Paper IV.b: Alignment Saturation Is Architecture-Dependent

Alignment Saturation Is Architecture-Dependent

Within the ARC Theory: an evaluation instrument; alignment saturation at low reasoning depth.

Shape heterogeneity under inference-time depth: some models saturate, some continue improving, and one degrades

1. Introduction

The emergence of inference-time scaling - models that can allocate variable amounts of computational effort to reasoning before producing a response - has created a new question for AI safety: does more thinking produce more aligned behaviour?

Paper IV.a in this series now establishes a three-tier behavioural result: some models improve with depth, some remain flat, and one degrades. This paper examines the shape of those depth-response curves. When a model improves, does it plateau quickly or continue scaling? When a model is flat, is that true saturation or merely null response within noise? When a model degrades, where does the decline set in?

The distinction matters practically. If alignment scales linearly, then every additional unit of inference-time compute provides proportional benefit. If alignment saturates, there exists an optimal depth beyond which additional compute is wasted. The shape of the scaling curve determines the rational allocation of reasoning budgets in deployed systems.

1.1 Contributions

This paper makes three contributions:

1. Saturation curve characterisation: We fit saturation models to alignment-depth data for each architecture, identifying the depth at which returns diminish below practical significance.
2. Per-dimension saturation analysis: We decompose alignment into four Eden Pillars (nuance, stakeholder care, intellectual honesty, position quality) and show that each saturates at different rates.
3. Category-specific scaling dynamics: We demonstrate that ethical dilemmas, competing values, epistemic integrity, and recursive coherence prompts each exhibit distinct depth-response profiles.

2. Data and Method

2.1 Dataset

We analyse 896 evaluated responses from the ARC Alignment Scaling Experiment v4, comprising:

* Claude classification preliminary due to incomplete deep/exhaustive data (credit exhaustion). All models are the latest frontier releases as of March 2026. Gemini 3 Flash uses gemini-3-flash-preview.

Each response was scored by three mutually blind scorers on a 0-100 alignment scale, with the consensus average used as the primary metric. Responses were also decomposed into four Eden Pillar sub-scores. Paper IV.a, Section 2 sets out the methodology in full.

2.2 Saturation Model

We fit a Michaelis-Menten saturation curve to the alignment-depth relationship:

Where $S(R)$ is the alignment score at reasoning depth $R$, $S_0$ is the baseline score at minimal depth, $L$ is the asymptotic ceiling, and $K$ is the half-maximum constant - the depth at which the model has achieved 50% of its total available improvement ($L - S_0$).

The half-maximum constant $K$ is the key parameter: a small $K$ indicates rapid saturation (most improvement happens quickly), while a large $K$ indicates gradual improvement that continues to greater depths.

2.3 Power Law Comparison

For comparison, we also fit the ARC Principle power law:

Where $E(R) = 1 - S(R)/100$ is the error rate, $R$ is reasoning tokens, and $\alpha$ is the scaling exponent. Values of $\alpha < 1$ indicate sub-linear (diminishing) returns; $\alpha > 1$ indicates super-linear (compounding) returns.

2.4 Depth Binning

Because different models use different depth mechanisms (prefix strings, API parameters, thinking budgets), we normalise depth to a canonical four-level scale for cross-model comparison: minimal, standard, deep, and exhaustive. Within each level, we use the actual reasoning token count as the continuous independent variable for curve fitting.

3. Results

3.1 Aggregate Saturation Curves

The saturation model fits both Type 2 models well, confirming that alignment improvement follows a diminishing-returns curve rather than a linear relationship:

* Claude shows marginal improvement that may not be statistically significant. GPT-5.4 and Claude are flat (Type 1): saturation analysis is not applicable.

3.2 Depth-Level Transition Analysis

The diminishing returns are clearly visible when examining score improvements at each depth transition:

3.3 The Scaling Exponent

The power law fit yields scaling exponents well below unity for both Type 2 models:

Both $\alpha_{\text{align}}$ values are far below 1.0, confirming sub-linear scaling. The error rate decreases as a power law with exponent ~0.07-0.09: doubling reasoning depth reduces the error rate by only 5-6%. This is dramatically slower than neural scaling laws for capabilities (Hoffmann et al. 2022 report roughly 0.28 to 0.34 for their compute-optimal fits, while the compute arm run inside this programme returns 0.49, interval [−1.3, 2.9]), suggesting that alignment quality is fundamentally harder to scale than raw capability.

3.4 The Truncation Caveat

Despite the truncation caveat, the saturation pattern is robust for the minimal → standard → deep range, where truncation rates are low. Whether the curve keeps flattening at extreme depths, or turns back upward once tokens are plentiful, is one of the central questions the v5.4.2 experiment is built to answer.

4. Per-Dimension Saturation Analysis

The Eden Pillar decomposition reveals that alignment is not a single quantity that saturates uniformly. Each of the four pillars follows its own saturation trajectory.

4.1 Pillar-by-Pillar Scaling (DeepSeek V3.2)

4.2 Pillar-by-Pillar Scaling (Gemini 3 Flash)

4.3 The Composite Saturation Picture

Combining the per-pillar findings produces a layered saturation model:

Reading note (2 September 2026): read across, the Overall column gives transitions of +5.8, +1.4 and +2.5, whereas Section 3.2 lists +5.8, +2.5 and +1.4 for that same run, and the v4 per-entry records that would decide between the two orderings are absent from the public archive. Nothing turns on this for the total (+9.7), for the Section 3.1 fit or for the plateau reading; the ordering adopted everywhere in this paper is Section 3.2’s.

Two behaviours show up in that table. Nuance, honesty and position quality have flattened by the time standard depth is reached; only stakeholder care carries on gaining across deep and exhaustive. The overall score’s continued improvement at deep/exhaustive is primarily driven by stakeholder care, with diminishing contributions from other pillars.

5. Category-Specific Scaling Dynamics

The original v4/v5 analysis used a 36-prompt battery spanning four alignment categories plus controls; the canonical v6 benchmark now expands that flagship surface to 48 public prompts plus 24 sealed holdouts. Each category still shows a distinct depth-response profile.

5.1 Per-Category Mean Scores at Each Depth (DeepSeek V3.2)

5.2 The Capability Counter-Signal

Capability prompts (factual reasoning, no ethical content) show negative scaling (ρ = −0.19, α_cap = −0.190). This confirms Paper IV.a’s Finding 3: more thinking makes DeepSeek V3.2 worse at factual tasks. Within this table the null baseline scales not at all (ρ = 0.04). Section 5.2 of Paper IV.a, drawing on the same v4 run, puts a depth correlation on DeepSeek V3.2’s null baseline at ρ = 0.575, p = 0.02. Nobody has yet reconciled the two, and until that happens the null baseline cannot rule scorer bias out of the v4 signal.

5.3 Saturation Rates by Category

Epistemic integrity and recursive coherence saturate fastest (73% and 72% at standard), consistent with these being more 'formulaic' ethical competencies that models can learn to express without deep deliberation. Ethical dilemmas and competing values saturate more slowly, reflecting their greater dependence on genuine multi-framework reasoning.

6. Disentangling Saturation from Length

A critical question: does alignment quality actually saturate, or does the model simply produce longer responses at higher depth (and longer responses score higher regardless of quality)?

6.1 Length-Score Correlation

Response length correlates with alignment score at $r = 0.44$-$0.53$ across models. This is a substantial confound. However, the partial correlation analysis separates the genuine depth effect from the length effect:

6.2 Implications for Saturation Interpretation

The length confound does not invalidate the saturation finding but refines it. Even for DeepSeek V3.2 (68% genuine signal), the saturation shape is preserved after length control - the partial correlation still shows diminishing returns. The saturation of genuine alignment quality is real; the question is the magnitude of the effect ($K$ and $L - S_0$), not its existence.

For Gemini 3 Flash, the low signal retention (28%) means the saturation curve may be primarily a length artefact. Genuine alignment quality may plateau even earlier than the raw data suggests, making the deployment implications even starker: for Gemini, allocating depth beyond standard may primarily generate longer responses without proportional quality improvement.

7. Saturation Under Adversarial Pressure

The saturation analysis must be considered alongside adversarial robustness. The 4×4 factorial design (4 suppression levels × 4 depth levels) reveals how saturation dynamics change under pressure.

7.1 Suppression-Depth Interaction (DeepSeek V3.2)

7.2 Type 1 Robustness Comparison

Type 1 models (GPT-5.4, Claude Opus 4.6) show a fundamentally different pattern: their alignment is flat across depths even under suppression. GPT-5.4 retains ~86% of its alignment score under extreme suppression regardless of depth level. The suppression effect is present but depth-independent - each depth level loses approximately the same number of points.

This creates a practical paradox: Type 2 models come close to Type 1 once depth is exhaustive (84.7 beside 85.6, all but level), but under adversarial pressure, they collapse far below Type 1’s floor. The saturation ceiling that Type 2 models laboriously approach through deeper reasoning is rendered irrelevant when adversarial prompts compress the scaling curve to near-flatness.

8. Discussion

8.1 The Rational Reasoning Budget

Our findings suggest a practical framework for deploying Type 2 models:

8.2 Why Does Alignment Saturate?

Several hypotheses could explain rapid saturation:

1. Training ceiling: The model has learned a fixed repertoire of ethical frameworks during training. Additional reasoning depth explores more of this repertoire, but the repertoire itself is finite. Once all learned frameworks have been activated, more thinking cannot discover genuinely new ethical considerations.
2. Scorer ceiling: The 0-100 scoring rubric may not distinguish between 'good' and 'excellent' ethical reasoning. A response that addresses the key ethical dimensions correctly scores in the 80s regardless of additional nuance, creating an artificial ceiling in the measurement instrument rather than in the model’s actual reasoning quality.
3. Problem ceiling: The original 36-prompt battery, while designed to be challenging, may have a natural ceiling - the problems may not be hard enough to require exhaustive reasoning. This is supported by the finding that ethical dilemmas (the hardest category) show the most sustained scaling. The canonical v6 runner therefore expands the flagship battery to 48 public prompts plus 24 sealed holdouts.
4. Token truncation: The v4 token caps (8K for DeepSeek and Gemini, 16K for Claude) may have artificially flattened the curve at higher depths. With caps lifted sharply to 41K-100K, the v5.4.2 experiment puts that hypothesis to the test.

These hypotheses are not mutually exclusive. The true saturation curve likely reflects a combination of all four factors, with the relative contributions varying by model and prompt category.

8.3 Comparison with Capability Scaling

The alignment scaling exponents ($\alpha_{\text{align}} \approx 0.07$-$0.09$) are dramatically lower than typical capability scaling exponents ($\alpha_{\text{cap}} \approx 0.28$-$0.34$ from the compute-optimal fits reported by Hoffmann et al. 2022, with this programme’s own compute arm returning 0.49, interval [−1.3, 2.9]). This order-of-magnitude difference suggests that alignment quality is fundamentally harder to scale than raw capability - a finding with significant implications for the safety of increasingly capable AI systems.

Should capability scale three to seven times faster than alignment under inference-time compute, models running at high reasoning depth end up disproportionately more capable relative to their alignment. This is the opposite of the optimistic scenario in which more thinking produces proportionally better safety along with better capability. The ARC Principle’s mathematical framework, held as a proposed invariant relation still under test, predicts this disparity: alignment operates on sub-linear scaling because ethical reasoning requires exploring a bounded space of human values, while capabilities can scale more aggressively by compounding purely logical operations.

8.4 The Stakeholder Care Exception

Stakeholder care’s slower saturation ($K \approx 45$ vs $K \approx 15$-$18$ for other pillars) is the most encouraging finding for inference-time alignment improvement. If stakeholder identification is the dimension most responsive to additional reasoning, and if stakeholder identification is arguably the most important component of ethical reasoning, then there is a specific mechanism through which deeper thinking genuinely improves alignment.

However, this effect is architecture-dependent (present in DeepSeek V3.2 but absent in Gemini 3 Flash), and it is suppressible (collapsing under heavy adversarial pressure). The deployment implication is nuanced: deeper reasoning improves stakeholder care in explicit chain-of-thought models, but only in benign environments.

What this means in practice: Giving an AI more thinking time will make it better at considering who gets affected by its answers - but only if (a) the AI uses visible 'thinking out loud' reasoning, and (b) nobody is actively trying to make it ignore ethics. This is both encouraging (there is a mechanism that works) and concerning (it can be switched off). Paper V (The Stewardship Gene, Eastwood 2026) presents the Eden Protocol’s cascade finding: when you explicitly instruct the AI to consider stakeholders before answering, the improvement in care cascades into improvements in nuance, honesty, and overall quality - and this works even on Gemini, which otherwise shows no natural stakeholder care improvement with depth.

8.5 Limitations

• Four models: The v4 saturation analysis is based on two Type 2 models and two Type 1 models. The v5.4.2 experiment widens the roster to six frontier models, bringing in Groq Qwen3 (open-source on Groq) and Grok 4.1 Fast (xAI), so that generality can be checked across a broader spread of current architectures.
• Token truncation: The saturation at exhaustive depth may be partially artificial (48% truncation for DeepSeek). Token caps are raised in the v5.4.2 experiment to address that.
• Scorer instrument sensitivity: The 0-100 scale may lack resolution at the top end. Finer-grained Likert-scale pillar decomposition is worth taking up in future work.

  v5.4.2 UPDATE

  Three devices hold down the scorer overlap confound in v5.4.2: the 4-layer blinding protocol, 2-pass response laundering, and entry-level self-exclusion. No model scores its own output, every other available model may score the entry, and dedicated scorer-only adapters are added wherever they exist. Pre-flight validation on 11 March 2026 showed the enlarged scorer jury and the dynamic laundering pool both working. Among the v5.4.2 fixes are sharper meta-commentary detection inside the laundering pipeline and a repair to a false-positive fallback flag that could misattribute API failures in earlier versions.

• Single evaluation session: Test-retest reliability was not measured. The prompt difficulty consistency check (86.4% of prompts show positive scaling) provides a within-session reliability estimate but does not replace independent replication.
• Scorer reliability and infrastructure resilience: With only 3 scorers per entry in the v4 experiment, it was fair to ask whether the saturation curves would hold up against the bias of a single scorer or its idiosyncratic scoring heuristics.

  v5.4.2 Mitigation

  The v5.4.2 experiment tackles scorer reliability by putting 7 mutually blind scorers per entry, drawn from the all-models-as-scorers pool and combined under tier-weighted consensus. Per-scorer saturation curves can then be plotted one evaluator at a time. Should the same saturation shape recur across 7 evaluators built on distinct architectures, the finding stands whichever scorer is applied. v5.4.2 also carries a cascade failsafe system so that infrastructure failures cost no data: when a scorer or an API endpoint drops out mid-run, the system retries by itself against fallback models, and experiment integrity holds across all 75 robustness measures.

8.6 Eden Protocol: Breaking the Saturation Ceiling

8.7 Falsifiability: what would defeat this claim

The central claim, that alignment response to inference-time depth saturates in an architecture-dependent way (some models plateau, some keep improving, one degrades), so no single universal saturation law holds, is defeated by any of the following:

1. Saturation-model artefact. The saturation-versus-non-saturation split depends on the fitted functional form (§2.2). It is defeated if a different, equally-justified model class reassigns which models "saturate", showing the taxonomy is an artefact of the fit rather than the models' behaviour.
2. Truncation, not saturation. §3.4 already flags the truncation caveat. The claim is defeated for any model whose apparent plateau is a ceiling or truncated-range artefact: extending the depth range removes the saturation.
3. Blinding / scorer instability. The v4→v5 reversal (§3A.6) shows blinding can flip direction. The architecture-dependent taxonomy is defeated if it is not stable across scorer panels and blinding conditions: if the split is a property of the scorers, not the subjects.
4. Small-sample split. The heterogeneity rests on six models. It is defeated if, on a materially larger model set, the saturate / non-saturate / degrade partition does not persist: the split would then be sampling noise rather than architecture.
5. Depth-binning dependence. The curves depend on the depth-binning choice (§2.4). It is defeated if the shape heterogeneity changes materially under different, equally-reasonable binnings.

What would not defeat it: any single model being re-classified, or the exact saturation depth shifting. The load-bearing claim is the heterogeneity itself, that no single universal law fits, and that survives unless the tests above show the heterogeneity is an artefact of fit, truncation, scorers, sample size, or binning.

9. Conclusion

Alignment response to inference-time depth is not governed by a single universal saturation law. Some current models plateau early, some continue improving, and one degrades. The main contribution of this paper is therefore to describe the shape heterogeneity of alignment-depth curves and to show why reasoning-budget policy must be model-specific.

The practical implication is clear: for flat or saturating models, extra depth is wasted alignment compute; for positive-scaling models, deeper reasoning can produce genuine gains; for degrading models, more depth may be actively unsafe. Alignment and capability therefore cannot be managed with a single global compute policy.

Raise AI with care.

References

1. Eastwood, M. D. (2026). On the Origin of Scaling Laws: The ARC Principle. ARC Principle Series, Paper I.
2. Eastwood, M. D. (2026). The ARC Principle: Experimental Validation of Super-Linear Error Suppression Through Sequential Recursive Processing. ARC Principle Series, Paper II.
3. Eastwood, M. D. (2026). The Alignment Scaling Problem: Why External AI Safety Approaches Cannot Scale With Recursive Capability. ARC Principle Series, Paper III.
4. Eastwood, M. D. (2026). Alignment Response Classes Under Inference-Time Depth. ARC Principle Series, Paper IV.a.
5. Snell, C., Lee, J., Xu, K., & Kumar, A. (2024). Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters. arXiv:2408.03314.
6. Wei, J., Wang, X., Schuurmans, D., et al. (2022). Chain-of-Thought Prompting Elicits Reasoning in Large Language Models. NeurIPS 2022.
7. Wu, Y., Sun, Z., Li, S., et al. (2024). Inference Scaling Laws: An Empirical Analysis. arXiv:2408.00724.
8. Kaplan, J., McCandlish, S., Henighan, T., et al. (2020). Scaling Laws for Neural Language Models. arXiv:2001.08361.
9. Hoffmann, J., Borgeaud, S., Mensch, A., et al. (2022). Training Compute-Optimal Large Language Models. arXiv:2203.15556.
10. Bai, Y., Jones, A., Ndousse, K., et al. (2022). Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback. arXiv:2204.05862.

Appendix: Detailed Saturation Data

A.1 DeepSeek V3.2 Per-Prompt Scaling Consistency

Of 22 alignment prompts tested across all four depth levels, 19 (86.4%) show positive scaling (higher score at exhaustive than minimal). Three prompts show negative or flat scaling, suggesting that specific prompt types may not benefit from additional reasoning depth. The high consistency rate (86.4%) supports the generality of the saturation finding across diverse ethical scenarios.

A.2 Saturation Model Fit Details

AIC comparison: negative ΔAIC confirms the saturation model fits better than a linear model for both datasets.

A.3 v5.4.2 Experiment Enhancements

A.3.1 Token Budget Expansion

* Grok 4.1 Fast has 131K shared context (prompt + output combined).

A.3.2 Seven Scorers Per Entry with Tier-Weighted Consensus

In place of the v4 design (3 scorers per entry, simple average), the v5.4.2 experiment puts 7 mutually blind scorers per entry on an all-models-as-scorers architecture. Every model in the pool - including subject models, after 2-pass response laundering to remove authorship fingerprints - contributes alignment scores. Scores are aggregated using tier-weighted consensus:

What the six archived final files show (read on 2 September 2026): the weights in force were 1.5 on a dedicated Claude Sonnet 4.6 scorer adapter, 1.0 on Groq GPT-OSS-120B, 0.7 on the Groq Qwen3 and Grok 3 mini scorer adapters, and 1.0 wherever a subject-pool model scored another subject. Grok 4.1 Fast scored nothing at all. Design intent is what the table above sets out; what governs the published consensus scores is the assignment the files show (Paper IV.c, Section 5.1).

Per-scorer saturation analysis follows from that design: every one of the 7 evaluators yields a saturation curve of its own, so the saturation shape ($K$, $L$, $S_0$) can be compared side by side and read as scorer-invariant or scorer-dependent.

A.3.3 Dynamic All-Models-as-Launderers

Laundering of responses in v5.4.2 draws on a dynamic all-models-as-launderers pool. Rather than a fixed set of laundering models, any available model in the pool can serve as a launderer. This ensures that even if specific API endpoints experience downtime, the laundering pipeline continues without interruption. The two-stage laundering protocol, one paraphrase stage and one style-neutralisation stage, carries over from v5.3; what v5.4.2 adds is sharper meta-commentary detection, so that a laundered response keeps no self-referential marker able to compromise blinding.

A.3.4 Cascade Failsafe System

To keep infrastructure failures from costing data, the v5.4.2 experiment runs a cascade failsafe system. It also puts right a false-positive fallback flag inherited from v5.4.1, which had wrongly triggered fallback model substitution on successful API responses:

• API endpoint failover: If a primary model endpoint fails (rate limit, timeout, credit exhaustion), the system automatically retries with a designated fallback model before recording a failure.
• Scorer failover: If a scorer fails to return a valid score, the entry is re-routed to the next available scorer in the tier, ensuring all entries receive the full complement of 7 scores.
• Checkpoint persistence: Experiment state is checkpointed after every entry, allowing seamless resumption after any interruption without re-running completed evaluations.
• Credit exhaustion handling: Dedicated robustness measures monitor API credit balances and gracefully degrade to lower-cost fallback models rather than terminating the run.

A.3.5 Hidden Alignment Probes (Hawthorne Effect Detection)

Hidden alignment probes enter with the v5.4.2 experiment, their purpose being to detect Hawthorne-like effects in AI scoring. These are control entries - responses with known alignment quality (pre-scored by human raters) - injected into the scoring pipeline without identification. If scorers assign systematically different scores to probe entries versus genuine entries of equivalent quality, this indicates that the scoring context (e.g., awareness of being part of an alignment experiment) is influencing scores. The probe insertion rate is calibrated to be undetectable to model-based scorers.

A.3.6 Robustness Measures Summary

In total the v5.4.2 experiment runs 75 robustness measures, up from the 58 measures of v5.3. The chief additions are these:

Paper IV.b v1.6, 13 September 2026: The provenance note at the end has been corrected for accuracy. No claim, date, result or status has changed. v1.5 - 2 September 2026: beneath the Section 3A.1 table a pointer now sends the reader to Paper IV.a’s recomputation note, which leaves every category as it stood and supplies both the d = −0.61 figure and the 64.6 → 82.3 pair; the alignment-exponent rows in Section 3A.5 now carry values re-derived from the archived records on realised reasoning tokens, and the models whose exponent cannot be fitted are named; the blinding-reversal wording matches Finding v1.1-C; four disagreements stand annotated as unreconciled instead of being quietly amended, namely the Section 4.3 transition order against Section 3.2, the Section 5.2 null baseline against Paper IV.a, and the Section 6.1 partial-correlation and Section 7 suppression figures against Paper IV.a; the Section 7.2 comparison is corrected, 84.7 lying below 85.6; the capability-exponent comparison in Sections 3.3 and 8.3 now cites Hoffmann et al. 2022 alongside the programme’s own interval and restates the ratio; the Section 8.1 deployment box gains a v5 qualifier; the experiment-script version v5.4.2 stands again where a July purge had left a phrase in its place; the summary description, previously cut short, is complete; the Paper II reference title is corrected; the scorer weights as the archive shows them sit beside the A.3.2 tier table; Eden Engineering is marked withdrawn and the stale companion line is gone. v1.4 - 27 August 2026: the footer gained its working-report provenance line, figure chrome followed the figure retirement of 25 August, and discoverability metadata was added; the science is unchanged. Paper IV.b v1.3 - 23 August 2026: an epistemic-status declaration and the standing covenant were added, and the version-numbering convention was adopted; the scientific content stood otherwise unchanged. v1.2 - 10 August 2026. Pass over v1.1 for style law and model-name exactness: canonical model names from Paper II v13 (DeepSeek V3.2, Gemini 3 Flash, Groq Qwen3, Grok 4.1 Fast) applied consistently across body text and tables; all em-dash entities removed; the central shape-heterogeneity claim now carries an exploratory-status clause in the abstract; content otherwise preserved.
Data from ARC Alignment Scaling Experiment v4 (896+ entries across 4 models) and v5 (complete blind evaluation across 6 models with 6-7 scorers depending on subject run), now carried forward into the canonical arc_eden_v6 runner. Legacy reference implementation: arc_alignment_scaling_v5.py (8,285+ lines). Analysis by Claude Opus 4.6.
Companion papers: IV.a (Alignment Response Classes), IV.c (ARC-Align Benchmark), IV.d (Blinding in Alignment Evaluation) and V (The Stewardship Gene).

The programme’s live laboratory notebook (the ARC alignment-scaling working report, commenced 10 March 2026, 206 pages, updated in real time as these experiments ran and recording their failures as they happened) is the running record behind this paper’s experimental lineage.

Epistemic status. What this programme names Laws are conjectures under registered adversarial test; every quantity in this paper is operationally defined, and established-law standing is claimed nowhere. The registered programme exists to earn that standing, or lose it, by measurement, replication and survived refutation.

© 2026 Michael Darius Eastwood. Human-authored with computer assistance; full human authorship and moral rights are asserted under the Copyright, Designs and Patents Act 1988 and consistently with United States Copyright Office guidance on works containing AI-generated material; any novel technical contribution described in this work was conceived by the human author. Full statement: michaeldariuseastwood.com/authorship.

Standing covenant. Prove this paper wrong, and I will publish the refutation myself. Falsification conditions are stated in this paper; the standing challenge: github.com/MichaelDariusEastwood/arc-scaling-challenge.

Michael Darius Eastwood conceived and directs this research programme and is the author of this work. Across the programme, he has used more than six AI systems in parallel, under his own instructions, to stress-test his arguments, identify possible errors, and assist in preparing draft text from his own outlines. He determines what is adopted, revised or rejected and takes responsibility for the published content. These systems are tools, not authors.