Local tomography of linearized gravity under its constraints

Summary

In exactly solved lattice models of QED and linearized gravity under their Gauss-law constraints, the paper settles how constrained gauge sectors fail local tomography (gravity fails it strictly worse than QED) and shows that the BMV-type entanglement protocol never occupies the failure directions: the entangling phase lives entirely in the locally tomographic sector.

Abstract

Proposed tests of gravitationally induced entanglement (GIE) infer a non-classical mediator from local spin correlations. This inference assumes local tomography: that products of local observables separate states of the composite. Constrained theories can violate it, and an explicit fermionic protocol shows the violation can fake entanglement witnesses through a locally classical mediator. We settle, in exactly solved models, the status of this assumption for linearized gravity. In constrained lattice models, with all algebraic claims in exact integer arithmetic certified modulo two primes, the product-observable span equals the commutant of a per-region charge multiplet fixed by the kernel of the adjoint constraint map: the boundary Poincaré ten-plet {E, K_(i), P_(i), J_(i)}(R), versus QED’s single Gauss charge Q(R), including a tier with no electromagnetic analog in which position itself is charged. Within a joint charge sector, tomography and standard tensor composition are restored exactly. Interior-generated dynamics conserves every region charge, so a closed-lab GIE protocol never occupies the failure directions at matter-source order: the constraint structure polices its own loophole. At order G, where branch interaction energy equals the witness phase, the would-be refinement dissolves, the interaction-energy assignment is scheme-dependent, the corrected commutant moves with the scheme, and no invariant branch splitting survives the admissible scheme family, leaving as invariant record only radiated gravitons, N_(g) ∼ 10⁻⁵⁷. QED protects mediation witnesses by conservation; linearized gravity protects them by dissolution. This supplies the explicit construction named as a central open goal by Spalvieri, Garmier, and Giacomini.

Cite

Vávra, D. (2026). Local tomography of linearized gravity under its constraints. vavradev.com/research, first published 2026-11-04.

@misc{vavra2026a,
  author       = {V{\'a}vra, David},
  title        = {{Local tomography of linearized gravity under its constraints}},
  year         = {2026},
  month        = aug,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-A-local-tomography-linearized-gravity.pdf}},
  note         = {Manuscript, Letter + Supplemental Material. First published 2026-11-04 at vavradev.com/research; SHA-256 93b44287621b920546242e6809b3b0e62a9da64d1383cb5de1f3fcf41249367c},
}