Pre-Registered Genesis Accounting for Recursive Self-Improvement: First Audited Operator-Genesis Events in a Physics-Discovery Runtime

Abstract

Claims of recursive self-improvement are easy to make and hard to falsify: did improvement come from re-using designer-provided mechanisms, or from mechanisms the system authored itself? We introduce a pre-registered, two-tier accounting: M1 counts machine-generated content instances within a designer-provided vocabulary, while M2 counts machine-authored mechanism types (new operators registered into the runtime's own vocabulary, with a held-out-validation certificate). We report the first audited M2 genesis events. In the primary event, depth-limited compositional search over elementary operators, judged by held-out R^2 on real NIST hydrogen Balmer measurements, produced the operator sq(inv(n)) = 1/n^2 -- the Rydberg-level form -- which no standard-library transform could express (held-out R^2: -0.546 best standard transform vs. 1.0000000 composed). A protocol flaw (independent variable built by inverting the very law under test) was caught in audit and repaired via an independent-label protocol; extrapolation to unseen levels (n=8,9 trained on n<=7) attains relative error ~10^-6, four to six orders beyond the best standard operator. A second event independently recovered sqrt(inv(a)) -- Kepler's velocity law -- from JPL ephemeris vectors. Also incorporated: an audited compounding channel (first domain-level measurement: 1.109x accuracy ratio on a real held-out domain) and blind, decurated genesis exams whose honest tally is zero. The Kepler event passes line audit; the hydrogen gap reproduces on He II; the certificate is threshold-stable. Against eleven prior systems, the contribution is the measurement and governance of machine-authored mechanisms, not the search algorithm or rediscovered physics. Limitations: exams were curated by agents who knew the textbook answer, triggers manual, grammar observer-injected; both events demonstrate capability to author, not yet autonomous genesis.