Published January 31, 2026 | Version v1
Preprint Open

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

Description

When claims become long, toolchain-dependent, numerically mediated, or operationally complex, “accepted by consensus” stops being sufficient as a closure mode: trust must travel. This paper specifies 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. The protocol enforces canonicalization of inputs and transformations; explicit move ledgers (receipts) with hash-chaining; admissibility rules that separate untrusted context from action; a numeric policy that certifies only consumed values (otherwise halting with a typed, checkable HOLD-certificate); and terminal anchoring in widely checkable clausal certificates (SAT witnesses and UNSAT DRAT/LRAT). The result is a governance-grade verification contract: either a claim closes under replayable receipts and bounded resources, or the system halts with a typed, checkable HOLD that localizes the missing obligation. Failure becomes a transportable scientific object. This manuscript additionally provides (i) a typed HOLD taxonomy with per-type receipt schemas, (ii) an operational refutation budget parameter B(·), (iii) a canonical attempt policy object, (iv) explicit schema objects that bind validation rules to object types, and (v) an end-to-end anchored soundness statement for receipt acceptance. 

Files

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