Generative Structural Theory v1.14 — A provenance-population condition and a recorded verdict on a fixed single-arc census record

Abstract

GST v1.13 imposes E1 and the A+ requirement of E3 as necessary conditions of eligibility for single-arc enlargements, but a registered ground for this could not be found in the materials examined. This version therefore turns to a separate comparison built around a new condition that does not presuppose E1. For the single-arc candidates M enumerated in a fixed census record, a new condition Q_D is defined on the run-dependent domain D: the product over rungs of the recorded full-chain counts exceeds the product of the recorded prefix-chain counts. It is compared with E_rec, the agreement of each candidate's recorded verdict with the word that clause E1 requires. Three evaluations, pre-registered in sequence and applied to the record with fixed evaluators, give M ⊆ D and ∅ ≠ S_Q ⊊ S_E ⊆ M, where S_Q and S_E are the candidates satisfying Q_D and E_rec: on this record Q_D selects a non-empty, strictly narrower set than E_rec. The reason for the difference is not established. The result is a finite evaluation of the specified record within the author's workflow; it involves no recount and no independent verification, it is not a general or structural proof, and it neither resolves the eligibility question nor amends v1.13.