cs.AIOct 10, 2026

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

Authors: Wenbin Mao, Pei Zou

Organizations: HoomanBio AI Lab, Huaman Biotechnology (Beijing) Co., Ltd.

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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 yyBest std.Std. R2R^{2}Best composedComp. R2R^{2}Cert.Extrap. rel. err. ( n=8/9n{=}8/9 )
wavenumberinv(n)\mathrm{inv}(n)−0.5464-0.5464sq(inv(n))\mathrm{sq}(\mathrm{inv}(n))1.00000001.0000000✓7.7 ⁣⋅ ⁣10−77.7\!\cdot\!10^{-7} / 9.6 ⁣⋅ ⁣10−79.6\!\cdot\!10^{-7}
binding energyinv(n)\mathrm{inv}(n)−0.5465-0.5465sq(inv(n))\mathrm{sq}(\mathrm{inv}(n))1.00000001.0000000✓8.5 ⁣⋅ ⁣10−78.5\!\cdot\!10^{-7} / 1.2 ⁣⋅ ⁣10−61.2\!\cdot\!10^{-6}
Baselines on binding energy: raw nn : 1.81.8 / 3.83.8 ; inv(n)\mathrm{inv}(n) : 0.520.52 / 0.930.93
Table 1: Independent-label redo. The composed operator is the unique closer, and extrapolates four to six orders of magnitude better than the best standard operator.
Figure 1: Measured hydrogen binding energies vs. the runtime-composed operator 1/n21/n^{2} (no free parameter shown; the fitted coefficient is b≈13.6b\approx 13.6 eV, the Rydberg energy). Points lie on the curve to ∼10−6\sim 10^{-6} relative error.
SystemJudgePersistence of authored mechanismsGenesis accounting
BACON.5 ’81none (fit all data)nonenone
AM/Eurisko ’77–84interestingness heuristics (no falsifiable judge)concept memorynone
Eureqa ’09held-out + derivative consistencynone across tasksnone
AI Feynman ’20fit error + physics priorsbenchmark corpusnone
AI-Descartes ’23logic + datanonenone
PySR ’23Pareto + hold-outlibrary-levelnone
Table 2: Eleven prior systems vs. this runtime, condensed to the three dimensions that carry our claim. “None” means not provided in the cited work, to the best of our search.
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