Form, Generation, and Selection of the Gravitational Coupling: The Zero Theorem T0-B Closure Record

Abstract

Paper III of the Zero Theorem cycle of the RCD 3.0 program. Paper I froze the question and its kill conditions before any search was run; Paper II recorded the adjudication of part A (rigidity of form). This Record closes part B — rigidity of normalization — under the category NO-SECOND-ROUTE: as far as the located and examined literature reaches, no second route to the gravitational normalization survives examination; every informational route imports κ through a single tollbooth, the area–entropy identification. The closure is not absence by exhaustion: a last call designed to kill it produced a material finding — induced Einstein gravity from infinite towers of states (Kehagias–Partouche–de Vaulchier) — which generates a finite, non-running G at one loop, with no tree-level Einstein–Hilbert term and no use of the area–entropy bridge in its derivation. An adversarial sub-proceeding with opposed counsel adjudicated its exact status: typed with the infrared spin-2 coupling (confirmed); composable as an EFT module with the classical form route (confirmed); non-selective — a parametric family, conditional predictivity rather than rigidity (fails); carrier genealogy indeterminate, after a dedicated diligence derived, as a result of this Record, that the model satisfies S = A/(4G_ind) by construction — a descendant identity of the effective action, not proof of ancestry. The resulting distinction — form, generation, selection — shows that structural rigidity of a law need not imply rigidity of its coupling. The remaining frontier is single and located: the microscopic status of the entropy density η — independent datum of the vacuum, or conical shadow of the gravitational effective action? Companions: Paper I (10.5281/zenodo.21781069), Paper II (10.5281/zenodo.21843483).