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arxiv: 2605.28958 · v1 · pith:KX6UDKWYnew · submitted 2026-05-27 · ✦ hep-th · gr-qc· quant-ph

Quantum State of a Gravitating Region

Raphael Bousso , Sami Kaya , Guanda Lin , Arvin Shahbazi-Moghaddam This is my paper

Pith reviewed 2026-06-29 10:26 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph
keywords quantum gravityentanglement entropypath integralRényi entropyminimal surfaceholographyelliptic data
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The pith

Any compact manifold with elliptic data prepares a quantum state on its boundary using the gravitational path integral.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes that any compact d-manifold with elliptic data prepares a quantum state on its boundary. Elliptic data means specifying either the metric and fields or their conjugates on the manifold. Inner products are defined using the gravitational path integral after gluing two such manifolds to close the boundaries. A prescription for Rényi entropies of boundary subregions is given, and in examples these are consistent, leading to a von Neumann entropy that matches the minimal surface prescription. This construction allows defining quantum mechanics in gravitating systems without asymptotic boundaries.

Core claim

We propose that any compact d-manifold with elliptic data, J, prepares a quantum state |J> on its (d-1)-boundary σ. No asymptotic structure is required. Inner products and traces are evaluated by the gravitational path integral with closed boundary conditions obtained by gluing elliptic data manifolds. We give a prescription for the Rényi entropies S_n of a subregion of σ. In examples, S_n is nonnegative and nonincreasing with n. The von Neumann entropy by analytic continuation agrees with the minimal surface prescription.

What carries the argument

Elliptic data J on a compact manifold preparing the state |J> with path integral inner products from gluing.

If this is right

  • Rényi entropies are nonnegative and decrease with n in the examples considered.
  • Von Neumann entropy agrees with the minimal surface prescription of Bousso and Penington.
  • The state preparation requires no asymptotic structure.
  • Traces are evaluated with closed boundary conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This could extend quantum information tools to regions in cosmological spacetimes.
  • Testing the prescription on more examples like de Sitter space could reveal limitations.
  • The gluing procedure might connect to other path integral definitions in quantum gravity.

Load-bearing premise

Inner products and traces are evaluated by the gravitational path integral with closed boundary conditions obtained by gluing elliptic data manifolds.

What would settle it

A specific computation where the continued von Neumann entropy for a subregion differs from the minimal surface area in a solvable gravitational model.

Figures

Figures reproduced from arXiv: 2605.28958 by Arvin Shahbazi-Moghaddam, Guanda Lin, Raphael Bousso, Sami Kaya.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
read the original abstract

We propose that any compact $d$-manifold with elliptic data, $\mathcal{J}$, prepares a quantum state $|\mathcal{J}\rangle$ on its $(d-1)$-boundary $\sigma$. Elliptic data consists of metric and field values, or their conjugates, but not both. No asymptotic structure is required. Inner products and traces are evaluated by the gravitational path integral with closed boundary conditions obtained by gluing elliptic data manifolds. In particular, we give a prescription for the R\'enyi entropies $S_n$ of a subregion of $\sigma$. In a class of examples, we find that $S_n$ is nonnegative and nonincreasing with $n$, as required for consistency. We obtain the von Neumann entropy by analytic continuation and find agreement with the minimal surface prescription of Bousso and Penington.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes that any compact d-manifold equipped with elliptic data J prepares a quantum state |J> on its (d-1)-boundary σ. Inner products and traces are defined via the gravitational path integral with closed boundary conditions obtained by gluing such manifolds. A prescription for the Rényi entropies Sn of a subregion of σ is given; these are verified to be nonnegative and nonincreasing in a class of examples. The von Neumann entropy is obtained by analytic continuation and stated to agree with the minimal-surface prescription of Bousso and Penington.

Significance. If the gluing construction can be shown to yield a genuine Hilbert space whose reduced density matrices satisfy the required Rényi properties for arbitrary elliptic data, the proposal would supply a general, non-asymptotic definition of quantum states in gravitational systems. The explicit consistency checks performed in the checked examples constitute a concrete strength of the current manuscript.

major comments (1)
  1. [Abstract] Abstract: the claim that Sn is nonnegative and nonincreasing is supported only by verification 'in a class of examples.' The subsequent analytic continuation to the von Neumann entropy, and the asserted agreement with the Bousso-Penington minimal-surface formula, both presuppose that these inequalities hold for the full state space defined by the gluing construction. No general argument establishing this is supplied.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on the manuscript. We address the major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that Sn is nonnegative and nonincreasing is supported only by verification 'in a class of examples.' The subsequent analytic continuation to the von Neumann entropy, and the asserted agreement with the Bousso-Penington minimal-surface formula, both presuppose that these inequalities hold for the full state space defined by the gluing construction. No general argument establishing this is supplied.

    Authors: We agree that the manuscript supplies no general proof that the Rényi entropies are nonnegative and nonincreasing for arbitrary elliptic data under the gluing construction. The verification and the subsequent analytic continuation to the von Neumann entropy, together with the comparison to the Bousso-Penington formula, are performed only within the class of examples where the inequalities hold. To prevent any implication that these results extend beyond the verified cases, we will revise the abstract to state explicitly that both the consistency checks and the agreement with the minimal-surface prescription are established in the class of examples considered. A general demonstration remains an open question. revision: yes

Circularity Check

0 steps flagged

No significant circularity; proposal and checks are independent of self-citation

full rationale

The paper proposes that compact d-manifolds with elliptic data prepare states |J> on the boundary, with inner products via gravitational path integral on glued manifolds. Rényi entropies Sn are prescribed for subregions and verified to be nonnegative and nonincreasing in a class of examples; von Neumann entropy follows by analytic continuation. The noted agreement with the minimal surface prescription of Bousso and Penington is a computed consistency check, not an input or assumption used to derive the state or entropy formula. No equation or step reduces by construction to a fitted parameter, self-defined quantity, or unverified self-citation chain. The self-citation is normal for comparison and does not justify the central premise. Limitation to examples is a scope issue, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The proposal rests on the assumption that the gravitational path integral with closed boundaries defines inner products, plus the existence of analytic continuation for Rényi to von Neumann entropy. No explicit free parameters or new particles are introduced in the abstract.

axioms (2)
  • domain assumption Inner products and traces are given by the gravitational path integral over manifolds obtained by gluing elliptic data.
    Stated directly in the abstract as the evaluation method for overlaps and traces.
  • domain assumption Rényi entropies admit analytic continuation to von Neumann entropy that matches the minimal-surface formula.
    Invoked to obtain the final entropy result.
invented entities (1)
  • Quantum state |J> prepared by compact manifold with elliptic data J no independent evidence
    purpose: To associate a quantum state to a gravitating region without asymptotic structure
    Newly proposed object whose inner products are defined via path integral; no independent falsifiable prediction given in abstract.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Pure states for subregions in gravity and their entanglement entropy

    hep-th 2026-06 unverdicted novelty 6.0

    A construction assigns pure states to subregions in quantum gravity via partially frozen path integrals and gives a holographic prescription for their entanglement entropy that satisfies consistency conditions and rec...

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