Holography of information on exact lattices: migration, irreducibility, and a controlled QED contrast

Summary

The first exact, finite-dimensional instantiation of holography of information with dynamics and controls: on a constrained one-dimensional lattice class the boundary algebra, its Hamiltonian translates and their commutant are computed exactly in integer arithmetic with dual-prime certificates, against a matched QED control.

Abstract

Holography of information, the claim that in quantum gravity all bulk information is available in an arbitrarily small time band of boundary data, because the Hamiltonian is a boundary term, exists as a continuum argument; no exact, finite-dimensional instantiation with dynamics and controls has existed. We construct one. In a constrained one-dimensional lattice class with an integer slaved field, we compute the boundary algebra B_(bd)^((n)) of collar data through second order in the coupling, the algebra D^((n)) generated by its Hamiltonian translates, and the commutant C^((n)) = D^((n)′), exactly, in integer arithmetic with dual-prime certificates, together with a matched QED control run through the identical pipeline at every order in α. Findings: (i) a migration theorem package, proven order-blind, each order’s constraint deposits that order’s total interaction energy and its dipole at the collar (a lattice ADM identity and filtration), while at linear order the boundary is dynamically dead; (ii) migration does not imply holography, the pre-registered dynamics is refuted by a symmetry-forced all-orders bulk survivor, and under generic repaired dynamics the commutant collapses to scalars per boundary-readable block exactly on the sector the boundary translates reach, with every survivor proven to be a register the translate algebra never reaches (one survivor is enrichment-absolute); (iii) in the matter-only enlarged class the commutant equals the boundary-readable superselection center, C^((n ≥ 1)) = Z, on all 74/74 admissible cells and for every constraint-compatible dynamics tested; (iv) QED, computed not assumed, never generates: its commutant is constant at the charge-superselection block algebra at every order, and a distractor control shows the pipeline separates constraint-forced migration from bookkeeping. The exact pair, conservation-protection versus dissolution-migration, is a lattice sharpening of the continuum theorems, decides the algebraic half of a cousin mechanism, and leaves the analyticity half untouched by construction.

Cite

Vávra, D. (2026). Holography of information on exact lattices: migration, irreducibility, and a controlled QED contrast. vavradev.com/research, first published 2026-11-04.

@misc{vavra2026c,
  author       = {V{\'a}vra, David},
  title        = {{Holography of information on exact lattices: migration--- irreducibility--- and a controlled QED contrast}},
  year         = {2026},
  month        = aug,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-C-holography-of-information-exact-lattices.pdf}},
  note         = {Manuscript, Article. First published 2026-11-04 at vavradev.com/research; SHA-256 0a7517f8a9707dc22f865f6a934ed39d986498b850cf283d535bdcc12368bf6e},
}