The Record-Species Constraint on Induced Gravity: Whether a World-Side Record-Relevance Filter Restricts the Induced-G Species Sum or Merely Re-weights Entanglement Entropy

This paper is the thirty-ninth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates. It is the second panel of the eleventh grouping — a Gate-VII / U3 audition, which asks whether the framework can force a distinctive world-side observable rather than one more warrant-side redescription. The three panels audit independent seams: Paper 38 a dynamical one (leading result: a null), this one a structural one, Paper 40 the synthesis. Paper 36 read the Clausius/entanglement entropy as a coarse-graining state entropy of a declared record-bearing support and imported the induced-gravity which-entropy / species problem as a live defect: in Sakharov-style induced gravity the effective Newton constant is a scheme-dependent sum over matter species, so G is not predicted and the cutoff and species content are declared. This panel asks the sharp question: does the record-bearing reading actually restrict which species enter that sum, or is it inert — a re-weighting of entanglement entropy with no bearing on G? The foil is the Global Species Census: the claim that the induced-G species content is a framework-external field-content declaration no record architecture can touch. Two moves make the audit honest. First, following Paper 30, Darwinist redundancy is grain-relative, not species-intrinsic; so the world-side record-relevance indicator A_s(gamma) = 1[R_s(gamma) >= R_*] is defined relative to a declared grain gamma (local algebra, exterior fragmentation, state class, anti-gerrymander covariance), with provenance kept out (the world/warrant split), and it is a reproducibility convention, not a new physical observable. Second, three species-contributions are kept type-distinct: contribution to the entanglement entropy (a), to the Einstein-Hilbert counterterm that renormalizes 1/G (b), and record-relevance (c). The pivotal fact is that (a) and (b) are the same ultraviolet heat-kernel quantity — at leading order in a fixed scheme, modulo well-known gauge/contact-and-edge-term, non-minimal-coupling, regulator, and Wald/geometric-entropy subtleties — while (c) is an infrared, environmental property. A field that fails Darwinist redundancy in the infrared — confined, massive, or sterile — still contributes to the ultraviolet counterterm according to its spin, multiplicity, and coupling. Therefore the record filter restricts (c), and hence a record-bearing re-weighting of (a), but does not restrict (b), the counterterm that fixes G. The leading result is a null / reduction conclusion (39-C, inert), stated honestly as a conditional argument, not an unconditional theorem: under the standard reading of the induced counterterm (assumption H — it is the local ultraviolet heat-kernel coefficient), the record reading has no world-side teeth on induced gravity, and the Global Species Census stands. A counterfactual finite species ledger shows the effect one would obtain — a factor of five in the ratio of induced increments, in the pure-induced limit — if the filter applied to the ultraviolet sum, which on the present analysis it does not; the ledger's low-energy redundancy entries are moreover not established at the Planckian cutoff, and its coefficients and multiplicities are illustrative toy arithmetic, not computed heat-kernel weights. A restriction (39-A) would survive only if one could construct a genuine, scheme-robust ultraviolet bridge from record-relevance to the counterterm; the honest prior is that no such bridge exists. Even a hypothetical 39-A would not predict G; it would at most narrow an induced increment in a declared scheme. The null is treated as a result: it locates the which-entropy problem's record reading firmly in the infrared, where it cannot fix an ultraviolet constant. Presents no new physics; results are interpretive (L2) on imported physics (L1) and the framework's domain-general discipline (L2-G).