semantic\-specific \(~55%\) components, with the two components contributing to different consistency dimensions \(structural scaffolding to SI only; reasoning\-semantic to both SI and DFR\)\. This decomposition meets theβ\\beta\(medium\) claim threshold: the effect is replicated across 12 primary models, the pairwise contrasts are statistically significant after Holm correction for the critical comparisons \(CKM vs\. Sham\-A/B:p<\.046p<\.046; CKM vs\. Vanilla:p<\.001p<\.001\), and the SI\-DFR dissociation provides a mechanistic signature that is not predicted by simpler accounts\.

#### 6\.6 Case Study: Behavioral Profile of a Compromised Model \(gpt\-4\.1\-mini\)

This section presents a case study of gpt\-4\.1\-mini, the sole model excluded from the primary NewModels analysis\. The purpose is twofold: to provide full transparency about the exclusion decision and to document a behaviorally anomalous profile that may be of independent scientific interest\.

##### Background

OpenAI issued a deprecation notice for gpt\-4\.1\-mini on 2026\-02\-13, two days before our data collection began \(2026\-02\-15\)\. During the collection window, independent reports documented degradation in instruction\-following behavior\. These circumstances raise concerns about whether gpt\-4\.1\-mini’s behavioral data reflect stable model characteristics or transient degradation artifacts\.

##### Behavioral Profile

Under the full 13\-model cohort, gpt\-4\.1\-mini exhibited a distinctive behavioral signature\. In Exp3 \(state persistence\), gpt\-4\.1\-mini was the sole model where DFR\_persist \(0\.281\) exceeded DFR\_ckm \(0\.231\), indicating that state injection increased rather than decreased decision instability\. This reversal was unique among all 13 models\.

In Exp6 \(5\-arm sham\-restriction ablation\), gpt\-4\.1\-mini showed dramatically elevated DFR\_persist across all sham arms\. The 5\-arm DFR profile \(all\-13 values\) is:

Table 14\. gpt\-4\.1\-mini DFRpersist\{\}\_\{\\text\{persist\}\}across Exp6 arms \(all\-13 basis\)\.

ArmDFRpersist\{\}\_\{\\text\{persist\}\}Vanilla0\.679Sham\-A0\.912Sham\-B0\.900Sham\-C0\.888CKM0\.281CKM reduced gpt\-4\.1\-mini’s DFR from the Vanilla rate of 0\.679 to 0\.281, a 59% reduction\. This suggests that F/H/E epistemic role separation partially stabilized even a compromised model\. However, the residual DFR of 0\.281 under CKM is substantially higher than the 12\-model primary median of 0\.000, and the extreme sensitivity to all sham arms \(DFR \> 0\.88\) is consistent with a model in a degraded operational state\.

##### Interpretation

We hypothesize that gpt\-4\.1\-mini’s behavior during the collection window reflected transient instability associated with the deprecation process, potentially including weight modifications, routing changes, or reduced infrastructure prioritization\. Under this hypothesis, the model’s elevated DFR across all conditions reflects a global instability mode rather than a condition\-specific interaction\. The partial stabilization under CKM is consistent with the general finding that F/H/E epistemic structure provides an anchoring effect, but the compromised baseline limits the interpretive value of condition\-specific comparisons\.

##### Limitations

This case study has several limitations\. First,N=1N=1: the behavioral profile describes a single model under specific temporal circumstances and cannot be generalized\. Second, we lack vendor documentation of what changes, if any, were applied to gpt\-4\.1\-mini during the deprecation window\. Third, we cannot distinguish between model\-intrinsic instability and infrastructure\-level variability\.

##### Exclusion Justification

The exclusion of gpt\-4\.1\-mini from primary analyses satisfies five criteria:

1. 1\.Vendor\-issued deprecation: OpenAI published a deprecation notice on 2026\-02\-13, overlapping with our collection window\.
2. 2\.Independent degradation reports: External users documented instruction\-following degradation during this period\.
3. 3\.Anomalous behavioral profile: gpt\-4\.1\-mini was the sole model where state injection increased DFR \(DFR\_persist \> DFR\_ckm\), a pattern not observed in any other model\.
4. 4\.Directional preservation: All primary findings \(SI improvement, DFR reduction, mechanism decomposition\) are preserved under both the 12\-model and 13\-model cohorts \(Supplementary §S\-Sensitivity\)\.
5. 5\.Full transparency: Complete data are reported in this case study and the sensitivity analysis; no data are suppressed\.

### 7\. Discussion

The results above support a narrow but deployment\-relevant claim: CKM increases behavioral consistency in the tested LLM decision scenarios, and the effect is not reducible to JSON formatting alone\. This section interprets that claim without expanding it into stronger claims about correctness, ethics, or general intelligence\. The discussion therefore follows three boundaries: what was measured, what the ablations support mechanistically, and what remains outside the present evidence\.

The empirical message of §6 is that behavioral consistency is measurable, model\-dependent, and partially reducible through F/H/E state enforcement\. CKM improves repeated\-output stability in most tested models, but the effect is not a generic consequence of making the output more structured\. The ablations show that the semantic role of the slots matters: Fact, Heuristic, and Emotion separation produces a different behavioral signature from non\-epistemic JSON scaffolds\.

This section interprets those findings\. §7\.1 argues that behavioral consistency should be treated as a candidate evaluation dimension alongside capability\. §7\.2 explains why structured state enforcement may work, while separating confirmed findings from hypotheses\. §7\.3 discusses the human pilot\. §7\.4 outlines practical implications of state\-persistence variation\. §7\.5 states the scope limits, and §7\.6 identifies the most important next experiments\.

#### 7\.1 Behavioral Consistency as an Evaluation Dimension

The results presented in §6 establish six empirical findings; we now consider their broader implications, beginning with what they reveal about consistency as an evaluation dimension\. Our data suggest that behavioral consistency is distinct from the dimensions captured by current capability benchmarks: this study did not measure capability scores directly, but the within\-suite dissociations we observe \(e\.g\., models with high SI but high DFR, or high FCS but low CRR\) imply that no single capability proxy in our suite predicts the others\.

The Tier B phenomenon, in which models achieve high single\-turn consistency yet poor multi\-turn stability, illustrates a failure mode that is not captured by any of our single\-turn measurements alone\. The metric suite captures failure modes that are partially independent of one another, and we treat the relationship between behavioral consistency and external capability benchmarks as an open empirical question for joint\-measurement studies\. Consistency profiling may therefore merit consideration as a candidate complement to existing LLM evaluation dimensions, pending such joint validation\.

#### 7\.2 Why Structured State Enforcement Works

Given that CKM improves consistency in our experiments, a natural question is why it works\. Before proposing mechanistic accounts, we first address a prior concern: whether the observed consistency gains could be explained trivially by output\-space compression, without invoking any reorganization of reasoning\. We then evaluate four candidate mechanisms as an interpretive framework consistent with the empirical patterns; the value\-only ablation \(§6\.1\) rules out one of them as a measurement artifact, leaving three operative mechanisms \(cognitive load reduction, epistemic boundary enforcement, and structural scaffolding as enabling context\)\.

Each of the three receives varying degrees of direct support from our data, and we note where the evidence is indirect rather than causal\.

Disentangling Restriction from Organization\.

A natural concern is that any form of output restriction would trivially reduce variability, rendering the observed consistency gains uninformative\. Under this view, CKM’s F/H/E scaffold would function as a more elaborate form of response\-space compression rather than as reasoning organization, and the improved Semantic Integrity would reflect narrower permissible outputs rather than better\-structured reasoning\.

We address this concern on two levels\. First, the value\-only SI analysis \(§6\.1, Supplementary §S\-Robustness\) directly controls for structural homogeneity: when JSON surface features are removed from the SI computation, JSON\-only structural enforcement shows no significant effect on semantic consistency \(g=−0\.20g=\-0\.20, non\-significant\), while FHE semantic separation preserves its effect \(g=2\.24g=2\.24\)\. Structural scaffolding alone is insufficient; the operative component is epistemic categorization\.

Second, and more decisively, the relationship between single\-turn semantic consistency \(SI\) and multi\-turn decision stability \(DFR\) refutes the uniform\-compression account\. Under a pure compression mechanism, both axes should co\-move: any restriction that tightens SI by narrowing the response space should also tighten DFR, because a narrower space contains fewer distinct actions\. The data do not exhibit this co\-movement\. Across the 24\-model union pool \(23 models with paired SI and CKM\_PERSIST DFR measurements\), SI and DFR do not co\-move positively as compression would predict; if anything the association is weakly negative \(Pearsonr=−0\.18r=\-0\.18,p=0\.41p=0\.41; Spearmanρ=−0\.40\\rho=\-0\.40,p=0\.06p=0\.06\)\.

When the SI×\\timesDFR plane is partitioned by median\-split \(SI median = 0\.967, DFR cutoff = 0\.15\), models populate all four quadrants: upper\-right \(high\-SI, high\-DFR\)n=2n=2; upper\-left \(high\-SI, low\-DFR\)n=9n=9; lower\-right \(low\-SI, high\-DFR\)n=5n=5; lower\-left \(low\-SI, low\-DFR\)n=7\.n=7\.The upper\-right quadrant \(high SI, high CKM\_PERSIST DFR\) is occupied by gemini\-2\.5\-flash and gpt\-4\.1\-mini, which achieve SI above the median under CKM while exhibiting substantial decision flips under state injection \(gemini\-2\.5\-flash DFR\_persist 0\.82\); gemini\-2\.5\-pro \(DFR\_persist 0\.644\) sits just below the SI median in the lower\-right region\.

A uniform output\-space compression would predict an empty upper\-right quadrant; its observed non\-emptiness with frontier occupants refutes the prediction\. This median\-split lens is complementary to the fixed\-cutoff Tier taxonomy of §6\.3; both partition the same plane but under distinct cutoff schemes\.

We acknowledge that orthogonality between axes does not, by itself, causally prove that F/H/E organizes reasoning rather than compressing output space along a different axis\. The 5\-arm sham\-restriction ablation \(§6\.5\) provides a direct empirical test: three sham arms matched to CKM in format complexity and slot count but containing non\-epistemic content all failed to replicate CKM’s joint SI↑\\uparrow\+ DFR↓\\downarrowpattern, confirming that structural restriction alone is insufficient\.

Exp6 Mechanism Decomposition\.

The 5\-arm sham\-restriction ablation \(§6\.5\) resolves the outstanding question from the preceding analysis by providing a direct causal test of whether F/H/E semantic separation organizes reasoning or merely compresses output space along a different axis\.

The compression hypothesis predicted that sham arms, which impose equivalent structural restriction with non\-epistemic content, would match CKM on all consistency axes\. The organization hypothesis predicted that sham arms and CKM would converge on SI \(both involve structural scaffolding\) but diverge on DFR \(only CKM provides epistemic anchoring\)\. The data strongly favor the organization account: all three sham arms achieve SI approximately 1 percentage point above Vanilla \(structural scaffold effect, ~45% of the total CKM gain\), but none consistently reduces DFR below Vanilla\.

CKM alone achieves the remaining 55% of the SI gain and is the only arm that simultaneously reduces DFR, a pattern consistent with reasoning reorganization rather than output\-space narrowing\.

The SI decomposition \(structural scaffold ~45%, reasoning\-semantic ~55%\) provides a quantitative partition of the CKM effect that was previously available only as a qualitative argument from the 4\-arm ablation\. The structural component corresponds to the format enforcement effect identified in §6\.1, while the reasoning\-semantic component corresponds to the F/H/E semantic separation effect\. Importantly, the sham arms demonstrate that the structural component contributes to SI but not to DFR, while the reasoning\-semantic component contributes to both, establishing that these are functionally distinct mechanisms rather than different aspects of the same process\.

Sham\-B Paradox and Contextual Disruption \(Hypothesis\)\.

The Sham\-B arm presents a theoretically informative anomaly\. Despite achieving SI comparable to the other sham arms, Sham\-B exhibits DFRpersist\{\}\_\{\\text\{persist\}\}= 0\.419, over five times the Vanilla rate\. We hypothesize that non\-reasoning semantic context \(time, place, participant\) disrupts action stability under state injection because these contextual framings are semantically rich enough to trigger re\-evaluation but lack the epistemic structure to anchor decisions\. This hypothesis is consistent with the observation that 11/12 primary models show higher DFR under Sham\-B than Sham\-A, and 11/12 show higher DFR under Sham\-B than Vanilla\.

If confirmed, this would suggest that the epistemic anchoring provided by F/H/E is not merely additive but protective: it prevents semantically rich context from destabilizing decisions\. This account remains a hypothesis pending targeted experiments that manipulate contextual framing independently of slot count; we do not elevate it to a confirmed finding\.

Mechanism Decomposition\.

The first mechanism is cognitive load reduction through forced categorization\. CKM imposes an epistemic hygiene discipline, requiring explicit labeling of observable facts, inferred heuristics, and affective signals before reasoning proceeds, thereby reducing the space of possible interpretations\. Without this separation, the model must simultaneously determine what information means and what kind of information it is; with separation, the categorization is resolved at the input stage, freeing subsequent processing to operate on pre\-classified inputs\. This mechanism predicts that CKM should be most effective in ambiguity\-dominant scenarios, where fact\-inference conflation is greatest\.

The scenario\-level data are consistent with this prediction in the Legacy cohort \(§6\.3\): ambiguity scenarios show 2\.4\-fold largerΔ\\DeltaSI \(\+0\.046 vs\. \+0\.019\) than scenarios with clearer factual constraints\. In the primary NewModels cohort, however, this differentiation is largely absent \(ambiguity \+0\.0416 vs\. non\-ambiguity \+0\.0443, 1\.07\-fold ratio\), suggesting that newer models may distribute the F/H/E benefit more uniformly across scenario types; this cohort\-dependent pattern warrants targeted investigation rather than serving as standalone confirmation of the cognitive\-load mechanism\.

The second mechanism is epistemic boundary enforcement\. The mandatory distinction betweenFFandHH, with explicit uncertainty markers on heuristic content, makes the epistemic status of each reasoning component transparent\. This can reduce a common failure mode in which models present speculative inferences with the same confidence as verified observations, a conflation that increases the variance of downstream conclusions\. The human pilot data \(§7\.3\) provide complementary evidence: participants achieved perfect F/H/E compliance across the manually reviewed subset \(0 violations in 15 annotated CKM responses; see Supplementary §S11\.2 for the review protocol\), suggesting that the boundaries correspond to cognitively natural categorization rather than arbitrary imposition\.

The third mechanism is output space reduction through structural scaffolding\. The requirement that each response populate specific fields \(facts, heuristics, emotion code, action, reason\) constrains the response space\. The original SI measurement attributed a large effect to this mechanism \(g=1\.87g=1\.87\), but value\-only analysis \(§6\.1, Supplementary §S\-Robustness\) revealed that this measured effect primarily reflects JSON structural homogeneity inflating cosine similarity\. The format enforcement component may still contribute to behavioral consistency through channels not captured by SI—such as ensuring complete slot coverage or reducing length variability—but its contribution to semantic convergence is not separable from measurement artifact within the current framework\.

This finding elevates the second mechanism \(epistemic boundary enforcement\) and the first \(cognitive load reduction through forced categorization\) as the primary explanatory accounts, both of which operate through F/H/E semantic separation rather than format constraints\.

The fourth consideration is the relationship between format and semantic constraints\. The original SI measurement suggested super\-additive synergy \(g=0\.835g=0\.835,p=0\.0199p=0\.0199\), but the value\-only analysis indicates that the apparent synergy was driven by JSON structural homogeneity compounding with semantic convergence in the Full CKM condition\. After artifact removal, the residual advantage of Full CKM over FHE\-Only is not attributable to genuine semantic synergy\. We therefore consolidate the mechanistic account around three operative mechanisms \(cognitive load reduction, epistemic boundary enforcement, and structural scaffolding as enabling context\), with semantic separation as the primary active ingredient\.

This consolidated interpretation is offered as a theoretical framework consistent with the corrected data; direct causal evidence would require interventions that independently manipulate each mechanism, which we identify as a direction for future work\.

It is important to note, however, that reduced variability does not imply improved reasoning quality\. Higher SI indicates convergence, but convergence toward shared error remains possible\. Our framework measures consistency, not accuracy, and these dimensions require independent assessment\.

#### 7\.3 Human Baseline Comparison

While the preceding mechanisms were developed to explain LLM behavior, the human pilot provides preliminary evidence that similar dynamics operate in human reasoning\. Exp1’s small sample \(n=6n=6\) precludes statistical generalization, but three directional findings merit attention\. CKM surfaced suppressed affective states \(anxiety reports: 0 → 6; “no emotion”: 5 → 2\), suggesting that structured prompting reorganizes the reasoning process rather than merely constraining it\.

F/H/E separation compliance was perfect \(0 violations across the 15 CKM responses for which the pilot protocol included manual compliance annotations; 4 additional CKM responses lacked reviewer annotations and were excluded from this subset; see Supplementary §S11\.2\), indicating that the structural requirements are cognitively natural for human reasoners\. SI improved 3\.3\-fold \(TF\-IDF proxy: 0\.025 → 0\.083\)\. A large\-scale replication \(n=30n=30\+\) with unified measurement methodology is needed to confirm these patterns\.

Ethics and scope\.Human participants in Exp1 provided informed consent and participated voluntarily\. The study involved minimal risk \(responding to hypothetical daily\-life scenarios\); all responses were anonymized prior to analysis\. Institutional review determinations for this pilot are documented with the canonical dataset \(Supplementary §S11\)\. Importantly, the core claims of this study—CKM’s effect on LLM consistency, the ablation decomposition, and cross\-vendor behavioral profiling—do not depend on the human pilot results\. Exp1 provides directional evidence that human participants can use the same F/H/E categorization interface, but it is not part of the evidentiary basis for Findings 1–5\.

#### 7\.4 State Persistence and Practical Implications

Turning from mechanism to application, state persistence response varied dramatically across models \(DFR: 0\.01–0\.85\), reflecting fundamentally different strategies for handling injected state\. Low\-DFR models treated injected state as authoritative context, while high\-DFR models treated it as new information triggering re\-evaluation\. SDR of approximately 1\.0 revealed that this re\-evaluation preserved semantic content while changing decisions, a pattern we characterize as meaning preservation with decision re\-evaluation\. This distinction has direct practical implications\.

Applications requiring state consistency \(e\.g\., multi\-turn advisory systems, persistent agent workflows\) should select models based on DFR profiles rather than capability scores alone, since a model with high benchmark accuracy but high DFR may produce contradictory advice across turns\.

The generational improvement \(6/12 primary NewModels achieving DFR = 0 vs\. 0/19 Legacy\) suggests that newer models are increasingly calibrated for state persistence, though gemini\-2\.5\-pro remains an outlier \(DFR\_persist = 0\.644\)\. More broadly, the DFR profile constitutes a model fingerprint that could serve as a pre\-deployment consistency audit: organizations could run a standardized battery of state\-persistence trials to characterize each candidate model’s behavioral profile before committing to production deployment\. Adaptive state gating, in which injection strength is modulated based on a model’s measured DFR, represents a natural extension of this profiling approach\.

#### 7\.5 Limitations

The claims above are bounded by nine scope restrictions\.

1. 1\.Human pilot size\.Exp1 used only six participants, so the human findings should be treated as directional rather than confirmatory\.
2. 2\.Consistency is not quality\.Higher SI does not show that the model reasons better; it only shows that responses converge more strongly under the tested protocol\.
3. 3\.Language scope\.All scenarios were presented in Korean\. Cross\-lingual validation is required before generalizing to other languages\.
4. 4\.Scenario scope\.The scenarios focused on student daily\-life decisions\. They do not yet test professional, safety\-critical, or evolving real\-world constraints\.
5. 5\.Embedding dependence\.SI and SDR depend on the embedding backbone \(§6\.4\), although sensitivity analyses reduce concern about a single\-backbone artifact\.
6. 6\.Temperature scope\.The temperature robustness probe assessed onlyT=0\.7T=0\.7\.
7. 7\.Power and substrate choice\.The Legacy parsed\-field effect is well powered \(g=1\.18g=1\.18,n=19n=19\), but the more conservative raw\-output basis is less powered \(g=0\.61g=0\.61, estimated post\-hoc power≈\\approx0\.55\)\. The combined random\-effects estimate \(gREg\_\{\\text\{RE\}\}= 1\.09, 31 model\-level pairs\) provides adequate power while preserving the high between\-cohort heterogeneity \(I2I^\{2\}= 77\.6%\) as an explicit qualifier\.
8. 8\.Influential model\.gemini\-2\.5\-pro shows persistently high DFR \(0\.644 in NewModels, 0\.80 in Legacy\) and influences Exp3 aggregate statistics\. Sensitivity analyses excluding this model are reported in Supplementary §S\-Exp3\.
9. 9\.Excluded deprecated model\.gpt\-4\.1\-mini was excluded from primary analyses because OpenAI issued a deprecation notice during data collection\. The case study \(§6\.6\) and sensitivity analysis \(Supplementary §S\-Sensitivity\) show that all directional findings are preserved under the 13\-model cohort, but the primary NewModels sample is thereforen=12\.n=12\.

#### 7\.6 Future Work

The limitations above define the next validation agenda\. Nine directions are especially important\.

1. 1\.Mixed\-effects variance decomposition\.Models such as SI ~ arm \+ \(1\|model\) \+ \(1\|scenario\) would clarify how much of the CKM effect is attributable to model\-level versus scenario\-level variation\.
2. 2\.Cross\-lingual validation\.Matched scenarios across English, Korean, and Japanese would test whether the consistency gains generalize beyond Korean prompts\.
3. 3\.Decision\-quality assessment\.Expert panels should evaluate whether reduced variability corresponds to better decisions, worse decisions, or merely more stable decisions\.
4. 4\.Formal state\-trajectory analysis\.The chain data \(§6\.2\) provide candidate measures for studying convergence and stability properties of CKM state trajectories\.
5. 5\.Adaptive state gating\.Deployment systems could adjust injection strength based on each model’s measured DFR profile\.
6. 6\.Domain transfer\.Translation, code generation, medical reasoning, and professional decision tasks should be tested to determine whether CKM generalizes beyond student daily\-life scenarios\.
7. 7\.Testimony axis extension\.Epistemological accounts often treat testimony as an independent source, distinct from perception and inference \[56, 57\]\. Adding a fourth axis that separately tags communicated or attested information is a theoretically motivated extension requiring independent validation, and is left as future work\.
8. 8\.Extension beyond language models\.Robotic and physical AI systems combine sensor data, probabilistic inference, and priority signals\. Testing whether F/H/E\-like separation helps these systems would assess the broader generality of epistemic provenance enforcement\.
9. 9\.Standardized professional examinations\.Bar examinations, medical licensing exams, and certified public accountant tests would provide researcher\-bias\-free question pools, reproducible difficulty metadata, and domain variation in fact\-inference ratios\.

The sham\-restriction ablation previously identified as a future direction has now been completed and is reported in §6\.5\. Its results support the organization hypothesis over the compression hypothesis\.

### 8\. Conclusion

This paper tested a direct and bounded claim:LLM behavioral consistency can be measured, and part of the observed instability can be reduced by forcing the model to separate facts, inferred assumptions, and evaluative signals before deciding\.This is a claim about behavioral stability under repeated and state\-persistent trials, not a claim about improved answer quality\.

Across four core experiments, a 4\-arm ablation, a 5\-arm sham\-restriction ablation, and a temperature robustness probe, we evaluated 26 unique LLM models from four vendors and two generations, producing 37,403 observations \(35,475 primary \+ 1,928 case\-study observations\)\. The main findings are:

1. 1\.CKM reduces repeated\-output variability\.In the Korean\-language student\-decision scenarios tested here, F/H/E decomposition increased SI across both model generations: Legacy models showed 17/19 positive effects \(parsed\-fieldg=1\.18g=1\.18\), NewModels showed 12/12 positive effects \(g=3\.08g=3\.08\), and the combined random\-effects estimate wasgREg\_\{\\text\{RE\}\}= 1\.09 \[0\.83, 1\.35\] across 31 model\-level pairs\.
2. 2\.The active mechanism is not JSON formatting alone\.The 4\-arm ablation showed that F/H/E semantic separation survives value\-only artifact control \(g=2\.24g=2\.24\), whereas the apparent JSON\-only effect disappears after structural syntax is removed\. The critical intervention is therefore epistemic role separation: making the model distinguish what is observed, what is inferred, and what is evaluative\.
3. 3\.State persistence reduces decision flipping in newer models but remains model\-dependent\.In the NewModels cohort, DFR dropped by 82% under CKM state persistence \(0\.385→\\rightarrow0\.069,g=1\.52g=1\.52\), with 6/12 primary models reaching DFR = 0\. However, DFR still varied widely across models, indicating that state\-persistence compatibility is a measurable model property rather than a guaranteed feature of modern LLMs\.
4. 4\.Multi\-turn instability is mainly a state\-construction problem in this setting\.FCS was approximately 1\.0 under fixed anchor states, suggesting that repeated stochastic sampling alone does not explain the observed multi\-turn instability\. The more important issue is how models construct, accept, and reuse structured state\.
5. 5\.Behavioral profiles reveal differences that capability benchmarks may miss\.Some models are stable in single\-turn repetition but unstable when prior state is injected\. This SI–DFR dissociation shows why consistency profiling should not be reduced to one score and why deployment audits may need repeated and state\-persistent tests\.
6. 6\.CKM’s effect decomposes into structural and reasoning\-semantic components\.The 5\-arm sham\-restriction ablation estimated that structural scaffolding accounts for roughly 45% of the SI improvement, while F/H/E reasoning\-semantic content accounts for roughly 55%\. Only CKM achieved the joint pattern of SI improvement and DFR reduction\.

These results are intentionally bounded\. They do not prove that CKM makes LLMs more correct, more ethical, or more capable\. They show that behavioral consistency is an empirical property that can be profiled across models and partially stabilized through prompt\-level epistemic state enforcement\. Within the tested envelope—Korean\-language student daily\-life decision scenarios, repeated\-trial evaluation, and a 12\-model active NewModels cohort with Legacy cross\-checks—CKM provides a reproducible framework for measuring and reducing one form of LLM behavioral instability\.

The broader implication is that future LLM evaluation should ask not only whether a model can produce a good answer once, but whether it can maintain a stable reasoning state when the same decision problem recurs\. CKM is one candidate structure for that evaluation agenda\. Further validation across languages, domains, professional decision tasks, and independent quality assessments is required before stronger claims can be made\.

### Reproducibility Statement

All experiments used publicly available LLM APIs \(OpenAI, Anthropic, Google, xAI\)\. API parameters: temperature = 0\.7 \(gpt\-5\-mini:T=1\.0T=1\.0, the minimum supported by the OpenAI API for this model at collection time\); Study A pilot atT=0\.T=0\.Top\-ppleft at provider defaults; OpenAIseedparameter not used \(no equivalent on Anthropic / Google / xAI\)\. Data collection: Legacy cohort 2026\-02\-15 to 2026\-03\-11; NewModels cohort 2026\-03\-10 to 2026\-03\-16 \(Exp1–Exp3X, Study A/B\); Exp6 sham arms 2026\-04\-23 to 2026\-04\-24\. See Supplementary §S22\.1 for the per\-cohort timeline\.

Per\-vendor model IDs and the per\-call snapshot string \(where exposed by the vendor\) are documented in Supplementary §S22 and §S\-App; readers should note that vendor\-side endpoint updates within the collection window may produce non\-identical reproductions even with matched IDs\. Embedding model:sentence\-transformers/paraphrase\-multilingual\-mpnet\-base\-v2\(768\-dim\) loaded via thesentence\-transformerslibrary \(release\-pinned in the repository\)\. Statistical seeds: permutation tests use 10,000 resamples with seed = 42; bootstrap CIs use 2,000 resamples with seed = 42\. Canonical analysis JSONs \(e\.g\.,ablation\_newmodels\_metrics\_v1\.2\_active12\.json,exp3extra\_newmodels\_metrics\_v1\.2\_active12\.json,exp6\_5way\_comparison\_v1\.2\_active12\.json,exp3\_newmodels\_metrics\_v1\.3\_active12\.json\) are versioned in\_CANONICAL/directories with SHA\-256 checksums recorded in Supplementary §S2 and the repository README\.

The main text is synchronized against the accompanying Supplementary Materials for section references, canonical dataset labels, and claim\-boundary wording\. The primary numerical claims in the main text follow the active\-12 basis stated in §5\.1 and the sensitivity reporting in Supplementary §S\-Sensitivity\.

CKM prompt template, scenario texts \(S1–S6, S9, S10\), 4\-arm and 5\-arm condition specifications, metric computation code, and aggregated data are available at https://github\.com/TeenyToolSoftware/cogos\-behavioral\-consistency\. The canonical data state is thearxiv\-v1\.0repository snapshot; no canonical datasets or reported statistics have been altered for this arXiv preparation\.

### Acknowledgments

We thank Youngjoon Suh \(University of Illinois Chicago\) for early discussions, methodological feedback, and review comments during the development of this work\. We also thank the anonymous reviewers and the automated LLM\-based multi\-agent audit pipeline \(HAWK multi\-pass internal audit, three\-vendor LLM cross\-evaluation\) that contributed to claim\-boundary tightening and readability improvements\. Any remaining errors are our own\. This research received no specific grant from any funding agency in the public, commercial, or not\-for\-profit sectors\.

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