Observing Spacetime

Tom Yildirim; Vijay Balasubramanian

REVIEW 3 major objections 4 minor 57 references

Observing Spacetime

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Using the gravitational path integral, this paper shows that an asymptotic observer can verify a proposed quantum-gravity microstate with a Lorentzian probe matched to the state-preparing operator, while generic probes reveal nothing.

desk verdict Explicit detection saddles and O(1) ratios make this a real step beyond the Library of Babel, but the single-boundary two-sided claim rests on an imported orientation rule that still needs justification. read the letter →

arxiv 2509.09763 v3 pith:2D56NXLE submitted 2025-09-11 hep-th gr-qc

Vijay Balasubramanian , Tom Yildirim This is my paper · ORCID

classification hep-thgr-qc

keywords gravitationalpathintegralwormholesaddlesblackholemicrostatesbabyuniversesstateverificationasymptoticobserverquantumgravityQMA

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the information hidden behind black-hole horizons or in disconnected baby universes is not completely invisible: an asymptotic observer who already has a candidate microstate in hand can verify it, even though determining the microstate from scratch is exponentially hard. The central claim is that the gravitational path integral gives a universal, state-independent response to generic Lorentzian probes, but a probe built from the same heavy shell operator that prepared the state receives extra wormhole contributions that make the response larger by an $O(1)$ factor. This turns state detection into a check: propose an operator, measure the probe correlator on many copies, and compare. The same mechanism lets a single boundary verify the state of a two-boundary black hole, despite the interior lying outside that boundary's entanglement wedge. If true, the results sharpen the picture of black-hole microstates as complex states that are easy to certify but hard to find.

What carries the argument

The central objects are heavy dust shell states $|i\rangle$, defined by cutting open the Euclidean gravitational path integral and inserting a shell operator $O_i$ on the asymptotic boundary, then evolving in Euclidean time; depending on the preparation temperature they describe a black hole with a shell behind the horizon (type A) or thermal space entangled with a compact big-crunch baby universe (type B). The mechanism that carries the argument is the classification of wormhole saddlepoints in the path integral for $|\langle i|O_P|i\rangle|^2$: universal saddles, which contribute for any $O_P$, and detection saddles, which require $O_P = O_i$ and add an $O(1)$ contribution. A bulk orientation rule—that Euclidean boundary time induces an orientation on the boundary condition which must be smoothly continued into the bulk—selects which saddles contribute. The ratio of detection to universal contributions is then computed in the large-shell-mass limit, where the shell homology regions pinch off and partition functions such as $Z(\beta)$ and $Z_{\mathrm{TAdS}}(\alpha)$ combine to give ratios such as $3/2$ for the one-boundary probe of a two-boundary microcanonical state.

What would settle it

Compute $|\langle i|O_i|i\rangle|^2$ by summing all wormhole saddles exactly in a toy model that needs no orientation rule; if the exact result shows no excess over the generic-probe response—a detection-to-universal ratio of 1 rather than $3/2$ or 2–3—the central claim is falsified.

Watch

Extended reading notes

Core claim

Working in the gravitational path integral with heavy dust shell states, the paper shows that the magnitude-squared probe correlator $|\langle i|O_P|i\rangle|^2$ has two classes of saddles. When $O_P$ differs from $O_i$, only universal wormhole saddles contribute and the normalized response is just $Z_{m_P}$, independent of the state. When $O_P = O_i$, four additional detection saddles exist, so the response is strictly larger; for single-boundary states the detection-to-universal ratio is about 2 or 3 depending on whether the state is above or below the black-hole threshold, and for microcanonical two-boundary states probed from one boundary it is $3/2$. Because the extra saddles exist only when the probe matches the preparing operator, a Lorentzian boundary observer can verify a proposed microstate, including the state of a disconnected baby universe. The paper further shows that a two-boundary black-hole state can be verified using operators localized on a single boundary, and argues that finding the state from scratch requires exponentially many trials, placing verification in QMA.

Load-bearing premise

The calculation assumes an unproven bulk orientation rule—only saddles in which the Euclidean-time orientation flows smoothly into the bulk contribute—so if that rule is wrong, the set of contributing saddles and the predicted detection ratios change; the verification protocol also assumes access to many identically prepared copies to measure the probe correlator.

Editorial extensions

If this is right

Generic Lorentzian probes of a shell-state microstate give a universal response proportional only to the probe's own mass, with no information about which operator prepared the state.
Probing with the same operator that prepared the state adds detection wormhole saddles, raising the response by an $O(1)$ factor: about 2–3 for single-boundary states and $3/2$ for a one-boundary probe of a two-boundary microcanonical state.
An asymptotic observer with many identically prepared copies can verify a proposed microstate by measuring Hermitian combinations $A=(O_P+O_P^\dagger)/2$ and $B=(O_P-O_P^\dagger)/(2i)$ and checking whether $|\langle i|O_P|i\rangle|^2$ exceeds the universal baseline.
The state of a two-boundary black hole can be verified from a single boundary, even though the interior is not in that boundary's entanglement wedge; coordinated two-boundary probes give an exponentially large signal.
Finding the state from scratch is hard: testing $N$ candidate operators takes $O(N)$ measurements ($O(\sqrt N)$ with a quantum search algorithm), while tomography is blocked by the coarse-graining of the path integral, so verification belongs to QMA rather than being an efficient discovery procedure.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the same detection mechanism should apply whenever a state is prepared by a structurally simple operator and probed by that same operator, suggesting a general operator-alignment criterion for when non-perturbative effects reveal hidden data.
Editorial inference: the $3/2$ ratio for the one-boundary probe of a two-boundary state is a sharp quantitative prediction that could be tested in an exactly solvable low-dimensional toy model, where summing all saddles without relying on the orientation rule would either confirm or refute the mechanism.
Editorial inference: because the orientation rule is the only thing selecting the detection saddles, varying the preparation temperature $\beta$ should change the ratios in a predicted step-like way near the threshold where the dominant Euclidean saddle switches between black hole and thermal space, giving a concrete signature to look for.
Editorial inference: the fact that a baby universe state with vanishing total energy behaves as a hard-to-probe complex state suggests that causal disconnection from the asymptotic boundary is itself a semiclassical manifestation of state complexity, and the same complexity could appear in other low-energy systems with fine quantum hair.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Let me skip the throat-clearing. The genuinely new thing here is explicit: a gravitational path-integral construction of "detection saddles" that only contribute when the probe operator matches the operator that prepared the state. The O(1) ratios — factor 2/3 in the single-boundary case, 3/2 in the single-boundary probe of a two-boundary state — are derived from saddlepoint combinatorics, not fitted to anything, and the normalization cancelation is satisfying. The paper also gives the first concrete version of the Library of Babel idea, which previously was qualitative. I agree with the reader's conditional verdict, and I think the strongest claim is the one the stress-test flags.

What does the paper do well? The construction is explicit and follows the prior shell-state framework carefully. The classification of universal versus detection saddles is the core contribution, and it is credible. Generic probes give universal, state-independent responses; matched probes see extra wormhole saddles. The microcanonical estimates are clean, and the conclusion that one can check a proposal but not efficiently find the state is well argued.

The soft spot is exactly the orientation rule in Sec. 3.2. The paper imports from Appendix B of [21] the rule that only saddles with smoothly continued boundary-time orientation contribute, and it is this rule that selects the two universal and four detection saddles in (3.11)-(3.12). The 3/2 ratio and the single-boundary detection of a two-boundary state stand or fall on that unproven input. The paper is honest about the import — it says the rule didn't matter in earlier sections — but honest import is still a gap. If a referee can get the authors to derive or at least evidence that rule, the paper's headline claim becomes much firmer.

Minor points. The text calls the fourth detection saddle a twice punctured torus while Figure 18 calls it a twice punctured sphere; that term is subleading in the microcanonical estimate, so cosmetic. The abstract's claim about detecting information in a baby universe is stronger than the protocol, which verifies a proposed state and needs many identically prepared copies. The QMA discussion is more sketch than theorem, fine as discussion. And the saddlepoint ratios carry no estimate of G_N or shell-mass corrections; for leading-order work in this literature that is acceptable, but it should be said explicitly.

Citation pattern: heavily self-referential, but appropriately so — the construction is built on [15,22,18-21]. Not padding.

Who should read this: anyone working on wormhole saddles, black hole microstate detection, baby universes, or Hilbert space factorization. It deserves a serious referee, not a desk reject. A referee should focus on the orientation rule and ask for a derivation or a clearly stated assumption.

Referee Report

3 major / 4 minor

Summary. This paper uses Euclidean gravitational path-integral saddles built from heavy dust-shell operator insertions ('shell states') to argue that asymptotic observers can verify, but not efficiently find, the state of a quantum-gravity universe. For single-boundary universes, the magnitude-squared probe correlator |<i|O_P|i>|^2 is computed by summing wormhole saddles; when O_P = O_i, four additional 'detection' saddles appear, making the normalized response larger by an O(1) factor than the universal baseline (Eqs. (2.4)-(2.8); microcanonical version in (2.18)). The construction is then extended to two-boundary states, where detection works with correlated probes on both boundaries (Sec. 3.1) and, remarkably, with a probe on a single boundary (Sec. 3.2), giving a microcanonical detection-to-universal ratio of 3/2. The paper concludes that these features realize a QMA-like asymmetry: checking a proposed state is easy, while finding the state from scratch is exponentially hard.

Significance. If the computations are correct, the paper provides an explicit gravitational setting in which the 'easy to verify, hard to find' scenario conjectured for black-hole microstates is realized by concrete wormhole saddles, and it extends this scenario to baby-universe states and to two-sided black holes probed from one boundary. The main strengths are the explicit saddle constructions, the cancellation of the state-dependent shell factors Z_mi and Z_mP in the detection-to-universal ratios, and the absence of fitted parameters: the O(1) ratios (2.18), (3.4), and (3.13) are derived rather than assumed. The principal weakness is that the single-boundary detection of a two-boundary state rests on an orientation rule imported from reference [21] that is not proved in this paper, and the paper also contains an internal inconsistency in the formula for the fourth detection saddle. Both issues are localizable and, in my view, repairable.

major comments (3)

[Sec. 3.2 (Universal saddles paragraph)] The 'natural orientation' rule for continuing the Euclidean boundary-time flow into the bulk is load-bearing but unproven here. This rule selects exactly the two universal saddles in (3.11) and the four detection saddles in (3.12); if it is wrong or is being applied too broadly, other pairings of the O_R and O_i shell endpoints that satisfy the junction conditions could contribute at the same order and change the ratio (3.13), on which the headline claim of single-boundary detection of a two-boundary state rests. Please either prove the rule from the cut-open path-integral boundary conditions, state it explicitly as an assumption with a careful discussion of its domain of validity, or enumerate all saddle pairings to show that no others survive.
[Eq. (3.12) and Fig. 18] There is a concrete internal inconsistency in the fourth detection saddle. The text preceding (3.12) says that this saddle contributes a factor Z(2*beta_L + 2*beta_R) * Z_mi^2 * Z_mP, while Eq. (3.12) contains an additional factor Z(beta_R). The two versions scale differently under the microcanonical Laplace transform: with E_L = E_R = E, the text version gives e^{-2E(beta_L+beta_R)+S(E)}, matching the claim that every class of saddle contributes an equal factor, whereas the equation version would give e^{-2E*beta_L-3E*beta_R+...}. Please correct the equation or the text and rederive the 3/2 ratio accordingly. The topology should also be reconciled: the text calls the saddle a twice punctured torus, while the Fig. 18 caption calls it a twice punctured sphere.
[Sec. 2.1 and footnote 6] The normalized correlators are defined by computing the observable and the state norm separately in the gravitational path integral and then dividing. Since the paper's ratios are leading-order saddlepoint results in the m_i -> infinity limit, with no estimate of G_N or shell-mass corrections, the O(1) detection factors may receive subleading corrections. Please state the expected size of the omitted terms and discuss whether they could mask the detection signal in the regimes where the paper predicts a factor of 2 or 3.

minor comments (4)

[Sec. 2.1, after Eq. (2.6)] There are several typos: 'wehther' should be 'whether', and similar misspellings appear elsewhere ('wether', 'analagously', 'annilihate', 'schwarschild', 'geomtries'). A careful proofread is needed.
[Sec. 4] The QMA statement is heuristic. If the complexity claim is meant literally, the paper should define the witness, the verification procedure, and the error bounds; as written, 'putting this problem in QMA' is an analogy rather than a formal result.
[Sec. 4] The verification protocol assumes access to many identically prepared copies of the state and the ability to measure the nonlocal Hermitian operators A = (O_P + O_P^dagger)/2 and B = (O_P - O_P^dagger)/(2i). This operational assumption should be stated already in the abstract or introduction, since it is essential to the practical claim that an observer can 'check' a microstate proposal.
[Sec. 5.2] The caveat that detecting the interior state from one boundary is not the same as reconstructing low-energy EFT excitations in the interior is useful and should be stated earlier, in Sec. 3.2, to prevent overreading of the single-boundary detection result.

Circularity Check

1 steps flagged · score 4.0 of 10

Single-boundary detection of a two-boundary state rests on a self-cited orientation rule from [21]; the rest of the derivation is a self-contained, parameter-free combinatorics calculation.

uniqueness imported from authors [Sec. 3.2, Universal saddles paragraph (before Eqs. (3.11)-(3.13))]
"As explained in Appendix B [21], the saddle geometries for these kind of quantities must satisfy an additional bulk constraint. In particular, the flow of Euclidean boundary time induces a natural orientation to the boundary condition computing overlaps such⟨i|j⟩due to operator ordering. The boundary condition for⟨j|i⟩is then given by replacing operators with their conjugate while keeping orientation of this flow fixed. Only the saddles in which this orientation is smoothly continued into the bulk contribute."

The rule is not derived in this paper; it is imported from Appendix B of [21], which shares the present first author. It is exactly the criterion selecting the two universal saddles in (3.11) and the four detection saddles in (3.12), so it controls the ratio (3.13) and the microcanonical estimate Z_D/Z_U=3/2. The paper says the rule 'does not lead to subtleties' in earlier sections, so it is introduced precisely for the new single-boundary/two-boundary claim. If the rule were absent or incomplete, extra pairings of O_R and O_i shell endpoints satisfying the junction conditions could contribute at the same order, changing both the universal baseline and the detection enhancement.

full rationale

The paper's main detection mechanism is not a fitted-parameter exercise: in Sec. 2.1 the universal and detection contributions to |<i|O_P|i>|^2 are summed from shell-pairing topologies, the state-dependent shell factors Z_mi^2 Z_mP cancel in the ratio, and the resulting O(1) enhancement (e.g., 2 in the type-B regime, 3 below the black-hole threshold) is computed from the partition functions Z and S. No parameter is tuned to the data being 'predicted.' The same holds for the two-boundary coordinated probe in Sec. 3.1, where the detection-to-universal ratio (3.4) is an explicit ratio of Z's. The partial circularity I find is confined to Sec. 3.2: the set of universal and detection saddles for the single-boundary probe of a two-boundary state is fixed by an 'orientation' rule imported from Appendix B of [21], a self-citation with overlapping authorship. The paper does not re-derive the rule, and the rule is exactly what produces the 3/2 microcanonical estimate. If the rule were wrong or incomplete, the saddle count and hence the predicted signal would change. I also note the text/Fig. 18 inconsistency (twice punctured torus vs. twice punctured sphere) as a separate correctness issue. Because Secs. 2 and 3.1 stand independently of the orientation rule, the circularity is partial rather than total.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper adds no fitted parameters. Its results depend on the shell-state basis and coarse-graining framework from the authors' prior work, plus the imported orientation rule. These are the main external assumptions; all are identified in the axioms list.

assumptions (5)

domain assumption Saddlepoint dominance of the Euclidean gravitational path integral, including the three disk saddles for AdS boundary conditions.
Invoked in Eq. (2.2) for Z(β) and throughout all saddle sums in Secs. 2 and 3.
domain assumption Sufficiently large sets of type A and type B shell states form a complete basis of the non-perturbative gravity Hilbert space.
Stated in Sec. 2 and used in Sec. 4 to extend probe results to arbitrary superpositions; established in [15,22].
domain assumption The gravitational path integral computes coarse-grained, ensemble-averaged magnitudes; phases make <i|O_P|i> average to zero while the magnitude squared remains meaningful.
Introduced near Eq. (2.1) and again before the universal saddle computation in Sec. 2.1.
ad hoc to paper Only wormhole saddles that continue the boundary Euclidean time orientation smoothly into the bulk contribute.
Imported from Appendix B of [21] in Sec. 3.2; it determines which saddles count for the single-boundary probe of a two-boundary state.
domain assumption The normalized probe correlator is obtained by dividing separately computed path integrals for the correlator and the norm.
Footnote 6 states this convention, following [20]; if invalid, the ratios shift.

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Cite this review

Pith. "Pith review of Observing Spacetime." pith.science (2026). https://pith.science/paper/2D56NXLE

@misc{pith2026250909763,
  author       = {Pith},
  title        = {Pith review of: Observing Spacetime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2D56NXLE}},
  note         = {Machine review of arXiv:2509.09763}
}

read the original abstract

Complex states of quantum gravity in flat and AdS gravity can have features that are inaccessible to classical asymptotic observers. The missing information appears to such observers to be hidden behind a horizon or in a baby universe. Here we use the gravitational path integral to ask whether quantum observables can access the hidden data. We show that generic probes give a universal result and contain no information about the state. However, a probe appropriately fine-tuned to the state can give a large signal because of novel wormhole saddles in the path integral. Thus, in these settings, asymptotic observers cannot easily determine the state of the universe, but can check a proposal for it. Using these fine-tuned probes we show that an asymptotic observer can detect information hidden in a disconnected baby universe. Furthermore we show that the state of a two-boundary black hole can be detected using Lorentzian operators localised on just one of the boundaries.

Figures

Figures reproduced from arXiv: 2509.09763 by the authors.

**Figure 2.** Shell-strip asymptotic boundary condition for the overlap [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** The saddle for the norm ⟨i|i⟩ is constructed by considering the shell propagating on a disk and strip separately for some propagation times ∆TS,D and then gluing them together along the i-shell worldvolume by discarding the shell homology region (purple). The junction conditions dynamically determine ∆TS,D to yield an on shell glued geometry. We have suppressed the angular directions in these diagrams, and represent… view at source ↗

Figures from the paper (15 more)

**Figure 4.** Figure 4: Analytic continuation of the single-sided shell state saddlepoints to Lorentzian signature, [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Path integral boundary condition for ⟨i|OP |i⟩ ⟨i|O † P |i⟩. again interpret this to be a by-product of the performing the coarse-gained/ensemble averaged nature of the gravity path integral, where erratic phases cause the correlator to average out to zero. Still, the …

**Figure 6.** Figure 6: Schematic of the classes of saddle geometry that contribute to [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: Construction of the two universal saddles to [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: (a) Construction of the D ↑ L saddles. (b) Construction of the D ↑ R saddles. (c) Construction of the D ↓ R saddles. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

**Figure 9.** Figure 9: Asymptotic boundary condition for the gravity path integral defining the shell state. ( [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]

**Figure 10.** Figure 10: Shell asymptotic boundary condition for ⟨j|i⟩, consisting of the operator insertions Oi and O † j separated by asymptotic time extent βL and βR respectively. The red lines represent the shells propagating into the bulk. Figure adapted from [22]. considered in [18]. 2.…

**Figure 11.** Figure 11: The saddlepoints for the shell norm path integral [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]

**Figure 12.** Figure 12: Diagrams showing the analytic continuation of the type 1-3 shell states to Lorentzian [PITH_FULL_IMAGE:figures/full_fig_p020_12.png]

**Figure 13.** Figure 13: Lorentzian two-sided shell detection. where the ration of the detection and universal contributions to ⟨β1, β2|O † P,LOP,R|β3, β4⟩ is given by ZD ZU = Z(β2/2)Z(β3/2)Z((β1 + β4)/2) Z((β1 + β2 + β3 + β4)/2) . (3.7) Upon evaluating the Laplace transforms in the saddlepoi…

**Figure 14.** Figure 14: (a) Universal saddle contribution to ⟨i|O † P,LOP,R|i⟩. (b) Propagation saddle contribution to ⟨i|O † P,LOP,R|i⟩ [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]

**Figure 15.** Figure 15: Boundary condition for detecting a two-boundary state using a single-boundary probe. [PITH_FULL_IMAGE:figures/full_fig_p022_15.png]

**Figure 16.** Figure 16: Construction of the universal saddle contributions to [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]

**Figure 17.** Figure 17: First three classes of detection saddle contributions to [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]

**Figure 18.** Figure 18: Fourth classes of detection saddle contributions to [PITH_FULL_IMAGE:figures/full_fig_p024_18.png]

Discussion (0). Continue with ORCID to comment.

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