The Species Bridge Without a Global Renormalizer: Auditing the Ultraviolet Entry of Record Relevance

Does the information-theoretic structure of records — which observables of a quantum field are redundantly, publicly registered in accessible environments — enter the renormalization of Newton's constant? In the induced-gravity (Sakharov) reading, 1/G is a one-loop species sum fixed by the effective theory's field content. Paper 39 of this sequence asked whether a record-theoretic filter — a grain-relative, infrared indicator of which species carry accessible redundancy — restricts that sum, and answered no, conditionally: under the standard effective-action reading of the counterterm (assumption H there), the filter moves accessible-entropy accounting, never the ultraviolet counterterm. One route was left flagged (39-A): a constructed, scheme-robust ultraviolet bridge from record relevance to the induced-1/G counterterm, with the burden of proof assigned; Paper 40 registered it as a missing postulate and Paper 42 as a theory-side debt. This paper — the forty-seventh in the sequence, capstone of its Debt-Discharge Program (Papers 45-47) — accepts the burden and audits the registered bridge route to completion over the declared one-loop class, built to close either way. The setting is fixed before any candidate is scored: one-loop induced gravity on flat and weakly curved backgrounds; the counterterm as the sqrt (g) R Seeley-DeWitt structure; the closed scheme class S = dimensional regularization, covariant proper-time cutoff, Pauli-Villars; and "scheme-robust entry" defined by three conditions on a record-conditioned difference at matched renormalization conditions — nonvanishing in every scheme, not absorbable into any record-independent convention, sign-stable — calibrated by a matched computation showing that physical-threshold effects pass the criterion and regulator-only effects fail it (a record-dependent physical cutoff is not struck as a regulator convention; it is new physics at the N2 door, priced at the bridge-postulate gate). A four-column species ledger (entanglement entropy; record-bearing state entropy; accessible/public record functionals; the counterterm) acts as type gate: an entry claim must move the counterterm column — an infrared or warrant relabeling has, by definition, not entered. Three declared bridge families are scored on five fixed criteria, and a two-tier entry test runs on the doors N1 (Hadamard short-distance structure), N2 (algebra or measure of the ultraviolet functional integral), N3 (a boundary sector that feeds the counterterm). Record-conditioned modular flow is refuted — record conditioning selects states within a fixed Hadamard folium and cannot touch the operator data the counterterm is built from; its crossed-product variant delivers neither a record-covarying algebra extension nor a record-dependent coupling shift. Horizon-algebra/edge-mode readings are refuted — edge content is fixed by gauge group, boundary conditions, and regulator: record structure selects which edge data are read, never which modes exist in the measure. Cutoff-scale Darwinist redundancy returns no entry on both horns of a displayed fork — if undefinable at the cutoff, there is nothing to score (ill-posed) ; if definable, its functional is state/accessibility data, refuted by the same engine — with the existence question, Paper 39's flagged open point, recorded open and verdict-irrelevant. The relative door lemma extends the refutations, conditional on the displayed typing premise L-type (record structure enters as state and accessibility data — the record architecture's own load-bearing typing), to every record functional respecting it; a candidate rejecting L-type is by that very act new physics, routed to a bridge-postulate normal form with a five-conjunct acceptance gate, and no candidate completed the gate. The verdict: the bridge is killed over the declared class — no declared family exhibits entry, none remains open in a way that could supply entry at the declared order, no normal form completed, and the door lemma closes all L-type-respecting functionals — strengthening Paper 39's verdict from inert-under-H to a no-go theorem at exactly its declared scope: one loop, over S, conditional on L-in and L-type. "No bridge ever" is never claimed: other loops, sectors, schemes, venues, L-type-violating record-fundamental physics, and undeclared families remain outside the theorem, and the theorem says so. The retired authority is the Global Renormalizer: the entry question needs no external arbiter — it is well-posed, auditable, and, within the declared class, answered in the negative. Within the current registered debt ledger, the last declared theory-side ultraviolet route to a framework-forced world-side shift (the series' U3 question) closes at the audited scope; world-side motion, if it ever comes, comes from Paper 44's laboratory program, not from the ultraviolet. Newton's constant is predicted on no branch; no evidential gate of the series is crossed; the thirteenth grouping closes with all three registered debts disposed — microcausality scoped, dressed sources scoped, species killed-with-content.