Research

Letter + Supplemental Material

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.

Final — two independent hostile-referee passes; every quantitative claim script-backed and re-run

PDF 125 KB

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@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 03a55bd19c74efb7bfb275d33f88fa2a06e35577ac3c35f94171e75cae351b04},
}

Article

A formal, theory-independent definition of “the entanglement was mediated by the gravitational field”, a proof that circuit topology alone cannot supply it, and a Bell-style theorem (Theorem W) stating what a certified positive result of the Bose–Marletto–Vedral protocol refutes under six priced assumptions, which alternatives survive, and what a null result certifies.

Abstract. Proposals to entangle two masses through gravity (Bose et al.; Marletto and Vedral) are widely described as tests of the quantum nature of gravity, but the field has no theorem stating what a positive result would certify, from which assumptions, with which alternatives surviving. We supply one. The central missing ingredient is semantic: a formal, theory-independent definition of “the entanglement was mediated by the gravitational field.” We prove that circuit topology alone cannot provide it—every bipartite gate decomposes exactly into mediator-local rounds—and construct a five-clause definition (interposition, autonomy, locally factorized coupling with a cut criterion, causal propagation, carriage) with three description-invariant operational signatures (retardation, interposed blockability, autonomy response). The definition is adequacy-tested against every configuration in the recent classical-gravity-produces-entanglement debate, is provably non-circular (an explicitly classical theory satisfies every clause and provably cannot entangle), and yields a slaving dichotomy: a candidate mediator is either constraint-slaved (no independent data, no dead time, fixed operator-Schmidt-rank-2 gate) or autonomous (retarded), with the two indistinguishable in all mass-side data. Around this definition we assemble a Bell-style certification theorem from three lemmas with stated scopes: a mediation definition adequacy lemma; a per-run Bell/steering inertness theorem for charge-transfer coherences, presented as a constrained-field-theory instantiation and strengthening of Baldijão et al., including a multi-copy activation boundary we exhibit exactly (joint processing of two runs restores Tsirelson-value violations, which forces an i.i.d. per-run clause into the certified statistic); and a continuum classical-mediator no-go, presented as a dynamical, instrument-level strengthening of Ludescher et al., covering back-reacting instruments with feed-forward over uncountable outcome spaces, continuous-time limits, and the Oppenheim classical–quantum framework, for which the anticipated “small” entanglement is shown to be exactly zero in the locally coupled and Diósi–Penrose classes. The resulting theorem: under six explicitly priced assumptions, a certified positive result implies that the degree of freedom coupling the two labs is non-classical in the state-space sense—either a non-classical mediator, or a nonseparable direct quantum gate with no carrier, the two separated in principle only by retardation. Both disjuncts are non-classical; every classical-gravity model in the current literature is refuted on its own formulation, while prequantum hybrids (van Hove) are correctly classified rather than excluded. We state the null-result converse, price its linear-additivity caveat, compare the theorem honestly with Bell’s, and give experimental guidance, including a visibility-scan certificate for the closed-lab assumption. All model-level claims are verified in deterministic ancillary scripts.

Final — two independent hostile-referee passes; every quantitative claim script-backed and re-run

PDF 251 KB

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@misc{vavra2026b,
  author       = {V{\'a}vra, David},
  title        = {{What gravitationally induced entanglement certifies: mediation semantics and a Bell-style theorem}},
  year         = {2026},
  month        = aug,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-B-what-gie-certifies-theorem-W.pdf}},
  note         = {Manuscript, Article. First published 2026-11-04 at vavradev.com/research; SHA-256 c57d8429b79dfeea8d02474fdd602a0a393d1f82c32829117310a03ddec64683},
}

Article

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.

Final — hostile referee plus full gate audit with fresh-prime re-certification

PDF 189 KB

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TeX 69 KB

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@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 6e4772cea50fcb6368f2c85b0d2f6c1b3358f7c8edfb0c4d8f4924724c291c77},
}

Article

On a closed ring and the open chain it is cut from, the paper computes exactly what imposing the Hamiltonian constraint does to the algebra of observables and what an adjoined quantum clock restores, ending in a certified clock–boundary isomorphism, with a matched QED control on the same graphs.

Abstract. On a finite, exactly solvable pair of lattices — a closed (boundary-deleted) ring and the open chain it is cut from — we compute, in exact integer/rational arithmetic with two-prime certificates and no floating point in any verdict quantity, what imposing the Hamiltonian constraint H ≈ 0 does to the algebra of observables, and what an adjoined quantum clock restores. Three registered instruments run against a matched quantum-electrodynamics (QED) control on the same closed graphs. (C-A) Constraint-role triviality: every populated constrained kernel of the gravity-class models is all-central wherever probed (integer and rational eigenvalues, orders ν ≤ 2), with one genuinely structured exception — non-gravitating frozen registers, whose non-central survivors span exactly the compressed register algebra M₂ at rational coupling at three sizes — while QED with H physical keeps the full matrix algebra (M₂₅₆, M₄₀₉₆) with genuine dynamics on the same graphs, and a role-swap control (QED with H imposed as a constraint) freezes too: triviality is driven by the constraint role, and gravity is special only in being forced to put H into that role. (C-B) The observer repair: adjoining a matched clock ladder turns the abelian regional algebra nonabelian; the computed shape of the covariant relational algebra is R_(rel)^(cov)(R) ≅ alg(A_(loc)(R)) — never the registered full matrix algebra — and the repair responds to clock resolution, not bare dimension. (C-C) Time from clocks: the Page–Wootters conditional-state identity holds exactly (a certified arithmetic identity, tautology-grade given exact projectors), with exact aliasing, detuning, and two-clock tables, and a QED control showing relational time is redundant where H is physical. The flagship result unifies the pair: at ν = 0, in the cut-remembering closure scheme, with the zero-mode anchor re-supplied in the counterterm-site gauge-equivalence class, conjugation by an explicit clock isometry Φ is a *-isomorphism taking the closed universe’s covariant relational algebra of every probed region onto the open universe’s gauge-invariant local algebra of the same region — equivalently, clock-free: the identity holds exactly where the anchored local algebra is stable under the constraint’s Heisenberg flow — up to the non-gravitating registers, which neither the constraint killed nor the boundary read. Eight negative controls fail in pre-registered directions and decompose “boundary” into three separately falsifiable ingredients (energy ledger, zero-mode reference, scheme memory of the cut); bounded-below clocks provably never internalize the full boundary. The program tests the constraint mechanism only and adjudicates no path-integral, wormhole, or ensemble statement; every number is reproducible from ancillary scripts, and all refutations of our own pre-registered expectations are reported.

Final — hostile referee plus full gate audit with everything re-executed

PDF 201 KB

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@misc{vavra2026f,
  author       = {V{\'a}vra, David},
  title        = {{The closed universe and its internalized boundary: exact constraint-role triviality, the observer repair, and a clock--boundary isomorphism on a lattice pair}},
  year         = {2026},
  month        = aug,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-F-closed-universe-internalized-boundary.pdf}},
  note         = {Manuscript, Article. First published 2026-11-04 at vavradev.com/research; SHA-256 c22e5df9bd60526c2f401c9af75cdcfbffdc8f3a179782257b8b4264e4c01cb4},
}

Article (companion to paper B)

Types the gate the gravitational hold implements in the committed BMV family: non-Clifford except on an exactly characterized exception set, so the output carries magic (nonstabilizerness). Upgrades the witness theorem to gate grade and gives the E1-M protocol that certifies it from fringes a run already records.

Abstract. The companion paper [What gravitationally induced entanglement certifies] establishes what a certified positive result of the Bose et al.–Marletto–Vedral (BMV) protocol certifies: under six priced assumptions, no classical degree of freedom carried the observed entanglement. We ask the next question, which is about the channel’s gate type rather than its classicality. Within the committed family the gravitational hold implements U = (P₁(a) ⊗ P₂(b)) CZ(Δ) with Δ = −2KΔx²/[d(d² − Δx²)], K = Gm²τ/ℏ. That a controlled-phase gate at a generic angle is non-Clifford, so that the output state carries magic (nonstabilizerness), is elementary and folkloric; it is never the claim here. The claims are certification statements. (i) The committed witness statistic is magic-blind at every value, including its maximum W = 2: an explicit stabilizer mixture reproduces the design correlators and W = 1.156350 exactly, the entire correlator square is stabilizer-reachable, and standard CHSH cannot witness magic at any violation—so added assumptions are forced, not optional. (ii) The family’s nonlocal Clifford-exception set is exactly Δ ∈ πℤ, splitting into the no-entanglement points 2πℤ and the maximal-witness Clifford points π + 2πℤ; requiring Clifford local phases as well yields explicit arithmetic ladders in K/d on each rational-shape family; at the committed operating point (Δ = −211/672 = −0.313988, ±5% calibration) the gate is certified outside LU ⋅ 𝒞₂ ⋅ LU by an exact census of all 11520 two-qubit Cliffords, with stabilizer 2-Rényi entropy M₂ ≥ 0.104444 and entangling power 0.005432. (iii) Theorem M: under the companion theorem’s assumptions plus five added, operationally certified assumptions M0–M4, a certified positive result whose extracted phase interval excludes πℤ additionally certifies that the gravitational coupling implemented a nonlocal non-Clifford gate—magic injected at gate grade, with cited monotone floors evaluated on the interval—stable across both readings of the companion theorem’s mediation disjunction. (iv) The converse: at Δ = π the same protocol attains its maximal witness value W = 2 on a stabilizer state delivered by a Clifford gate, so the family’s best entanglement point is provably a zero-magic point; non-classicality is angle-generic, magic is angle-conditional, and along the hold-time scan the witness grows linearly while the certified magic floor grows quadratically (anti-alignment). The experimental price is measured: the primary instrument is a re-scoring of conditional fringes the witness protocol already records—the Z-conditioned fringe difference Δ̂ = φ_(c)(B = R) − φ_(c)(B = L), exactly invariant under local phase doping, with zero added settings and shots— resolving the committed angle at 12.3σ with 10⁴ shots per setting at 70% visibility, and needing 1105 shots per setting for 5σ; the witness itself, not the extraction, is the binding cost (F ≥ 0.926 for a 5σ witness at 10⁴ shots on the white-noise benchmark), while a state-level magic witness would need visibility 0.9756 against the entanglement witness’s 0.8648—a gap of 0.1108 that prices the upgrade on that route. A null of any branch never certifies that gravity is classical; in particular a classical measure-and-act channel imprints the full second-difference phase in the conditional fringes, so the extraction alone is never a non-classicality certificate. Every certified value is verified in deterministic exact-arithmetic ancillary scripts.

Final — hostile-referee pass with all repairs folded and record-verified

PDF 1.6 MB

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@misc{vavra2026m,
  author       = {V{\'a}vra, David},
  title        = {{When gravitationally induced entanglement certifies magic: Clifford exceptions and a gate-typing upgrade of the witness theorem}},
  year         = {2026},
  month        = aug,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-M-gie-certifies-magic-gate-typing.pdf}},
  note         = {Manuscript, Article (companion to paper B). First published 2026-11-04 at vavradev.com/research; SHA-256 b834df8a6214236420a9c308273fdd9aed3128fae5d55a19cba09eeae74fda98},
}

Article (self-contained)

Re-runs a battery of structural results about constrained, linearized-gravity-shaped systems over registered classical models and answers at certificate grade which of those results ever needed quantum mechanics, locating and typing the quantum load.

Abstract. A battery of structural results about constrained (linearized-gravity-shaped) systems—boundary completeness of the algebra, closed-universe triviality, observer repair, a clock–boundary isomorphism, self-reading emptiness, charge walls with an exact crossing price, a capacity deficit, clock necessity, and a Diophantine timing floor—was previously established on exact finite lattices with quantum mechanics in the engine room. We ask, and answer at certificate grade, a question that battery could not answer about itself: which of those results ever needed quantum mechanics? Three computations, one arc. (1) The battery is re-run, kernel by kernel, over two registered classical model classes (a simplex/GPT model and a Koopman–von Neumann model with commutative readout). The quantum load localizes to exactly two carriers—the payload read of a written boundary record (a coherence rotation), and the irrational spectral gaps behind the timing floor—while the kernel-, counting-, and arithmetic-carried content persists classically, one central forecast of ours dying honestly on the way (self-reading emptiness did not need quantum mechanics: the classical cells are empty too, re-carried by an exact all-negative discriminant census). (2) Both carriers are typed at the sharpest available classical boundary: the epistricted / nonnegative discrete-Wigner sector at odd prime (Gross), on registered analogue cells at p = 3 with exact faithfulness gates. Both return NEGATIVITY-REQUIRED—non-membership in the nonnegative, stabilizer-reachable sector, never “no nonnegative model exists” and never “not simulable”—with the negativity exactly located: write-channel kernel entries exactly −2/9 under both label identifications, and an exact-algebraic negative entry $-(2381/153596547)\sqrt{5688761}$ in the effective readout’s eigenstructure; the floor’s in-class dynamics is confined to root-of-unity spectra while the analogue frequency module leaves ℚ at every registered coupling, the committed rational-escape point closing at p = 3 against our own forecast. (3) The bridge to the physical side: the gravitationally mediated two-qubit gate of the entanglement-witness proposals, (P₁(a) ⊗ P₂(b)) CZ(Δ) with Δ = −211/672 at the committed geometry, is certified non-Clifford away from the exact exception set Δ ∈ πℤ, the strict (locals-included) exception set being an explicit arithmetic K-ladder on each registered shape family; on the registered analogue cells its negativity sits at the same write-channel/controlled-Weyl locus as the first carrier (species 1, by the profile door, both identifications); the two located species are mutually non-interconvertible within the registered operation class—a two-sided wall, found refutation-first against our own one-way-valve forecast—and the same physical family is beyond-matchgate on a different exception set (2πℤ) than its Clifford set (πℤ). All verdicts are exact-arithmetic, deterministic, and doubly adversarially verified; scope is the registered model classes and analogue cells, never the continuum.

Final — hostile-referee pass with all repairs folded and record-verified

PDF 198 KB

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@misc{vavra2026s,
  author       = {V{\'a}vra, David},
  title        = {{Where physical law needs magic: locating and typing the quantum load of a gravitational-witness battery}},
  year         = {2026},
  month        = aug,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-S-where-physical-law-needs-magic.pdf}},
  note         = {Manuscript, Article (self-contained). First published 2026-11-04 at vavradev.com/research; SHA-256 758c39139a0def1e53c9b44df4eda75baff4729a7560b1d3b79eaa592df8d6da},
}

Final v1.0

Certifying, under stated added assumptions, that the gravitationally mediated gate was non-Clifford, from the conditional fringes a run already records

The experiment-facing deliverable of the witness–magic programme: what an experimental campaign must add to its witness run, and what it may then conclude, with every assumption priced in a ledger.

Finalized after two adversarial verifications

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@misc{vavra202621a,
  author       = {V{\'a}vra, David},
  title        = {{E1-M: a ledgered upgrade layer over the BMV entanglement witness}},
  year         = {2026},
  month        = aug,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-record-21a-E1M-upgrade-layer-note.pdf}},
  note         = {Programme record, Final v1.0. First published 2026-11-04 at vavradev.com/research; SHA-256 543fad4070acfe9619b710f1441edfaabfa204f9d27554588ab00a35535ed76a},
}

v1.2

Programme decision document of the anchor-margin front

A role-blind margin theorem on the gravity cells of the constraint-role lattices with an explicit margin per cell, a role-decided anchor on the split cells, and the anchor lemma lifted over the order-1 family — with the full gate chain, repairs proven verdict-neutral, and the closing audit at an untouched prime reserve.

Margin theorem and anchor lemma; closing audit passed 84/84 with a pre-registered hand probe; external quotation conditional on a post-meeting literature sweep

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@misc{vavra202627,
  author       = {V{\'a}vra, David},
  title        = {{The Anchor and the Margin: is self-blindness a threshold or an anchor?}},
  year         = {2026},
  month        = sep,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-record-27-anchor-margin-program.pdf}},
  note         = {Programme record, v1.2. First published 2026-11-04 at vavradev.com/research; SHA-256 e5dea2fb527b005dbe5c346dc25344d273eda9786c9df26072cb417c631dd3ee},
}

v1.0

Programme decision document of the ADJUDICATOR front

How the exclusion table was built and verified: twenty-three published classical and hybrid accounts of gravity typed against a certified positive result, a null result, and the saturation map of what no experiment of the BMV class can split.

Decided at duty grade; pilot, verifier gate, scout lanes and two adversarial legs

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@misc{vavra202630,
  author       = {V{\'a}vra, David},
  title        = {{The Living Exclusion Table: what the first tabletop test of gravitationally induced entanglement kills, leaves standing, and can never decide}},
  year         = {2026},
  month        = sep,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-record-30-adjudicator-program.pdf}},
  note         = {Programme record, v1.0. First published 2026-11-04 at vavradev.com/research; SHA-256 54241953bf085bec0a20fe73623541540632ede494f3939fcd147e6595da9e34},
}

Final v1.0

The table itself, model by model: nine accounts refuted by a certified positive result, three reclassified, eleven compatible; what a null refutes only under stated conditions; and the saturation map with its sizes. A null never feeds “gravity is classical” and a positive never feeds “gravity is quantum”: Theorem W’s disjunction is the licensed form.

In-house deliverable; two adversarial verifications

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@misc{vavra202630a,
  author       = {V{\'a}vra, David},
  title        = {{The living exclusion table: what the first tabletop test of gravitationally induced entanglement refutes, what it leaves standing, and what no experiment of its class can decide}},
  year         = {2026},
  month        = sep,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-record-30a-living-exclusion-table.pdf}},
  note         = {Programme record, Final v1.0. First published 2026-11-04 at vavradev.com/research; SHA-256 aaebbc2c5fb0dd9b7957e39b30bb5cfb1d358fcbb32481a4b762d901f602b80c},
}

v1.0

Decision document selecting programme LAMBDA

Six frontier scouts, an instrument-portability scout and a bigness adversary surveyed quantum foundations, black holes and spacetime, cosmology, field theory and arithmetic, quantum information and many-body physics for questions an exact finite computation can decide; the judge’s own pre-checks, the scoring matrix, the kills, and the programme design for the recommended question.

Survey of six frontiers; forty-two candidates scored; one recommended

PDF 796 KB

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@misc{vavra202631,
  author       = {V{\'a}vra, David},
  title        = {{Dream Question 5: a fresh multi-frontier survey}},
  year         = {2026},
  month        = oct,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-record-31-dream-question-5-survey.pdf}},
  note         = {Programme record, v1.0. First published 2026-11-04 at vavradev.com/research; SHA-256 34ace8ad343aab52e1d4e6291790d0beaf6d97d908cc026e2b4f1a7ee2acf98c},
}

v1.1

Programme decision document, decided at the second freeze

At one qutrit the constructible (CNC) class of the Λ-polytope model hosts every state; at two qutrits its convex hull hosts the three cubic diagonal-phase states and none of the registered product-of-magic, quartic or random states, each refusal carried by an exact Farkas certificate re-derived by independent routes. At d = 3 the copy-number threshold of the Strange and Norrell states is two, and every larger copy number lies outside by corollary.

Decided; adversarial rigor leg passed, physics leg passed with rewordings applied; closing audit at the reserved prime band still owed before external quotation

PDF 1.3 MB

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@misc{vavra202632,
  author       = {V{\'a}vra, David},
  title        = {{LAMBDA: where the constructible (CNC) description of odd-prime quantum computation ends}},
  year         = {2026},
  month        = oct,
  howpublished = {\url{https://vavradev.com/research/vavra-2026-record-32-lambda-program.pdf}},
  note         = {Programme record, v1.1. First published 2026-11-04 at vavradev.com/research; SHA-256 984ab99424be3f58dcc1043c621390efee68ecbbf501ab2a1b3c8488cbdf0340},
}