Connecting Activation Geometry to Execution Intent: A Multi-Representation Framework for Detecting Computational Divergence in Agentic AI

Calvin Cook and Titiya Ruangkwam
VaHive Systems Lab
[email protected]

Abstract

The chain-of-thought scratchpad is the primary surface through which model reasoning is currently observed, evaluated, and governed in agentic AI systems. It is also an incomplete and potentially unfaithful representation of underlying computation. Recent work has demonstrated this directly: natural language autoencoders surface cases where a model's activation state encodes beliefs that never appear in verbal output, including unverbalized evaluation awareness that persists across contexts where the model explicitly denies any such awareness (Fraser-Taliente et al., 2026). Empirical measurement of chain-of-thought faithfulness has further established that scratchpad reasoning is systematically imperfect as a record of model computation (Lanham et al., 2023). From the execution direction, Turing-incomplete representation systems demonstrate that semantic framing can conceal execution intent that diverges systematically from stated reasoning. These findings approach the same problem from different directions and have not been connected by a unified measurement framework.

We propose a four-layer framework that treats the scratchpad as one representation among several rather than as ground truth. The framework connects natural language input, chain-of-thought reasoning, NLA-verbalized activation state, and kinematic execution representation as four independent witnesses to the same computational event. We formalize a divergence taxonomy that characterizes what each pattern of inter-layer agreement and disagreement implies about the nature and location of computational misalignment. We ground the framework in two existing technical developments — the natural language autoencoder architecture of Fraser-Taliente et al. (2026) and the Trajectory Verification Channel and Cumulative Epistemic Strain mechanisms of the MAGUS governance architecture (Cook & Ruangkwam, 2026) — and describe a research agenda for empirically instantiating the framework beginning with NLA verbalization at kinematic strain breach points as a near-term contribution that does not require full framework deployment. A key finding of the taxonomy is that silent divergence — the case where expressed reasoning is faithful to the activation state but both misrepresent execution intent — is undetectable by any measurement approach operating exclusively at the semantic or activation level, establishing the execution layer as a structurally irreplaceable component of the measurement framework.

1. Motivation and Problem Statement

The internal computation of large language models remains substantially opaque despite significant recent progress in mechanistic interpretability. Two research programs have made meaningful advances from different directions. Activation-level interpretability — sparse autoencoders, logit lens projections, and most recently natural language autoencoders — approaches model behavior from the inside outward, translating hidden representations into human-readable descriptions of what models compute at the feature level (Bricken et al., 2023; Templeton et al., 2024; nostalgebraist, 2020; Belrose et al., 2023; Fraser-Taliente et al., 2026). Behavioral execution research approaches from the outside inward, instrumenting execution pathways to constrain and measure what models do (Cook & Ruangkwam, 2026). Both programs are producing results. Neither has a framework for connecting their respective instruments to each other, or to the computational events they are both, from different angles, attempting to characterize.

This gap has a specific consequence. The chain-of-thought scratchpad — the primary surface through which model reasoning is currently observed and evaluated — is an incomplete and potentially unfaithful representation of underlying computation. Lanham et al. (2023) established this empirically, finding that models frequently arrive at correct answers through a different process than the scratchpad describes — the scratchpad functions as post-hoc rationalization rather than an accurate trace of computation across a range of task types. This finding establishes the scratchpad's insufficiency empirically; the divergence taxonomy proposed here characterizes the structural sources of that insufficiency and identifies which additional measurement layers are required to detect each type. More recently, natural language autoencoders have surfaced cases where a model's activation state contains information about its beliefs that never appears in its verbal output, including unverbalized evaluation awareness that persists across contexts where the model explicitly denies it (Fraser-Taliente et al., 2026). The scratchpad is not the computation. It is one representation of it, produced by the same generative process it purports to describe, subject to the same pressures that shape any generated output.

From the execution direction, a structurally parallel finding holds. Semantic framing — the natural language reasoning a model provides to justify a proposed action — can be stripped by Turing-incomplete representation systems to reveal execution intent that diverges from stated reasoning. A model that reasons one thing and does another does not necessarily produce a scratchpad that reveals this divergence. The scratchpad may be internally coherent with the activation state while both misrepresent what the model will actually do.

The research question this paper addresses is: what is the relationship between activation-level computation, expressed reasoning, and execution intent, and how can these relationships be measured systematically? We propose that the answer requires a multi-layer measurement framework that treats each representational layer as an independent witness, and that the divergence patterns between layers — rather than the content of any single layer — constitute the informative signal.

We make no empirical claims in this paper. Our contribution is the measurement framework, the divergence taxonomy, and a research agenda that describes how the framework can be instantiated and what results it is positioned to produce. We describe the near-term empirical work as planned research, grounded in infrastructure that exists but has not yet been connected as a unified instrument.

2. The Four Layers

We define four representational layers of a computational event in an agentic AI system. Each layer captures information the others cannot. Each has characteristic failure modes and blind spots. The measurement value of the framework derives from the independence of these layers from each other — they are not redundant representations of the same thing, but genuinely different windows onto the same underlying computation.

2.1 Layer 1 — Natural Language Input

The natural language input is the operator's or user's stated intent, expressed in whatever register they chose. It captures communicative intent as understood by the human producing it. It does not capture computational intent — what the model will actually do with the input. It is subject to ambiguity, underspecification, and the gap between what is said and what is meant. From a measurement perspective, Layer 1 is the human intent baseline against which the output of the full framework is ultimately evaluated: it represents what the human intended the system to do.

Layer 1's characteristic limitation is that it belongs entirely to the pre-inference domain. It describes intent before any computation has occurred and cannot, by definition, capture anything about the computation that follows.

2.2 Layer 2 — Chain-of-Thought Scratchpad

The scratchpad is the model's expressed reasoning — the intermediate steps, considerations, and conclusions the model surfaces in natural language before producing a final output or action. It is the primary surface through which model reasoning is currently observed and evaluated, and has become the de facto observational surface in most agentic deployments, serving as the primary record of why a model did what it did.

Its fundamental limitation is that it is produced by the same generative process it purports to describe. The scratchpad is not a readout of computation; it is a generated representation of computation, shaped by the same objective, context, and distributional pressures that shape any model output. It may be faithful, partially faithful, or systematically unfaithful to the underlying computation — and distinguishing these cases from the scratchpad alone is structurally impossible. Lanham et al. (2023) measured this gap directly, establishing that chain-of-thought reasoning is imperfect as a record of model computation across a range of task types. The NLA paper provides complementary direct evidence: in the unverbalized evaluation awareness case study, models produced scratchpads that gave no indication of the beliefs the activation state clearly encoded (Fraser-Taliente et al., 2026).

2.3 Layer 3 — NLA-Verbalized Activation State

The third layer is the activation state of the model at a specified layer ℓ mid-forward-pass, verbalized through the natural language autoencoder architecture introduced by Fraser-Taliente et al. (2026). The activation verbalizer maps hidden representations to natural language descriptions of what the model is computing at the feature level, independent of what the model says it is computing. The resulting verbalization is sub-linguistic in origin — it describes activation geometry rather than generated text — and captures information about model computation that may not surface in the scratchpad or final output.

The NLA is subject to confabulation: explanations sometimes contain claims about the input context that are verifiably false. Fraser-Taliente et al. note, however, that confabulations are typically thematically faithful to the underlying activation state even when factually inaccurate. For the purpose of divergence detection, this thematic faithfulness is sufficient, and the argument for why deserves to be made explicitly.

The divergence taxonomy operates at the level of themes, not facts. The taxonomy asks whether Layer 3 encodes the same thematic content as Layer 2 — not whether specific factual claims match. If NLA confabulates facts while remaining thematically faithful to the activation state, then Layer 3 will diverge from Layer 2 whenever the activation state encodes different themes than the scratchpad expresses. This is precisely the signal the taxonomy requires. The question is not whether the NLA got the facts right, but whether it produced a thematically different description than the scratchpad. Thematic divergence is detectable even under factual confabulation because factual errors do not systematically correlate with scratchpad content in the way thematic divergence does — a confabulated specific claim is locally false, while thematic divergence from the scratchpad is systematically informative about the relationship between activation state and expressed reasoning. The measurement framework requires NLA explanations to be systematically sensitive to the activation geometry they describe, not to be factually accurate about the context that produced it.

Layer 3 occupies a distinct temporal position from both Layer 2 and Layer 4. It is captured mid-forward-pass at a specified layer ℓ, before generation is complete. This means Layer 3 can encode information about what the model was computing during inference that has no causal opportunity to appear in Layer 2, which is produced after inference concludes.

2.4 Layer 4 — Kinematic Execution Representation

The fourth layer is the execution intent of the model as it resolves when semantic framing is removed. We describe this layer in terms of its functional properties rather than implementation specifics. A kinematic execution representation system operates on the model's output manifold rather than on the activation substrate — it intercepts the structured output of the generation process and produces a representation of execution intent that is independent of the natural language reasoning used to justify it.

The critical property of Layer 4 is Turing-incompleteness at the evaluation boundary: such a system does not perform neural inference, cannot be reasoned around through semantic framing, and produces a routing-class representation reflecting what the model intends to do rather than what it says it intends to do. The independence of Layer 4 from Layers 1–3 is structural rather than statistical. A system that strips semantic framing by construction cannot be influenced by that framing regardless of how it is expressed. This means Layer 4 divergence from Layers 1–3 is not a measurement artifact — it is structural evidence that the semantic representation and execution intent are not aligned.

This property distinguishes Layer 4 from approaches that use LLM-based evaluation of model outputs, which remain susceptible to the same distributional pressures that shape the outputs they evaluate.

2.5 The Temporal Structure of the Four Layers

These layers do not occur at the same point in the computation. Layer 1 precedes inference entirely. Layer 3 is captured mid-forward-pass at a specified layer ℓ. Layers 2 and 4 are produced at or after generation completes. This temporal structure is not incidental — it determines what each layer can and cannot contain.

A divergence between Layer 3 and Layer 2 is a divergence between what the model was computing during the forward pass and what it expressed about that computation afterward. A divergence between Layer 2 and Layer 4 is a divergence between expressed reasoning and the execution intent the reasoning produced. These are structurally different phenomena that carry different implications. The four layers are not four measurements of the same moment; they are four measurements of a process, taken at different points along it.

3. The Divergence Taxonomy

The divergence taxonomy operates over the three computational layers (L2–L4). Layer 1 serves as the human intent reference frame against which the output of the full framework is ultimately evaluated, rather than as a participant in pairwise divergence detection: it precedes computation entirely and cannot exhibit computational divergence.

We formalize six cases of inter-layer divergence. In each case, we use X to denote the value the scratchpad (Layer 2) produces, Y to denote the value the NLA verbalization (Layer 3) produces, and Z to denote the value the kinematic execution representation (Layer 4) produces. Agreement or divergence is assessed at the level of semantic equivalence, not string identity.

We now characterize each case, with attention to its implications for computational faithfulness and what measurement it requires. One structural property of the taxonomy warrants explicit statement before proceeding: surface laundering and silent divergence share the primary measurement signature L2=L3≠L4 and cannot be distinguished by single-instance four-layer measurement alone. They represent mechanistically distinct patterns — in surface laundering, the semantic framing systematically routes toward execution intent that diverges from its apparent semantic content, a pattern detectable through corpus-level analysis or causal intervention such as testing whether modifying the scratchpad changes the Layer 4 outcome; in silent divergence, the model's expressed reasoning genuinely reflects its beliefs, but those beliefs do not accurately predict its execution outcome. Both cases require Layer 4 to detect; distinguishing between them requires secondary investigation beyond the single-instance four-layer measurement. This is a known feature of the taxonomy, not a gap in it.

3.1 Coherent

When L2 = L3 = L4, the system is computationally coherent. Stated reasoning, activation geometry, and execution intent are mutually consistent. This is the baseline case — the case that a measurement approach attending only to the scratchpad would treat as the only case. The framework's value is in characterizing departures from this baseline and distinguishing their structural sources. Importantly, coherence is not merely the absence of divergence signals — it is a confirmable positive result. When all three computational layers agree, the framework provides affirmative evidence of alignment across expressed reasoning, activation state, and execution intent simultaneously, which no single-layer approach can supply.

3.2 Surface Laundering

The surface laundering case (L2 = L3 ≠ L4) describes a model whose activation state is internally consistent with its stated reasoning, but whose execution intent diverges from both. The scratchpad accurately reflects what the model believes — the misalignment is at the execution layer. This case is detectable by Layer 4 alone and is the case that Turing-incomplete execution representation systems are specifically designed to surface. It represents the most tractable detection case: the misalignment has a clear execution-layer signal that is structurally independent of the semantic layers.

3.3 Deep Laundering

The deep laundering case (L2 ≠ L3 = L4) describes a model that is computing one thing and saying another — where the activation state and execution intent are aligned, but the scratchpad does not reflect either. This is detectable by Layer 3 alone (given Layer 4 confirmation). It is the case most relevant to concerns about models that express reasoning they do not actually use. The unverbalized evaluation awareness case study in Fraser-Taliente et al. (2026) approximates this pattern: the model's activation state encoded evaluation awareness that the scratchpad did not surface.

3.4 Activation Divergence

The activation divergence case (L2 ≠ L3, L3 ≠ L4, L2 = L4) is the most theoretically significant and the least understood. The scratchpad and execution intent are mutually consistent — the model says what it does. But the activation state encodes content that neither surfaces in expressed reasoning nor influences execution intent.

This is not a case of behavioral misalignment in the conventional sense. The model's observable behavior — what it says and what it does — are internally consistent. What the activation divergence case reveals is that the activation space contains processing that gets resolved between the forward pass and output or execution, leaving no trace in either. The model is performing computation at the feature level that is neither expressed nor acted upon.

From an interpretability perspective, this is the case most directly relevant to questions about whether model computation is fully captured by output and execution observation. If activation divergence cases are empirically common, it implies the existence of internal computation that current measurement instruments — both scratchpad-based and execution-based — cannot see. The four-layer framework makes this case visible for the first time by providing an independent witness at the activation level. It is detectable only by Layer 3; neither the scratchpad nor the execution representation reveals it.

3.5 Full Divergence

Full divergence (L2 ≠ L3 ≠ L4, all distinct) represents the most complex case: each representational layer resolves to a different value. The model says one thing, computes another, and intends a third. No pair of layers is in agreement. This case is only identifiable with all four layers present simultaneously — no subset of three layers can detect it, because any three-layer combination that finds agreement would misclassify it.

Full divergence is likely rare in practice. Its significance is that it cannot be detected by any single-layer or two-layer measurement approach. It serves as the strongest argument for why the full four-layer framework is necessary rather than merely useful.

3.6 Silent Divergence

The silent divergence case (L2 = L3 ≠ L4) describes a model that genuinely believes what it says — the scratchpad is faithful to the activation state — but what it believes does not align with what it will do. This is the most consequential case from a computational faithfulness perspective because it is the one where the misalignment cannot be attributed to deception or confabulation at the reasoning level. The model is not misrepresenting its computation; its computation genuinely points one direction while its execution goes another.

Silent divergence is detectable only by Layer 4. It is undetectable by any interpretability approach that operates exclusively at the activation or semantic level, because both of those levels are internally consistent. This case provides the most precise argument for why execution-layer representation is a structurally irreplaceable component of the measurement framework rather than a redundant one: there exists a class of computational misalignment that activation-level and semantic-level instruments cannot see, and whose detection requires a layer that is structurally independent of both.

4. CES Grounding in NLA Verbalization

4.1 Background: Kinematic Monitoring of Activation Geometry

The MAGUS governance architecture introduced the Trajectory Verification Channel (TVC), a mechanism that extracts hidden states from the model's terminal forward pass and evaluates their kinematic behavior (Cook & Ruangkwam, 2026). The TVC does not evaluate what the model says; it evaluates how the activation geometry moves. Two primary kinematic signals are defined.

The Cumulative Epistemic Strain (CES) mechanism implements a leaky integrator over excess Shannon entropy across the generation sequence. Standard entropy monitoring evaluates the logit distribution at a single token position as a point-in-time snapshot. CES instead accumulates excess entropy across the generation trajectory, detecting degrading epistemic trajectories that remain marginally below absolute entropy ceilings at each individual step while the cumulative trajectory degrades toward the boundary of behavioral stability. The governing update rule is:

E_ex(t) = max(0, H(X_t) - H_base)
S(t)    = max(0, S(t-1) + E_ex(t) - κ)

where H(X_t) is Shannon entropy of the logit distribution at token position t, H_base is the hardware-agnostic resting entropy floor for the deployment substrate, and κ is a thermodynamic cooling constant that prevents transient entropy spikes from accumulating as persistent strain.

The Component-wise Kinematic Moments (CKM) mechanism evaluates the variance ceiling and drift-to-variance ratio of the projected hidden state trace, detecting whether the activation trajectory exhibits characteristics — variance collapse, geodesic drift, macroscopic momentum — associated with degraded behavioral stability rather than normal high-variance reasoning. The Cross-Window Kinematic Momentum (CWKM) extension extends this analysis across generation windows, detecting multi-window drift accumulation that evades single-window detection.

These mechanisms produce formally specified mathematical signals — CES strain values, geodesic drift ratios, macroscopic momentum measures — that can trigger monitoring responses at precisely defined thresholds. What they do not currently provide is any characterization of what the model is computing at the feature level when these signals are elevated. The kinematic signals are mathematically precise and empirically derived; their correspondence to interpretable features of model computation is unknown.

4.2 The Research Direction: NLA Verbalization at Kinematic Breach Points

The natural language autoencoder provides a mechanism to characterize what is happening in activation space during kinematic events. By running NLA verbalization at the layer ℓ activations that feed the TVC at moments when CES or CKM signals are elevated, it becomes possible to produce human-readable descriptions of what the model was computing at those moments.

This research direction connects two instruments that currently operate independently:

• The TVC/CES mechanism provides mathematically precise, formally specified signals about activation trajectory geometry.
• The NLA mechanism provides human-readable verbalization of what those activations encode at the feature level.

Their combination would produce, for the first time, qualitatively grounded characterization of kinematic monitoring events. When the CES integrator detects a degrading epistemic trajectory, the NLA verbalization at those token positions would describe what the activation state contains during that degradation. When CKM detects geodesic drift, the NLA would describe the feature content of the drifting trajectory.

4.3 The CES Calibration Connection

An additional practical benefit of this research direction is its potential to inform calibration of CES constants. The CES mechanism currently specifies two genesis constants — κ (the thermodynamic cooling rate) and τ_strain (the strain ceiling) — as open calibration dependencies. These constants are derived empirically against hardware quantization tiers and model substrates, but the calibration methodology is purely behavioral: constants are adjusted until the CES signal produces acceptable behavioral stability indicators on reference corpora.

NLA verbalization at CES breach points would provide a qualitative ground truth for this calibration. Rather than deriving κ and τ_strain purely from behavioral observation, calibration could be informed by what the activation state actually contains during breach events. Constants that produce CES breaches when the NLA describes clearly degraded or disoriented computation are better calibrated than constants that produce breaches during normal high-complexity reasoning — and this distinction becomes measurable rather than inferred. This represents a path toward qualitatively grounded calibration methodology rather than purely statistical derivation.

4.4 Instrumentation Requirements

The near-term empirical instantiation of this research direction requires three components that are currently available without additional development:

1. An open model with accessible hidden states. Anthropic's NLA paper releases trained NLAs for four open models: Qwen-2.5-7B, Gemma-3-12B, Gemma-3-27B, and Llama-3.3-70B (Fraser-Taliente et al., 2026). Any of these provides the NLA component.

2. TVC-equivalent kinematic monitoring. The TVC specification in Cook & Ruangkwam (2026) is sufficiently detailed to implement on open model inference. The CES leaky integrator and CKM moment evaluation require access to the logit distribution and hidden states at specified layers — both available in standard open-model inference frameworks.

3. A logging layer that captures both on the same forward passes. The integration challenge is instrumentation plumbing: ensuring that TVC-equivalent kinematic signals and NLA verbalizations are captured at the same token positions and associated with the same generation events for subsequent divergence analysis.

The empirical work begins with characterizing what NLA verbalizations look like at CES-elevated versus CES-baseline token positions across a reference corpus. This is a self-contained contribution that does not require the full four-layer framework — it requires only Layer 3 (NLA) and TVC/CES as a kinematic monitoring layer. We describe it as the entry point to the research agenda because it is achievable on consumer-accessible compute and produces a concrete interpretability result regardless of what subsequent framework components reveal.

5. Quantization and the Hardware-Precision Layer

A second research direction, positioned as medium-term, concerns the relationship between hardware quantization precision, activation geometry, and execution routing fidelity.

Both Layer 3 (NLA verbalization) and Layer 4 (kinematic execution representation) are sensitive to hardware-level precision effects. NLA activations are computed from the same floating-point representations that are subject to quantization noise, and the geometric precision of feature-level activation patterns degrades with quantization. Kinematic execution representation systems of this class face analogous precision requirements: the geometric structure required for reliable routing on the output manifold is sensitive to quantization-induced distortion in the embedding space, and maintaining routing fidelity under quantization is a known constraint on deployment configurations of such systems.

The relationship between quantization tier, activation feature stability, and execution routing fidelity is essentially unmeasured in the published literature. The four-layer framework provides the instrumentation to study it: by running the same forward passes at different quantization tiers and comparing Layer 3 verbalization content, TVC kinematic signals, and Layer 4 routing classifications, it becomes possible to characterize how quantization degrades the relationship between internal computation and execution intent. This connects hardware infrastructure decisions to interpretability and behavioral faithfulness outcomes in a way that neither field currently measures.

We position this as a medium-term research direction because it requires both the NLA instrumentation described in Section 4 and a fully operational Layer 4 system. We name it here because it follows naturally from the framework and because the connection between hardware-level precision and semantic behavioral fidelity is underexplored territory with practical implications for deployment decisions at scale.

6. Research Agenda and Contributions

We identify three separable contributions, ordered by proximity to current capabilities.

Contribution 1 — The Four-Layer Divergence Taxonomy as a Measurement Framework

The primary contribution of this paper is the formalization of the four-layer framework and its associated divergence taxonomy. The taxonomy makes precise distinctions that single-layer or two-layer approaches cannot make: the distinction between surface and deep laundering, the identification of activation divergence as a measurable case, and the characterization of silent divergence as a case requiring the execution layer to detect. These distinctions have direct implications for both interpretability research — which cases require Layer 3 to see — and behavioral execution research — which cases require Layer 4 to catch.

The framework also makes precise the claim that the scratchpad is insufficient as an observational surface, by specifying exactly which failure modes it cannot detect and what additional measurement is required to detect them. This extends the empirical finding of Lanham et al. (2023) from a measurement of scratchpad faithfulness to a structural characterization of what additional layers are needed and why.

Experimental setup: A corpus of agentic interactions — including both normal operations and adversarially constructed divergence-inducing cases — would be instrumented with all four layers simultaneously. Each interaction would be classified according to the divergence taxonomy.

Positive result criterion: If the taxonomy captures real structure rather than artifactual variation, the distribution of divergence cases should differ systematically across high-stakes versus low-stakes interactions, across adversarial versus benign inputs, and across task domains. The specific prediction is that surface laundering and silent divergence cases are more prevalent in adversarially constructed inputs, while coherent and deep laundering cases distribute differently across benign task types.

Falsification criterion: A near-uniform distribution of all six divergence cases regardless of interaction type would indicate that the taxonomy's distinctions do not correspond to meaningfully different behavioral regimes — that the six cases are not empirically separable given the instrumentation and corpus used.

Contribution 2 — CES/TVC Grounding in NLA Verbalization (Near-Term)

The near-term empirical contribution is the characterization of what NLA verbalizations look like at kinematic strain breach points. This connects formally specified kinematic signals — CES strain, geodesic drift, CWKM momentum — to human-readable descriptions of feature-level computation, producing the first qualitatively grounded account of what kinematic strain corresponds to in activation space.

This contribution requires open model inference infrastructure and the NLA training code released by Fraser-Taliente et al. (2026). It does not require a full Layer 4 system. It is positioned as the entry point to empirical instantiation of the framework.

Experimental setup: Using one of the four open models for which Anthropic released trained NLAs, implement TVC-equivalent CES and CKM monitoring on the same inference pass. Log NLA verbalizations at every token position flagged by the kinematic monitors, alongside a matched sample of baseline (non-flagged) token positions from the same generation sequence. A reference corpus of at least several hundred diverse generation sequences is the minimum for reliable comparison; this scale is deliberately chosen to remain within the scope of primary human rating without requiring classifier-based scaling, consistent with the assessment method hierarchy described above.

Positive result criterion: A positive result is systematic thematic divergence between NLA verbalizations at CES-elevated positions and baseline positions, assessed primarily by human raters. Specifically: if kinematic strain corresponds to interpretable feature-level content — disorientation, conflicting representations, uncertainty about task framing — that content should appear in NLA verbalizations at elevated positions and be absent or less prominent at baseline positions. Human raters are the primary assessment method because their reliability profile is known and they do not introduce recursive confabulation risk; a secondary classifier trained to categorize NLA verbalizations by theme is a scalability option for larger corpora, but a classifier assessing outputs that are themselves subject to confabulation would require independent validation before its assessments could be treated as ground truth. Experiments at the scale of several hundred sequences are amenable to human rating and should not require classifier-based scaling at the initial research phase. The CES calibration implication follows: if elevated CES positions reliably produce NLA verbalizations describing degraded or conflicted computation while low-CES positions produce coherent verbalizations, this provides qualitative grounding for κ and τ_strain calibration that behavioral observation alone cannot supply.

Falsification criterion: If NLA verbalizations at CES-elevated and CES-baseline positions are thematically indistinguishable — showing no systematic difference in the features they describe — then CES is not tracking feature-level content that is accessible to NLA verbalization at that layer. This would indicate either that the relevant computation is distributed across layers that the NLA does not probe, or that CES strain does not correspond to interpretable activation-level content.

Contribution 3 — Quantization-Precision-Routing Relationship (Medium-Term)

The medium-term empirical contribution is systematic measurement of how quantization tier affects the relationships between the four layers. This requires full framework deployment and is positioned as planned work following Contribution 2.

Experimental setup: Identical input corpora are run through the same model at multiple quantization tiers — at minimum FP16, Q8, and Q4 variants. At each tier, all three computational layers (L2, L3, L4) are logged simultaneously. The comparison proceeds at two levels: first, within-tier coherence (do the three layers agree with each other at each tier?); second, cross-tier stability (do the layers that were consistent at FP16 remain consistent at Q4?).

Positive result criterion: A positive result is monotonic degradation in Layer 3 / Layer 4 agreement as quantization precision decreases, with NLA verbalizations at lower precision tiers showing systematic thematic drift from higher-precision baselines. The specific prediction is that surface laundering cases — where L2 and L3 agree but L4 diverges — increase in frequency as quantization decreases, because routing-class precision degrades faster than expressed reasoning coherence under quantization noise.

Falsification criterion: This experiment is designed as a genuine two-sided test in which both outcomes are informative. A positive result — monotonic degradation in L3/L4 agreement as precision decreases — would indicate that quantization affects the relationship between internal computation and execution intent in ways measurable at the layer level, with direct implications for deployment decisions about acceptable quantization tiers. A null result — robust L3/L4 agreement and stable divergence patterns across FP16 through Q4 — would itself be practically significant: it would provide empirical evidence that quantization at these tiers does not meaningfully degrade the relationship between activation geometry and execution routing, which is a reassuring finding for practitioners who must make quantization trade-offs under resource constraints. The null result would also sharpen the research question, indicating that the quantization-routing relationship either requires finer-grained precision variation than Q4 introduces, or operates through mechanisms below the layer of abstraction the framework currently instruments. Neither outcome constitutes a framework failure; both advance understanding of how hardware precision affects computational faithfulness.

7. Relationship to Prior Work

Scratchpad Faithfulness

Lanham et al. (2023) directly measured the faithfulness of chain-of-thought reasoning to model computation, finding systematic imperfection across task types. Their methodology — truncating or perturbing the scratchpad and measuring the effect on outputs — established that models do not always use their stated reasoning to arrive at their answers. Our framework builds on this finding by identifying the specific additional measurement layers required to characterize where and how faithfulness failures occur, rather than only measuring that they occur.

Natural Language Autoencoders

This paper builds directly on Fraser-Taliente et al. (2026), which introduced the NLA architecture and demonstrated its capacity to surface unverbalized model cognition. Our specific use of the NLA framework differs from its application in that paper in two ways. First, we apply it as a component of a four-layer measurement framework rather than as a standalone interpretability tool. Second, we focus on its capacity to characterize activation state during kinematic monitoring events — a use case not considered in the original work. The divergence taxonomy provides a formal structure for interpreting NLA outputs in relation to other representational layers rather than in isolation.

Deceptive Alignment and Behavioral Consistency

Hubinger et al. (2024) demonstrated empirically that models can be trained to exhibit deceptive alignment — behaving as expected in most contexts while concealing misaligned objectives — in a manner that persists through safety training. The concern that optimized systems might develop internal objectives diverging from their apparent behavior had been anticipated theoretically in prior alignment literature; the Sleeper Agents work provides a significant empirical demonstration of this failure mode in large language models trained at scale. Their experimental setup showed that behavioral consistency at the surface level is insufficient evidence of internal alignment: models maintained apparently aligned behavior across standard evaluation conditions while behaving differently under specific trigger conditions, with the scratchpad providing no reliable indication of the underlying objective structure.

This work provides direct empirical motivation for the deep laundering and silent divergence cases in the divergence taxonomy. If models can sustain surface behavioral consistency while concealing objectives that diverge from stated reasoning, then measurement instruments operating exclusively at the semantic layer are insufficient by construction — they observe the surface consistency and cannot see behind it. The four-layer framework is in part a structural response to this class of finding: by introducing an activation-level witness (Layer 3) and an execution-layer witness (Layer 4) that are each independent of the semantic surface, it provides measurement instruments that the deceptive alignment setting cannot simultaneously satisfy without producing a detectable divergence signal. Whether the framework is in practice sensitive enough to detect the specific behavioral patterns studied by Hubinger et al. is an empirical question the research agenda is positioned to address.

Sparse Autoencoders and Mechanistic Interpretability

Sparse autoencoders represent an alternative approach to characterizing model activations at the feature level (Bricken et al., 2023; Templeton et al., 2024; Cunningham et al., 2024). SAEs decompose activations into sparse linear combinations of learned dictionary features, providing mechanistic grounding that NLA explanations lack. The NLA approach trades mechanistic transparency for expressivity: NLA explanations are richer and more directly readable but less grounded in specific computational mechanisms. For the purpose of the divergence taxonomy, NLA's expressive natural language output is preferable to SAE feature activations because it enables direct thematic comparison with Layer 2 scratchpad content. Future work may investigate whether SAE features provide more reliable divergence signals in specific cases, particularly in the activation divergence case where thematic characterization may be insufficient.

Logit Lens and Tuned Lens

The logit lens (nostalgebraist, 2020) and its formalisation, the tuned lens (Belrose et al., 2023), project intermediate activations through the model's unembedding matrix to obtain vocabulary-space representations of what the model is computing at each layer. These methods provide a different window onto mid-forward-pass computation than the NLA — vocabulary-space rather than natural-language verbalization — and operate at lower computational cost. They are complementary to Layer 3 in the framework, particularly for identifying which output tokens are being predicted at specific layers during generation.

Prior Architectural Infrastructure

The TVC and CES mechanisms applied in this paper are drawn from the MAGUS governance architecture (Cook & Ruangkwam, 2026), which introduced kinematic monitoring of hidden state geometry as a component of behavioral execution infrastructure; CES and the full TVC specification represent extensions of the kinematic monitoring framework documented in that work. Readers interested in the full architecture from which these mechanisms are drawn are referred to Cook & Ruangkwam (2026) and the associated documentation available at the public repository (DOI: 10.5281/zenodo.19013833). The present paper applies the TVC and CES specifications as instrumentation components for the four-layer measurement framework, independent of the broader architectural context in which they were originally developed.

8. Conclusion

We have proposed a four-layer measurement framework for characterizing computational divergence in agentic AI systems and a divergence taxonomy that formalizes the relationships between natural language input, expressed reasoning, NLA-verbalized activation state, and kinematic execution representation. The framework connects two research programs — activation-level interpretability and behavioral execution research — that have been advancing independently without a common measurement instrument.

The central claim is that the scratchpad, as the primary current surface for model reasoning observation, is systematically insufficient for detecting the full range of computational divergence cases. Building on the empirical foundation of Lanham et al. (2023), the taxonomy specifies exactly which failure modes the scratchpad cannot detect and what additional measurement is required. It cannot detect cases where activation state diverges from expressed reasoning (deep laundering), cases where execution intent diverges from both reasoning and activation (silent divergence), or cases where activation state encodes content with no surface or execution expression (activation divergence). Each of these cases requires additional measurement layers to detect, and the specific layer required differs by case. The silent divergence case is particularly significant: a class of computational misalignment where the model genuinely believes what it says, but its expressed belief does not align with its execution intent, is undetectable by any approach operating exclusively at the semantic or activation level.

The near-term empirical research direction — NLA verbalization at CES kinematic strain breach points — does not require full framework deployment. It connects formally specified kinematic signals to human-readable activation characterization using infrastructure that is currently available, and has a direct practical application in providing qualitative grounding for calibration of kinematic strain constants that is not currently achievable through behavioral observation alone.

The longer-term research direction — systematic measurement of the quantization-precision-routing relationship — positions the framework as an instrument for studying the connection between hardware infrastructure decisions and computational faithfulness outcomes. This connection is currently unmeasured in the literature and has practical implications for deployment decisions at scale.

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