Proof Room
Working proofs and formal derivations for the ARC / Eden research programme. Every proof is independently verifiable.
Core Derivations
ARC Principle Derivation
U = I x g(R) where g(R) = [1 + (a/alpha)R]^alpha. Derivation from first principles of recursive systems. The exponent alpha is not asserted — it is measured from data. The coupling parameter beta determines whether recursion amplifies or saturates.
Paper I → Paper VII →Published
Cauchy Unification
The Cauchy distribution is the natural prior for recursive amplification. Alpha follows a Cauchy distribution because recursion compounds multiplicatively. This means the expected value of alpha can diverge — tail risk is the norm, not the exception. Paper VII provides the formal derivation.
Read →Published
Undecidability of External Alignment
arXiv 2606.28639. Formal proof that external (non-embedded) alignment verification is undecidable for frontier-scale models. The Trilemma: any external verification protocol either (a) is incomplete, (b) is inconsistent, or (c) requires embedded access to the model internals. Only (c) works. This is the mathematical reason Caretaker Doping is necessary.
arXiv →Published (arXiv)
Working Proofs
Coupled Co-Scaling Correction
Alpha and beta are not independent parameters. The coupling term adjusts the measured exponent based on the self-referential feedback observed in the data. Paper X formalises the measurement protocol. Preliminary DGM v4 data suggests coupling in the expected direction.
Paper X (draft) →In Progress
Convergence Probability
The probability that 29 independent findings across 11 domains would all converge on the same framework by chance. Binomial model: each domain has a prior probability of converging independently. Joint probability computed and published in the convergence register.
Paper XI (draft) →In Progress