Abstract

This paper is the thirty-second in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates. It opens the ninth grouping — the quantum-mechanics–gravity interface trilogy — and is the first paper to cross Gate IV (geometry sensitivity): the metric is a quantum degree of freedom, not a fixed background. Papers 8 and 31 localized records relationally but on one fixed geometry; when the geometry is itself superposed there is no physically privileged cross-branch map (a common manifold is mathematical scaffolding, not a physical identification), and a tempting shortcut appears: compare branches on one external background and read "the same event" off coordinate coincidence. The claim is that there is no Global Background. The hole argument's lesson — that a record-formation event is individuated by relational coincidences and what is recorded there, not by a manifold point (Stachel, 2014; Rovelli, 2002) — sharpens, under superposition, into a problem no background can solve: across inequivalent geometry branches even the relational strategy must be carried by a declared, admissibility-constrained comparison map. Throughout, an event is a record-formation event, kept type-distinct from the record token and from its provenance; unrecorded events are out of scope. The flagship R-A is a separation, not a denial: a two-branch geometry-superposition state for which the background-label map (a relabeling-dependent presentation artifact) and the admissible relational/provenance comparison return different verdicts, only the latter invariant under relabeling — so event identity is not background-readable, but specification-relative under an admissible map (relabeling/gauge-invariant, support-conditioned, provenance-preserving, anti-gerrymandered, challenge-open). A worked finite model on record-coincidence graphs with no shared vertex set — including a same-labels, same-contents hard case — computes the divergence and the determinate / admissibly-open / incomparable trichotomy. R-B extends Paper 31's localization profile to a geometry-indexed GeoLocProf that strictly generalizes it, built over an identity fiber. R-C lifts the disposition trichotomy to geometry branches; R-D handles region and local-algebra correspondence as induced-where-possible or deferred. This crosses Gate IV, carries Paper 9's record arrow into the interface as a provenance-compatibility clause, retires the Global Background, and hands backreaction to Paper 33 and causal order to Paper 34. Geometry is quantum; its dynamics is not derived.