How are the ARC exponents obtained, and with what uncertainty?
Measured or conjectured, with the uncertainty printed beside every estimate, and no claim of the programme rests on a numeric coincidence. Paper II's surviving estimate of the improvement exponent is about 0.49 by regression (standard error 0.20) and 0.59 by endpoint estimate, whose bootstrap interval runs from -1.3 to 2.9: inconclusive, and what survived the retraction of 2.24. Conduct is checkable: a falsification register, a public retraction, priors credited by name.
Text reviewed 2026-10-31. Any earlier audio edition may differ; the dated text and linked records govern.
Each estimate travels with its own uncertainty. The standard error of 0.20 belongs to the regression estimate of 0.49, from Gemini 3 Flash, the one model in Paper II's capability arm that scaled smoothly; the bootstrap interval belongs to the endpoint estimate of 0.59. Attaching the interval to 0.49 would misreport the analysis. The interval holds zero and two, so it does not yet distinguish sub-linear recursion, no recursion or a value at the conjectured ceiling. The early single-model estimate of about 2.24 was retracted when a blinded replication on five frontier models did not reproduce it.
The other exponents are not interchangeable with alpha. Law II compares a correction exponent, beta, with a drift exponent, k; Law III's ceiling is written in a correction-leverage exponent, gamma. None of the three has yet been measured on any real system. The operational definitions register (DOI 10.17605/OSF.IO/GVQ82) pairs each symbol with the measurement that would produce it, and writing a quantity into an equation does not measure it.
Priors are credited by name: the exponent family d/(d+1) to West, Brown and Enquist (1997) and later groups, and the difficulty-of-control argument to Yampolskiy (2020).
Disclosure: the corpus does mention the fine-structure constant, in a terminology note that separates the December 2024 formalism's use of the letter alpha from the scaling exponent, in the programme's cosmology paper, on its speculative rung, and in passages of the book. None of these supports a measured claim.