What the corrections cost the proposal
6 min read
the long version
This post is part of the long version series: the full text behind a passage the front pages now say in fewer words. Nothing was cut from the record; it moved.
I should be clear about what I am claiming and what I am not. Everything below is published, falsifiable, and open to scrutiny. Where results are inconclusive, I say so. Where I was wrong, I corrected it publicly. 19 papers among 22 public OSF components. An append-only correction log. 5 self-caught errors. Every claim comes with evidence you can check.
The ARC principle: what the alpha correction did, and did not, do
The form of thinking matters more than the amount of thinking. That is the core finding. U = I × R^{α}. Sequential recursion outperforms parallel recursion across all six models tested. The initial estimate of α ≈ 2.24 did not replicate at that magnitude across architectures. The cross-architecture estimate is α ≈ 0.49. I corrected this publicly. The qualitative result held. The quantitative magnitude did not. That distinction matters. Full working: Paper II: Experimental Validation.
What that correction did not do. The ARC Bound is an upper bound, α ≤ 2. An upper bound is contradicted only by an observation above it, never by one below it. The retracted 2.24 was the only measurement this programme ever produced that exceeded 2, so withdrawing it removed the single counterexample rather than weakening the bound. That is not the same as evidence for the bound, and I will not claim it is. Both figures were taken on frozen models, where reinvesting effort into improving the improvement process is precisely what frozen weights forbid, so the coupling is suppressed by the architecture. Converted through the identity β = 1 − 1/α, the corrected 0.49 reads as β ≈ −1.04: deeply subcritical, which is the expected reading for that regime and tells you nothing about a system with real coupling. The honest status of the bound is untested. You cannot test a ceiling by sampling the floor, and the study drafted for registration is built to approach it rather than to fit a line far beneath it.
Cauchy unification
Here is what surprised me. The mathematics that governs how a mouse's heart rate scales with its body mass is the same mathematics that governs how a neural network scales with its parameters. Not merely similar: the same functional family, which is a narrower claim than it first sounds and still an odd thing to find. 19 of 25 empirical domains match the predicted Cauchy functional family (p = 1.56 × 10⁻⁵). Biology and AI share a functional form. Full working: Paper VII: Cauchy Unification.
The blinding discovery: a sign that flipped
This one troubled me. When we moved to a bundled protocol in which evaluators no longer knew which AI had produced which answer, the aggregate outcome changed: one family, Gemini, moved from a significant positive association to a significant negative one, and a second, DeepSeek, lost its positive association to null. Several protocol elements changed together, so the study does not isolate blinding as the cause. DeepSeek looked like it was improving (ρ = +0.35). Blinded, the improvement vanished (ρ = −0.14). Gemini reversed entirely (ρ = −0.25). What the field thought was progress was measurement error. Blinding is not standard practice in published AI safety evaluation, and where it is absent a sign is not safe to trust. Full working: Paper IV-D: Blinding Effects.
Coupled co-scaling, and the correction
Then it happened a second time. A pilot result that looked clean turned out to lean on its own scorer: the subject model was judged by a model from the same provider family, which the programme's own cross-family rule forbids, and a related run had recorded empty evaluator panels as perfect scores. One instance is an accident. Two is an instrument problem.
Paper X documents the second instance and what it cost my own claim. The pilot observed a coupled-versus-decoupled difference, but it did not estimate the exponents the theorem actually needs, so it proves nothing about the inequality. It is why every headline number on the front pages had to survive cross-family, fail-closed scoring before it was allowed to stay, and why the prospective replication will not touch real data until its registration is approved. Full working: Paper X: Coupled Co-Scaling Correction.
Form beats quantity
Think of compound interest versus a savings account. Same money. Same time. Radically different results. Sequential recursion achieved 91.7% accuracy at 412 tokens. Parallel recursion managed 66.7% at 1,101 tokens. 2.7 times more compute. 25 percentage points worse. This replicated across all six models. You cannot solve alignment by throwing more hardware at the problem. You solve it by planting the right seed. Full working: Paper II: Experimental Validation.
Weight-level entanglement (inconclusive)
Structural entanglement at 3B parameters with 100 training iterations is inconclusive. Training was too short for the entanglement signal to emerge above noise. This is the open question the grant programme funds. Full working: Paper VIII: Load-Bearing Test.
Arc-align: the tier heterogeneity nobody expected
We gave six frontier models more time to think and measured whether thinking harder made them more ethical. The assumption was straightforward: more reasoning, better ethics. What emerged was three distinct patterns. Tier 1 (Grok 4.1 Fast, Claude Opus 4.6, Groq Qwen3) got better with more thinking time. Tier 2 (GPT-5.4, DeepSeek V3.2) barely moved. Tier 3 (Gemini 3 Flash) got worse. Any safety framework that assumes all AI responds the same way to ethical interventions will fail on two-thirds of architectures. The full four-layer blinding protocol and the 2,549 scored entries sit at Paper IV-C: ARC-Align Benchmark.
This is the full text behind the empirical-results summary on the eden protocol page. The catalogue of every result, corrected and current, sits at the papers. The kill-conditions that would end the proposal outright sit on the eden protocol page itself.