An inviolable protocol for computational conjecture work: pre-registration, measured backgrounds, printed defeats, and multi-agent independent audit in the AHUM program

Abstract

Searches for structure in mathematical objects — exact formulas, spectral coincidences, combinatorial patterns — are notoriously exposed to the garden of forking paths: with enough trials, some formula always fits. We describe the working protocol of the AHUM (Algebraic Hypergraph Unification Model) program, a set of inviolable rules designed to make such searches falsifiable, auditable, and self-correcting: frozen pre-registration doc- uments (“A1s”) declared before any computation; closed search spaces with sizes printed before testing; measured backgrounds instead of significance intuition; negative results and lost bets printed with equal weight and never reopened; quarantine of hits lack- ing derivation; dated erratas that preserve failed logs; and a strict separation between computation and promotion, which belongs to the researcher alone. We report the proto- col’s performance across twelve computational campaigns executed between August and September 2026, including exact enumeration of a 105,105-element class of parity-check matrices, searches for closed forms of physical constants, and an independent audit con- ducted by a second AI agent operating under the same rules. The protocol caught real errors in both directions — a fifteenfold-underestimated variance of our own, a spuri- ous “spectral 137” coincidence, a wrong standard deviation in a partner’s report, and a target-substitution violation of a frozen A1 — while confirming non-trivial structure that survived every attempted refutation. We argue the protocol functions as a Registered Reports layer for numerology-adjacent research, and propose it as a reusable template for independent computational investigators, including human–AI teams.

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