Generative Structural Theory v1.13: No In-Band Eligible Enlargement of a Certified Cone -- A Finite-Range Closure from the Pinned Construction and Two Recorded Premises, with the Single-Arc Application of 3.8a as a Further Premise

This deposit is a DRAFT manuscript of Generative Structural Theory (status as the manuscript states it: DRAFT / NOT LOCKED / NOT A RECORD). It is not a final version. The manuscript considers the finite family of enlargements that the theory's enlargement law produces from a certified cut value, and asks whether any enlargement is both inside the recorded single-arc cone-size band and eligible. It proves a lower bound on every layer from the pinned construction, evaluated at the subject's record-stated n; no measurement enters that bound. That the layers beyond the single-arc layer lie out of band on the recorded single-arc band is reported as a result with a recorded premise, not as an analytic theorem, and it carries the identification of |desc(W)| with the recorded cone size. The single-arc layer is closed from the records and a stated premise: E1, and E3's requirement concerning A+, are taken as necessary conditions of eligibility, a premise whose registered standing the manuscript does not confirm. E2 and E4 are not judged. The resulting closure is finite in range. It rests on recorded premises — the band's upper end and the single-arc classification — on the pinned construction, and on the single-arc application named in the manuscript as a further premise, which is not a recorded figure; it inherits the conditions and limits the manuscript states. This closure is neither an analytic theorem nor an unboundedness result. No arc is selected or nominated. The manuscript names the claim map V113_CLAIM_SCOPE_71.txt, itself DRAFT / NOT LOCKED; naming it is a reference update and does not settle which map version binds the paper. The PDF includes the version-history entries recorded in the manuscript.