Seven Sessions, One Caught Flaw: Running a Mathematics Program Under a Provenance Discipline When the Operator Cannot Check the Math

On 2026-07-03, a research-program specification for a mathematics framework - entropic optimal-transport couplings, total positivity, and truncated embeddings into the positive Grassmannian - was taken from intake to a completed, audited, third-party-witnessed body of work in one day, across seven LLM-collaborative sessions governed by an explicit provenance discipline. The operator is a Master Electrician and Master HVAC Technician who started writing code on April 4, 2026, and cannot verify the mathematics himself. That is the point of the study. In a domain where the operator has no independent judgment, the discipline - append-only trace, ratification gates, counterexample-first probes, adversarial audits by fresh model sessions, honest-negative closes, cryptographic witnesses - is the only mechanism standing between him and confidently-stated nonsense. It caught two real errors the same day it produced the work: a wrong formula (a threshold stated as temperature-dependent when the proof gives it temperature-independent) and a genuine proof flaw (a contraction argument using the two-step ratio where the one-step ratio belongs; the intermediate inequality was numerically falsified by the auditing session, then repaired with an explicitly larger constant). It also killed two of the source program's dreams honestly. The mathematics itself - seven proved statements, an exact perturbation envelope, three scope-fencing counterexamples - is reported in calibrated terms: proved modulo four page-level-unverified classical citations, adversarially audited by fresh model sessions of the same model family (six sound, one caught and repaired), and reviewed by no human mathematician. Every quantitative claim resolves to a workspace artifact anchored by SHA-256 (verification appendix), and the paper deposits its own sealed provenance trace so the record is self-verifying. Either the mathematics survives human review, or its failure will be traceable to a specific hashed artifact. Either outcome is information.