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

arXiv: https://arxiv.org/abs/2610.14843 · HTML: https://mlsanity.com/paper/2610.14843/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 5 of 5)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Darwin Godel Machine: Open-Ended Evolution of Self-Improving Agents](https://mlsanity.com/paper/2505.22954/) (2025)
- [AutoML-Zero: Evolving Machine Learning Algorithms From Scratch](https://mlsanity.com/paper/2003.03384/) (2020)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023)

## Abstract (arXiv)

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.