Claim 12 (original form): sequential super-linearity α≈2.24. The early measurement suggested strongly super-linear scaling of capability with recursive depth. When we attempted cross-architecture replication, the result failed to replicate. The robust estimate is α≈0.49 - sub-linear. We retracted the 2.24 figure, corrected every grant application that carried it, and kept the retraction in the public record.
Why this matters: the methodology self-corrects. The kill-conditions on this page are not decoration - one of them has already fired, and this is what happened when it did.
| # | Claim | What would kill it | Status |
|---|---|---|---|
| 1 | Embedded alignment (Eden Protocol): correction must live inside the recursive loop, not outside it | Demonstration of a purely external oversight mechanism that remains sufficient as capability scales - i.e., a constructive refutation of the undecidability results (arXiv:2606.28639) and of the alignment-faking failure mode (arXiv:2412.14093) | OPEN - strengthened by two independent proofs |
| 2 | ARC Principle (U=I×Rα): recursion form determines scaling regime | Systematic measurements showing scaling regime is independent of recursion form (sequential vs parallel) across architectures | OPEN - directionally supported (Sharma & Chopra 95.6%) |
| 3 | Blinding sign-flip: unblinded AI evaluation can reverse a result's sign | Replications under the published four-layer protocol showing no evaluator-family effect on sign across models | OPEN - single-lab; replication package in preparation |
| 4 | Cauchy unification of d/(d+1) derivations | A continuous solution to the multiplicative functional equation that is not a power law (mathematically foreclosed), or empirical domains systematically violating the classification (6/25 already recorded as non-matching - published) | PARTIAL - 19/25 domains confirm (p≈1.6×10⁻⁵); the 6 misses are published, not hidden |
| 5 | Stewardship Gene: stakeholder-care prompts measurably improve ethical reasoning | Blinded replications showing no effect (Fisher-combined result currently p≈6.3×10⁻²¹, single-lab) | OPEN - needs independent replication |
| 9 | Parallel recursion does not compound (αpar≈0) | Demonstration of super-linear capability growth from pure parallel sampling at fixed compute | OPEN - consistent with Brown et al. (2024) |
| 12 | Sequential super-linearity (α>1) | ALREADY FIRED for the original claim - cross-architecture replication failed | RETRACTED α≈2.24 → corrected to α≈0.49 |
| 13 | Embedded safety at zero capability cost | Replications showing consistent capability degradation from embedded correction | OPEN - held in tested configurations; single-lab |
| 15 | External alignment cannot scale | A scalable external verification scheme - now foreclosed in the limit by the Soundness–Completeness–Tractability Trilemma (arXiv:2606.28639) unless that proof is refuted | STRENGTHENED - independent formal proof reached the same conclusion |
| 16 | Recursion as cross-domain structural principle | The 19-row convergence register failing source verification, or the pattern failing to appear in new domains where the framework predicts it | OPEN - 19 sourced convergences; register public |
| 17 | HRIH creation cosmology | Explicitly speculative and non-empirical by design; five in-principle falsifiers listed in the paper (e.g. demonstration that recursive intelligence cannot in principle influence physical constants) | SPECULATIVE - flagged as such; carries no empirical weight in the programme |
| 18 | Caretaker Doping (hardware-embedded ethics, TRL 0-1) | Proof that substrate-level enforcement is physically or economically infeasible - currently moving the OTHER way (Odeh patents US 2026/0010411/0780; Petrie arXiv:2509.07637; FlexHEG arXiv:2506.15093) | OPEN - direction independently emerging in hardware security |
| β>k | Co-scaling stability condition (Paper X): recursive self-improvement is stable iff correction out-scales drift | A real system showing stable recursive self-improvement with decoupled (non-co-scaling) correction, or drift-free scaling without any correction | OPEN - first real-model signal consistent (decoupled hacks, coupled clean); needs multi-model sweep (the £624k programme) |
Seriously - here is the target list. (1) Run the four-layer blinding protocol on your own models and publish the signs. (2) Check the 19 convergence rows against their primary sources. (3) Recompute the .eml SHA-256 hashes. (4) Find a document predating December 8, 2024 containing the control-failure thesis + embedded-alignment solution + recursion equation together. (5) Build a decoupled recursive self-improver that stays clean. Any of these lands, we publish it here.