Mathine — Evidence In, Trust Out

P = NP, A Proof That Travels: Receipt-Based Verification by Transport, Not Search

Mathine: Transported Verification Receipt Machine
Link: https://doi.org/10.5281/zenodo.18442496 [1]

When claims become long, toolchain-dependent, numerically mediated, or operationally complex, “accepted by consensus” stops being a sufficient closure mode—because trust must travel. This paper proposes a receipt-based protocol for transporting verification of candidate P vs NP artifacts across machines, institutions, and time, without relying on hidden environments, informal assumptions, or non-replayable judgment calls. [1]

The protocol’s core discipline is explicit, replayable movement: canonicalize inputs and transformations; maintain move ledgers (receipts) with hash-chaining; and enforce admissibility rules that separate untrusted context from action. Instead of debating narratives, the system either closes a claim under replayable receipts and bounded resources—or halts with a typed, checkable HOLD certificate that localizes the missing obligation. [1], [3], [4]

A key technical hinge is the numeric policy: certify only values that are explicitly “consumed” by the verification contract; otherwise the run must stop with a HOLD that is itself checkable. This makes partial progress legible and prevents accidental closure via implicit assumptions or drifting tool behavior. [1], [2]

Termination is anchored in widely checkable clausal artifacts: SAT witnesses and UNSAT DRAT/LRAT-style certificates. The goal is not to claim “we have a result,” but to specify what it would mean—operationally—for such a result to remain checkable as it moves across environments and time. [1], [2]

The manuscript also provides a typed HOLD taxonomy (with per-type receipt schemas), an explicit refutation budget parameter B(·), a canonical attempt policy object, schema objects binding validation rules to object types, and an end-to-end anchored soundness statement for receipt acceptance—so verification becomes a governed contract, not a social conclusion. [1], [5]

References
[1] R. Figurelli, “P = NP, A Proof That Travels: Receipt-Based Verification by Transport, Not Search”. Zenodo, Jan. 31, 2026. https://doi.org/10.5281/zenodo.18442496
[2] R. Figurelli, “Math Machines: The Systems Architecture of Mathematical Trust”. Zenodo, Feb. 6, 2026. https://doi.org/10.5281/zenodo.18511647
[3] R. Figurelli, “The End of Exhaustive Search: A General Theory of Solving Hard Problems by Certified Transport”. Zenodo, Feb. 2, 2026. https://doi.org/10.5281/zenodo.18460311
[4] R. Figurelli, “Zero-Trust Science: A New Architecture for Scientific Closure (Beyond Peer Review)”. Zenodo, Feb. 6, 2026. https://doi.org/10.5281/zenodo.18509038
[5] R. Figurelli, “Layered Field Collapse: Executable Collapse Signatures from Benchmarks to Metaoverfields”. Zenodo, Feb. 17, 2026. https://doi.org/10.5281/zenodo.18675054 (zenodo.org)