Emergent Spacetime Without a Global Reconstructor: Record-Relational Reconstruction of Geometry, Compatible-Set-Valued Bulks, and the Absence of Strictly Local Gauge-Invariant Observables

This paper is the thirty-fifth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of independently existing objects. It is the opening panel (first of three) of the tenth grouping — the dynamical quantum-mechanics–gravity interface, or emergent-spacetime, trilogy (35 Emergent Spacetime → 36 Gravitational Dynamics → 37 Cosmological Boundaries). It recasts the region/algebra reconstruction and Donnelly–Giddings dressed/nonlocal-observable debt that Paper 32 explicitly deferred "to the emergent-spacetime paper," and it does so kinematically: it supplies reconstruction kinematics only and does not cross the dynamical-coupling gate (that is Paper 36's). When the metric is a quantum degree of freedom and geometry is read only through records, it is tempting to posit a Global Reconstructor: a physically privileged, uniquely authoritative dictionary mapping the quantum state — its entanglement and record structure — to the bulk spacetime, with strictly local bulk observables read off coordinate-wise. The thesis is that no such reconstructor exists. Reconstruction is treated as Paper 19's inverse problem specialized to X = geometry, and two type-distinct non-uniqueness layers are kept rigorously apart, neither of which is gauge redescription of a single geometry. R-A (flagship, layer ii): at identical accessed records — even at the same fitted graph — two admissible reconstructions that differ only in relational anchoring can disagree on the locale / region-support correspondence, with only the relabeling-invariant content objective. The two anchorings are physically inequivalent (they anchor on provenance-distinct records, related by a symmetry of the coincidence data alone but by no provenance-preserving admissible map), not gauge-equivalent; pure gauge re-dressings are quotiented. Crucially, fixing an anchoring determines a region; what R-A denies is that the accessed record data canonically select one admissible anchoring — the absence of the canonical anchoring-selection step, not indeterminacy after fixing an anchoring. This is not a claim that anchoring yields distinct bulk metrics. R-B (layer i): finite/partial access leaves a compatible set of genuinely different bulk structures, collapsing to a (near-)singleton only when the reconstruction forward map is injective (Paper 19's protocol-kernel condition), not merely at full access. R-C: gravity admits no strictly local gauge-invariant observable and physical observables are dressed and nonlocal (Donnelly & Giddings, 2016) — imported, not proven by the toy; it supplies only the relational character of localization, while the layer-(ii) non-uniqueness arises solely when the declared anchoring family holds inequivalent, provenance-distinct choices. R-D: reconstruction is provenance-gradable — same accessed records and the same verdict can carry different warranted standing (GeomRecStandProf), the world/warrant split applied to geometry reconstruction itself. R-E: no reconstruction self-certifies its completeness, uniqueness, or correctness; the entanglement–geometry (holographic) dictionary stays a background/worked model — not the computed toy and not the universe — while the computed model is a finite record-coincidence graph exhibiting both layers by explicit, checked calculation. The Global Reconstructor is thereby retired relative to the framework's declared architecture (its strictly-local clause independently untenable on the imported obstruction); the question of the geometry–record dynamical coupling is handed to Paper 36. Paper 35 supplies reconstruction kinematics only, does not cross the dynamical-coupling gate, and claims no novel empirical prediction. Presents no new physics; results are interpretive (L2) on imported physics (L1) and the framework's domain-general discipline (L2-G).