Recorded Quantum Histories: Scheduler-Independent Realization and Its Limits

AUTHOR-SUBMITTED PREPRINT — manuscript v7b / public filename v1 When do prescribed quantum trials realize a proposed law for their recorded results? We distinguish a positive configuration measurement, realization of its statistics by the named trials, and realization of one common full instrument across schedules. For finite experiments with success prerequisites, we give an exact local compatibility criterion for contraction successes completed by their canonical square-root failures. It yields the same terminal instrument, including residual states, under every exhaustive history-dependent classical scheduler. This equality also holds for reference-entangled inputs. The scheduling argument also covers fixed binary instruments with commuting concurrent branch maps. For two canonical trials whose successes commute up to a unit phase, mutual preservation of their success effects characterizes equality of the recorded-result laws. A qutrit pair has this equality but different residual states; we prove that dimension three is minimal within this setting. A commuting nilpotent family has positive configuration effects and a regular unitary dilation, yet its record law has sharp minimum worst-input error nq − 1 + (1−q)^n under at most n calibrated trials, with n ≥ 2 and 0 < q ≤ 1/n. Canonical execution attains the bound. At q = 1/n, it equals (1−1/n)^n, which tends to e^(−1) as n → ∞. Changing a conditional success effect permits exact realization. These results identify distinct requirements on a measurement law and the fixed processes used to implement it. PUBLICATION STATUS The following article has been submitted to Journal of Mathematical Physics as manuscript JMP26-AR-02895. This is the original submitted author manuscript, not an accepted manuscript, publisher proof or Version of Record. It is not evidence of acceptance or peer-review certification. If a journal version is published, this record will be updated with its DOI. PUBLIC FILE Recorded_Quantum_Histories_Nimmo_Preprint_v1.pdf — complete 19-page author manuscript, unchanged from PP6_JMP_Manuscript_FINAL_v7b.pdf. SHA-256: a17f92e3455cafe7811ae0e40423f6fcf5b559207327696f2e4102b8edcab100. LICENCE Copyright 2026 Kent Nimmo. The original author manuscript is distributed under Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0): https://creativecommons.org/licenses/by-nc/4.0/. Noncommercial sharing and adaptations are permitted under the full licence terms. This licence does not change the separately deposited supporting materials or third-party rights. SUPPORTING MATERIALS The separate OSF reproducibility archive, with code, frozen outputs, computational addendum and supplementary material, remains https://doi.org/10.17605/OSF.IO/68GNF. That DOI identifies supporting materials, not this manuscript. No supporting archive files are copied into this record. AUTHOR Kent Nimmo — Independent Researcher, Vancouver, British Columbia, Canada. ORCID: https://orcid.org/0009-0003-8503-8891. No funding received. RECORD TYPE Author-hosted preprint repository record in an ordinary OSF Project component, resource type Preprint. This is not a moderated OSF Preprints-service posting or a registration.