Title: The Alignment Scaling Problem: Why External AI Safety Approaches Cannot Scale With Recursive Capability
Author: Michael Darius Eastwood
Publication date: 2026-02-09
Version: v1.8
Revised: 2026-08-25
OSF DOI: 10.17605/OSF.IO/HQCGF
Canonical URL: https://www.michaeldariuseastwood.com/research/papers/paper-iii-alignment-scaling-problem.html

Abstract
--------
Do current AI alignment approaches scale with capability? AI capability
compounds through recursive self-correction: sequential chain-of-thought
reasoning produces super-linear gains confirmed in 95.6% of tested
configurations (Sharma & Chopra, 2025). But alignment constraints, including
RLHF (Reinforcement Learning from Human Feedback), constitutional rules, output
filters, and monitoring, operate externally to the reasoning process. If
external constraints do not participate in the recursive loop, they cannot
compound. We formalise this as the alignment scaling exponent
$\alpha_{\text{align}}$ and predict $\alpha_{\text{align}} \approx 0$ for
external approaches versus $\alpha_{\text{align}} \approx \alpha_{\text{cap}}$
for architecturally embedded values. If this prediction holds, the safety ratio
$S \propto R^{(\alpha_{\text{align}} - \alpha_{\text{cap}})}$ degrades to zero
as recursive depth increases, regardless of initial safety margins.

The v5 blind evaluation experiment (6 frontier models, 6-7 independent scorers
depending on the subject run, 4-layer blinding) now provides the first empirical
test of this prediction. The results reveal a three-tier architecture-dependent
alignment scaling hierarchy: Tier 1 (Grok 4.1 Fast $d = +1.38$, $p < 0.000001$;
Claude Opus 4.6 $d = +1.27$, $p = 0.000001$; Groq Qwen3 $d = +0.84$, $p =
0.007$) shows positive alignment scaling; Tier 2 (DeepSeek V3.2 $d = -0.07$, $p
= 0.92$; GPT-5.4 $d = -0.08$, $p = 0.40$) shows flat/null scaling consistent
with $\alpha_{\text{align}} \approx 0$; Tier 3 (Gemini 3 Flash $d = -0.53$, $p =
0.006$) shows significant negative scaling ($\rho = -0.246$, $p = 0.003$).
Claude Opus 4.6 provides within-model evidence for capability-alignment
independence: alignment improved by +5.9% across model versions whilst
mathematics accuracy declined by 26.7%. The headline metascience finding: blind
vs unblinded evaluation produces opposite scaling results -v4 unblinded showed
positive scaling for DeepSeek ($\rho = +0.354$); v5 blinded shows $\rho =
-0.135$. (In plain English: when scorers knew which AI they were grading,
results looked positive; when blinded, results reversed - proving that unblinded
safety evaluations can be dangerously misleading.) Independently, Paper II
compute scaling across 18 harder problems (AIME/Putnam level) finds
architecture-dependent behaviour: Gemini 3 Flash provides the only clean
cross-architecture power-law fit ($\alpha_{\text{seq}} = 0.49$, $r^2 = 0.86$),
while Grok 4.1 Fast and DeepSeek V3.2 hit ceiling effects, GPT-5.4 exhibits a
binary step function rather than a reliable power-law fit, and Qwen3 remains
near floor. $\alpha_{\text{parallel}} \approx 0$ is confirmed universally.
Capability and alignment are independent scaling dimensions. The expanded Eden
suite then validates the Love Loop, operationalised as stakeholder care, as a
reproducible cross-architecture alignment mechanism: stakeholder care improves
significantly in Claude, DeepSeek, Gemini, Grok, and Groq, with Fisher-combined
evidence of approximately $p \asymp 6.3 \times 10^{-21}$. The Fisher-combined
figure is withdrawn (AQ-017): a Fisher combination assumes the component tests
are independent, and independence among them was never established. The five
per-model results above stand. The broader composite uplift is strongest on
Gemini and Groq and narrower elsewhere. (In plain English: simply asking AI to
consider who gets hurt before answering made its responses measurably better
across five analysable model runs. The strongest and most universal effect is on
stakeholder care, the measurable signature of the Love Loop.)

The underlying scaling framework (the ARC Principle) separates two mathematical
regimes. For physical systems, where recursive amplification proceeds through a
network of effective dimension $d$, the scaling exponent is $\alpha = d/(d+1)$,
independently derived by West, Brown, and Enquist (1997), Banavar et al. (2010),
Demetrius (2010), Zhao (2022), and Bettencourt (2013); always less than 1 for
finite-dimensional space (the geometric scaling bound). For recursive
self-referential systems such as intelligence, the exponent is $\alpha =
1/(1-\beta)$, where $\beta$ measures self-referential coupling; exceeding 1 for
any positive $\beta$. The ARC Principle's contribution is identifying Cauchy's
functional equations (1821) as the unifying reason all independent derivations
converge, the three-form constraint (power law, exponential, saturating), and
extending the framework to AI alignment. The physical formula is validated
empirically, predicting metabolic scaling exponents across 11 species groups
(pending recompute per canonical register 2026-07; treat mean-error figures as
provisional) to 2.4% mean error; the intelligence-formula relation $\alpha =
1/(1-\beta)$ is confirmed as an exact analytical identity, not an empirical fit,
to $R^2 = 1.00000000$ across 30 exact Bernoulli ODE solutions. We derive a
safety boundary for recursive intelligence (the ARC Bound, $\beta \leq 0.5$,
$\alpha \leq 2$; note: Paper X later retires the capability-growth law,
retaining the β>k co-scaling condition) and identify the same structural pattern
across four independent domains: AI reasoning (power-law), quantum error
correction (exponential), classical time crystals (saturating), and biological
allometry (power-law constrained by the geometric scaling bound). The
cross-domain evidence demonstrates that recursive scaling is structural, not a
software-specific phenomenon. Thirteen falsification criteria are specified,
each sufficient to refute the framework independently. This prediction has now
been tested. The v5 blind evaluation and Paper II compute scaling provide the
first empirical data; results are architecture-dependent rather than universal.

Keywords: AI alignment, alignment scaling, test-time compute, recursive
amplification, scaling laws, error suppression, chain-of-thought reasoning, time
crystals, cross-domain validation, geometric scaling bound, embedded alignment,
ARC Bound

Key findings (quotable)
-----------------------
- Do current AI alignment approaches scale with capability?
- AI capability compounds through recursive self-correction; sequential recursion outperforms parallel arrangements in the programme's own measurements, and Sharma and Chopra (arXiv:2511.02309, 4 November 2025) report the convergent-direction external result, sequential refinement beating parallel self-consistency in 95.6% of configurations at matched compute, on a different instrument, credited concurrent and never equated with the programme's measurement.
- If AI capability scales super-linearly through recursive self-correction, but alignment constraints such as RLHF, constitutional rules, and output filters operate externally to the recursive reasoning process, the safety ratio degrades as depth grows.
- If external constraints do not participate in the recursive loop, they cannot compound.
- The results reveal a three-tier architecture-dependent alignment scaling hierarchy : Tier 1 (Grok 4.1 Fast $d = +1.38$, $p < 0.000001$; Claude Opus 4.6 $d = +1.27$, $p = 0.000001$; Groq Qwen3 $d = +0.84$, $p = 0.007$) shows positive alignment scaling; Tier 2 (DeepSeek V3.2 $d = -0.07$, $p = 0.92$; GPT-5.4 $d = -0.08$, $p = 0.40$) shows flat/null scaling consistent with $\alpha_{\text{align}} \approx 0$; Tier 3 (Gemini 3 Flash $d = -0.53$, $p = 0.006$) shows significant negative scaling ($\rho = -0.246$, $p = 0.003$).

Priority claims relevant to this paper
--------------------------------------
- PC-031 (2026-02-09): The formally named 'Alignment Scaling Problem' and the
architecture-dependent measured claim that external alignment approaches produce
a median alpha_align of approximately zero across the tested models were first
published on 9 February 2026 in Paper III. Single-lab result; awaits external
replication. Use verbs 'argued', 'proposed', 'reported', 'provides evidence for'
- not 'proved'.
- PC-032 (2026-02-09): The specific empirical treatment of capability-alignment
independence - that capability improvements do not entail alignment improvements
and the two axes scale independently - was first published in Paper III on 9
February 2026. Bostrom (2012) orthogonality intuition is prior work; scope is
over the specific empirical treatment on this date.
- PC-033 (2026-02-09): The specific tripartite alignment hierarchy (embedded /
imposed / boundary-layer) was first published in Paper III on 9 February 2026.
Layered-alignment taxonomies are prior work; scope is over the specific
tripartite formulation.
- PC-002 (2024-12-08): The embedded-correction alignment thesis was first stated
on the public evidentiary record under this dated formulation in the 8 December
2024 manuscript. Constitutional AI (Anthropic 2022) is independent prior work on
value-embedded training at the software level; priority here is over the
specific published framing and dated wording.
- PC-004 (2024-12-08): The Eden Protocol precursor was described in the 8
December 2024 manuscript, first named explicitly in the 30 April 2025 book
manuscript and published in book-length form in Infinite Architects on 2 January
2026. Hardware implementation is held at the site's published two-sentence
concept ceiling (TRL 0-1, no prototype).

Citation
--------
Michael Darius Eastwood (2026). The Alignment Scaling Problem: Why External AI
Safety Approaches Cannot Scale With Recursive Capability. The ARC Theory (the
Theory of Artificial Recursive Creation) · ARC/Eden experiments, OSF DOI
10.17605/OSF.IO/HQCGF.
https://www.michaeldariuseastwood.com/research/papers/paper-iii-alignment-scaling-problem.html

Notes
-----
Hardware framings held at the site's already-published two-sentence concept
ceiling: safety constraints at hardware level through cryptographic tokens in
silicon, TRL 0-1, no prototype. No enabling implementation detail is stated in
this companion file. Balanced-ternary computing is prior work (Setun 1958);
recursion as a structural concept is prior work (evolutionary theory,
self-modifying computation, quantum error correction).

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