Pre-Registered Genesis Accounting for Recursive Self-Improvement: First Audited Operator-Genesis Events in a Physics-Discovery Runtime
Organizations: HoomanBio AI Lab, Huaman Biotechnology (Beijing) Co., Ltd.
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.
Figures & tables
| Target | Best std. | Std. | Best composed | Comp. | Cert. | Extrap. rel. err. ( ) |
| wavenumber | ✓ | / | ||||
| binding energy | ✓ | / | ||||
| Baselines on binding energy: raw : / ; : / | ||||||
| System | Judge | Persistence of authored mechanisms | Genesis accounting |
|---|---|---|---|
| BACON.5 ’81 | none (fit all data) | none | none |
| AM/Eurisko ’77–84 | interestingness heuristics (no falsifiable judge) | concept memory | none |
| Eureqa ’09 | held-out + derivative consistency | none across tasks | none |
| AI Feynman ’20 | fit error + physics priors | benchmark corpus | none |
| AI-Descartes ’23 | logic + data | none | none |
| PySR ’23 | Pareto + hold-out | library-level | none |
Recursive Self-Improvement
Recursive self-improvement studies AI systems that use feedback from their own work to modify and evaluate future versions.
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