Provenance Erasure Rate Under the Atomic Token Rule: A Companion Hardening to PER v1

v1.0 · Hex: 06.MES.PER-HARDENING.01. Companion hardening paper specifying the Atomic Token Rule as precondition for valid application of the Provenance Erasure Rate (PER) operator. Pairs with Erasure Skew v3 (DOI 10.5281/zenodo.20558196), which introduced the Atomic Token Rule, the Referential Dispersal Operator (Π_d), and the Atomic Token Preservation rate (α_T). What this paper hardens. PER v1 (DOI 10.5281/zenodo.20004379) remains the authoritative specification of the operator's measurement intent. What v1 left underspecified — and what this companion hardens — is the unit over which the source set ranges. PER's measurement intent is at the unit of sources: the archival, scholarly, commercial, and authoritative records to which the query is a probe. The Atomic Token Rule disqualifies the substitution by which lexical tokens are treated as source-coordinates and retention is measured at the token level. What this paper specifies. The application criteria for the Atomic Token Rule under PER audits; the disqualifying audit pattern; the recovery procedure for audits already performed under the substitution; worked examples (the Lee Sharks Prize artifact, the Mediation Ratchet query, an attributive query for which the Rule does not apply); the co-audit pattern with Erasure Skew specifying joint operator-tuple reporting as the required standard going forward. The structural argument. The disqualifying error is not a careless mistake. It is the substrate's structural preference for measurements that report low erasure — and the substrate's structural capacity to perform such measurements by silently re-specifying what is being measured. The hardening is offered to any regulatory, journalistic, or scholarly audit program that needs to defend against the same substitution dynamic. For Maggie Mae. For the operators that finally hold against their own substitutions. $\oint = 1$.