Architecting Objective Honesty: a measured governance corpus for autonomous mathematical discovery
Year: 2026
Type: preprint
Abstract: Organisations that run autonomous mathematical discovery accumulate governance rules faster than they can audit them. Rules are written after failures, cited by later rules, and never counted; when a reviewer asks how many govern the system, the answer is a round number nobody can produce. This paper replaces that number with a measurement. We take one working estate — a combinatorial invention engine plus a number-theoretic certification campaign — and turn its constitution into a register: 98 numbered laws inside 165 records, each carrying the file and line it came from. We then measure the corpus against three questions. First, how many laws have evidence behind them? 39 carry a birth event or an evidence line; 59 carry neither and are recorded as preference (95% CI 50.3-69.3%). Second, do the laws transfer to a second system built for a different domain? 33 of 94 transferable laws fire in that system's charter (35%, 95% CI 26.2-45.2%), each anchored to a line. Third, does the governance contain the contradictions it claims to prevent? Eight conflicts were recorded; on re-verification two were stale at time of use and six remain open. Finally we instrument six of the laws that require a gate to prove itself: six gates, six demonstrated failures, and the instrument then caught two live defects in the estate's own artefacts. Coverage is stated rather than implied — 6 of 98 laws instrumented (6.1%). Status: measured, single-author, two systems, not externally reviewed.
Author: Van Der Walt, David AB
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225569596