{"id":"bd17ea5b-e439-4d4b-b96c-1708c7c50f89","arxiv_id":"1908.03975","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The reconstructable bulk region for a boundary subregion can be macroscopically smaller than the entanglement wedge in horizon-free AdS/CFT code subspaces, with arbitrary large gaps in large low-density dustball states.","lead":"This paper shows that in AdS/CFT, the part of the bulk a boundary region can actually reconstruct can be far smaller than the entanglement wedge, even without black holes and with weak gravity. It provides explicit qubit and dustball models where this 'reconstruction wedge' is arbitrarily small compared to the naively reconstructable region.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Near-vacuum examples rely on O(1) entropy differences at an exact QES degeneracy; graviton area fluctuations of order sqrt(l/G_N) swamp them, so the reconstruction wedge is not well defined there.","rationale":"The paper's central claim has two pillars. The dustball construction uses O(1/G_N) entropy, so entropy differences dominate; assuming the QES placements are correct, it yields large RW-EW separations without horizons. The near-vacuum pillar, however, requires an O(1) entropy difference to resolve an exact classical degeneracy. In a genuine quantum-gravity treatment, the area is an operator with fluctuations delta A ~ sqrt(l G_N); these produce fluctuations in generalized entropy much larger than the log 2 terms as G_N -> 0. The authors' footnote 6 states exactly this caveat. Additionally, at the maximally mixed state of Qubit 1 in the Bell-pair example, the generalized entropies of the two candidate surfaces are equal even before including graviton fluctuations, so the assertion that A's EW includes the middle 'for all states' is already ambiguous at the semiclassical level. This does not destroy the dustball result, and the broader conclusion that reconstruction wedges can be much smaller than entanglement wedges without black holes may survive; but the near-vacuum headline separation is not presently established. A controlled computation, e.g. in fixed-area states, could settle it. The reader's conditional verdict is appropriate; no verdict change.","tokens_in":7536,"tokens_out":7714,"duration_ms":93709,"concrete_test":"Evaluate the two candidate QES in the Section II Bell-pair example using fixed-area states (Dong-Harlow-Marolf) rather than the vacuum, and compute the variance of Delta(Area)/(4G_N) in the code subspace. If sigma(Delta A/(4G_N)) >> log 2 as G_N -> 0, the phase transition is unresolved and the near-vacuum examples fail; if fixed-area states restore a unique minimum, the concern is met.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The Section II examples place the reconstruction-wedge claim on O(1) generalized-entropy differences at an entanglement phase transition. In the vacuum four-interval setup the two candidate RT surfaces have exactly equal areas; a single mixed qubit contributes log 2, and a Bell pair contributes log 2. The QES prescription is only meaningful when the comparison is controlled. Graviton fluctuations make area differences fluctuate by delta A/(4G_N) ~ sqrt(l/G_N), which diverges as G_N -> 0 and overwhelms the O(1) bulk-entropy terms; footnote 6 concedes this. Therefore, for the near-vacuum code subspaces, there is no reliable selection of a unique QES, and the 'arbitrarily large' RW-EW separation advertised for near-vacuum states is not established. The dustball example, with entropy O(1/G_N), is not subject to this objection and still supports the broader claim; hence the verdict should remain conditional pending a controlled computation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper defines the reconstruction wedge of a boundary region A as the intersection, over all states in a code subspace, of the entanglement wedges of A. It then constructs two families of examples in AdS3/CFT2 where this reconstruction wedge is claimed to be macroscopically smaller than the entanglement wedge of a particular state. The first family (Section II) places a few bulk qubits and Bell pairs at an entanglement phase transition in near-vacuum states. The second (Section III) considers a large, low-density dustball with O(1/G_N) internal entropy and a boundary region A made of O(G_N^{-1}) small intervals. The paper argues that in the maximally mixed dustball state, the entanglement wedges of A and its complement exclude the dustball, while in a pure dustball state A's entanglement wedge includes it, leading to an arbitrarily large gap.","tokens_in":7774,"tokens_out":22007,"duration_ms":222387,"significance":"If established, the result would show that subspace-dependent bulk reconstruction is not a peculiarity of black hole horizons, and that quantum extremal surfaces can differ macroscopically from classical RT surfaces. The paper is clearly written and the dustball construction is a useful tractable model. The definition of the reconstruction wedge is clean, and the paper correctly emphasizes the role of mixed states in the code subspace. The dustball example, which uses O(1/G_N) entropy differences, appears to avoid the main caveat affecting the near-vacuum examples. However, the near-vacuum claims are not presently supported, and the dustball geometry requires explicit checks.","major_comments":[{"comment":"The near-vacuum examples select a unique QES using O(1) differences in generalized entropy at an exact phase transition. As footnote 6 concedes, graviton area fluctuations give delta A/(4G_N) ~ sqrt(l_AdS/G_N), which diverges in the G_N -> 0 limit and is much larger than the O(1) entropy differences. Therefore the QES prescription is not controlled for these code subspaces, and the abstract's claim of arbitrarily large separations in near-vacuum states is not established. The dustball example is not subject to this objection, but the Section II examples and the abstract need to be revised, for example by using fixed-area states as the footnote suggests.","section":"II, footnote 6"},{"comment":"The central geometric input is that for n ~ R/l_AdS the QES of every connected component of A and \\bar A lies outside the dustball, and that the area difference between the two candidate configurations is Eq. (9) with an O(1) constant gamma independent of n. These facts are asserted without derivation. An explicit computation using the metrics in Eqs. (3)-(8) is needed to verify the scaling and to confirm that the dustball entropy can dominate the area difference while the QES remain outside the dustball.","section":"III.C"},{"comment":"The reconstruction wedge is defined as the intersection over all states in the code subspace, but the examples include states in which the QES is exactly degenerate. For instance, in the Bell Pair 1 example, the maximally mixed state of Qubit 1 gives equal generalized entropy for including and excluding the middle, so the entanglement wedge is not unique. The paper states that the EW includes the middle for all states in this code subspace, but under a strict intersection over all degenerate choices the middle would be excluded for that state. A tie-breaking prescription or a fixed-area-state treatment is required before the Section II conclusions follow.","section":"II and Definition in Introduction"}],"minor_comments":[{"comment":"In the paragraph after Figure 1, 'reigon' should be 'region'.","section":"II"},{"comment":"After Eq. (2), the text should state explicitly that eta is the small parameter controlling the validity of the near-vacuum exterior metric in Eq. (8), and that all subsequent equations are leading-order in eta.","section":"III.A"},{"comment":"The extension to even dimensions is presented as an expectation; it would be clearer to label it as a conjecture and indicate what a proof would require.","section":"IV"},{"comment":"The claim that dressing the qubit equally to A and \\bar A 'does not affect the degeneracy' deserves a fuller explanation, since the dressing crosses an RT surface and changes its area by an amount of order the qubit entropy.","section":"Footnote 3"}],"recommendation":"major_revision","confidential_remarks":"The near-vacuum examples are the weakest part of the manuscript, and the authors' own footnote 6 acknowledges the central difficulty. I would advise the editor that acceptance should be conditional on either a fixed-area-state computation for Section II or a revision of the abstract to place the dustball example as the primary claim. The dustball construction is the more solid contribution and, if the QES computation is supplied, would justify the paper's broader conclusion."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know: this paper gives us a useful, explicit notion of the reconstruction wedge and a convincing dustball example where it is macroscopically smaller than the entanglement wedge with no horizon in sight. The near-vacuum examples in Section II are the advertised headline, and they are the weak part; the O(1) entropy differences at the phase transition are swamped by graviton area fluctuations, as the authors admit in footnote 6. So treat the near-vacuum claim as not established.\n\nWhat's new: Hayden-Penington had state-dependence for black holes; this paper decouples the phenomenon from horizons. The reconstruction wedge definition—intersection of entanglement wedges over all states in the code subspace, including mixed—is clean and should stick. The dustball code subspace has O(1/G_N) entropy, so the separation between RW and EW can be made arbitrarily large while backreaction stays small. That example is the real contribution and it holds up. The observation that QES can be macroscopically different from RT is also useful.\n\nSoft spots: Section II's whole mechanism is a degeneracy between RT surfaces broken by one qubit's entropy. The generalized-entropy difference is O(1), but the area fluctuations are order sqrt(l/G_N), which diverges as G_N -> 0. The authors' footnote 6 is honest but it undercuts the section. The Bell-pair bookkeeping is cute, but it doesn't fix the fluctuation problem. For the dustball, the QES positions are asserted rather than derived; I believe the claims are right—the low-density, large-radius limit makes it plausible—but a referee should ask for the computation or at least a sharper estimate. The higher-dimensional generalization in Section IV is a sketch, not an argument. Citation pattern is fine; they build on HP and Engelhardt-Wall appropriately.\n\nBottom line: the paper deserves a serious referee. The dustball construction alone is worth publishing. A revision should either put the near-vacuum examples in fixed-area states or clearly demote them to heuristic illustrations. I'd bring it to the reading group and would cite it.\n\nRecommendation: send to peer review, with the expectation of a major revision on Section II.","headline":"Trust the dustball, not the near-vacuum qubits — the reconstruction wedge concept is solid and the paper deserves refereeing, but Section II's O(1) entropy differences are too fragile.","tokens_in":8210,"tokens_out":2852,"would_cite":true,"duration_ms":29282,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The bulk reconstructable from a boundary subregion can be arbitrarily smaller than its entanglement wedge, even with small backreaction and no horizon.","keywords":["AdS/CFT","entanglement wedge reconstruction","reconstruction wedge","quantum extremal surface","quantum error correction","state-dependent reconstruction","dustball","holographic entanglement entropy"],"falsifier":"Perform a detailed calculation of the generalized entropy of the two candidate quantum extremal surfaces in the four-interval AdS$_3$ vacuum with one mixed qubit in the middle, including graviton fluctuations; if the fluctuations wash out the $O(1)$ entropy difference, the middle remains reconstructable and the near-vacuum separation disappears. For the dustball, compute the quantum extremal surface of A for a pure dustball state within the code subspace that also contains the maximally mixed state; if the surface does not move by an $O(1/G_N)$ area as the state changes, the claimed macroscopic gap is absent.","tokens_in":7322,"feed_emoji":"🧩","tokens_out":6187,"duration_ms":62386,"temperature":0.7,"pith_summary":"The paper tries to establish that in AdS/CFT the bulk region reconstructable from a boundary subregion A — the reconstruction wedge, defined as the intersection of A's entanglement wedges over all states in a code subspace — can be arbitrarily smaller than the entanglement wedge of a particular pure state, even when backreaction is small and the setting is far from black hole interiors. It constructs code subspaces whose states share one bulk geometry but differ in internal spin degrees of freedom. Near an entanglement phase transition in the vacuum, a handful of qubits can exclude the 'middle' of the bulk from the reconstruction wedge; in a low-density dustball with entropy of order $1/G_N$, the reconstruction wedge excludes the whole dustball while the pure-state entanglement wedge contains it. The result implies that bulk reconstruction is generically subspace-dependent, not a special feature of black hole physics.","feed_headline":"Reconstructable bulk shrinks far below the entanglement wedge","feed_subtitle":"Near-vacuum qubits and dustballs show a boundary region can lose most of its reconstructable bulk.","key_machinery":"The central object is the reconstruction wedge, the intersection of all entanglement wedges of A over states in the code subspace. The mechanism that does the work is the competition between bulk entropy and surface area in the generalized entropy: because the quantum extremal surface is selected by minimizing generalized entropy, a bulk state with high entropy can shift the surface and exclude a region that lower-entropy states would include. Bell pairs act as a controlled entropy budget that can be spent to keep the middle inside the reconstruction wedge, while the dustball supplies an entropy reservoir of order $1/G_N$ without changing the metric at the order of interest.","core_discovery":"The central claim is that the reconstruction wedge — the intersection of the entanglement wedges of A for every pure or mixed state in a code subspace — can be macroscopically smaller than the entanglement wedge of any given pure state. The paper proves this by explicit construction in AdS$_3$. With the boundary split into four equal intervals and a single qubit at the center, the maximally mixed state of the qubit breaks the degeneracy between the two competing extremal surfaces and pushes the entanglement wedge of A away from the middle, so the reconstruction wedge of A excludes it. Adding Bell pairs can restore the middle to A's reconstruction wedge, one Bell pair per qubit, showing a precise counting rule. In the dustball example, a spherical cloud of pressureless dust with total entropy of order $1/G_N$ sits at the center; a boundary region A formed from many small intervals has a quantum extremal surface whose area is only $O(G_N^0)$ away from its complement's, so the dustball's entropy dominates and excludes the dustball from the reconstruction wedge even though pure states include it. These examples also exhibit quantum extremal surfaces macroscopically different from the classical RT surface.","pith_inferences":["If the $O(1)$-entropy caveat is overcome with fixed-area states, the qubit examples would imply that even a single mixed bulk qubit can dictate the reconstruction wedge; the threshold for state-dependence would be entropy of order one, not order $1/G_N$.","A natural boundary diagnostic suggested by the dustball construction is a sharp drop in the mutual information between A and the dustball degrees of freedom as the bulk state passes from pure to maximally mixed, which could be probed holographically.","The same intersection construction could be applied to other holographic settings, such as evaporating black holes, where the reconstruction wedge may track the island region, suggesting a common mechanism: the most entropic state in the code subspace controls the reconstructable region."],"forward_implications":["Complementary recovery — the statement that A and its complement reconstruct complementary bulk regions — fails macroscopically whenever the code subspace contains a sufficiently entropic mixed state.","Entanglement wedge reconstruction as usually stated holds only for fixed code subspaces; a single reconstruction prescription cannot work on the full code subspace when the reconstruction wedge is smaller.","The quantum extremal surface can jump from the near-A surface to the near-complement surface as the bulk state varies within one code subspace, so the location of the QES is genuinely state-dependent even in near-vacuum geometries without horizons.","Boundary regions composed of $O(G_N)$-sized intervals have severely limited reconstructability, since that is the regime where the dustball example shows the largest separation."],"supporting_citations":[{"why":"introduced the idea that the reconstructable region is the intersection of entanglement wedges, which the paper formalizes as the reconstruction wedge.","marker":"[8]"},{"why":"defines quantum extremal surfaces and the generalized entropy that makes entanglement wedges state-dependent.","marker":"[7]"},{"why":"defines the Ryu-Takayanagi surface whose entanglement wedge is the baseline being compared to the reconstruction wedge.","marker":"[5]"},{"why":"established leading-order entanglement wedge reconstruction, the statement whose breakdown the paper demonstrates.","marker":"[2]"},{"why":"gives the bulk-boundary relative entropy equality used to justify reconstruction at leading order.","marker":"[6]"},{"why":"provides fixed-area states, cited by the paper as a possible way to avoid the graviton-fluctuation caveat in the near-vacuum examples.","marker":"[12]"}],"fun_headline_variants":["Reconstruction wedge can be far smaller than entanglement wedge","Near-vacuum qubits and dustballs shrink reconstructable bulk","Quantum extremal surfaces deviate macroscopically from RT","Entanglement wedge reconstruction fails even with weak backreaction","Reconstructable bulk shrinks; entanglement wedge stays big"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The weakest load-bearing premise is that an $O(1)$ entropy difference can robustly select the quantum extremal surface and fix the reconstruction wedge, despite graviton-induced area fluctuations of order $\\sqrt{G_N}$ that are much larger than that entropy difference in the classical limit.","fun_headline_variants_meta":{"raw":{"variants":["Reconstruction wedge can be far smaller than entanglement wedge","Near-vacuum qubits and dustballs shrink reconstructable bulk","Quantum extremal surfaces deviate macroscopically from RT","Entanglement wedge reconstruction fails even with weak backreaction","Reconstructable bulk shrinks; entanglement wedge stays big"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000783,"raw_usage":{"total_tokens":3415,"prompt_tokens":859,"completion_tokens":2556,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":475,"completion_tokens_details":{"reasoning_tokens":2475}},"tokens_in":475,"tokens_out":2556,"duration_ms":21130,"temperature":1.0,"reasoning_tokens":2475,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:56:14.222334+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform a detailed calculation of the generalized entropy of the two candidate quantum extremal surfaces in the four-interval AdS$_3$ vacuum with one mixed qubit in the middle, including graviton fluctuations; if the fluctuations wash out the $O(1)$ entropy difference, the middle remains reconstructable and the near-vacuum separation disappears. For the dustball, compute the quantum extremal surface of A for a pure dustball state within the code subspace that also contains the maximally mixed state; if the surface does not move by an $O(1/G_N)$ area as the state changes, the claimed macroscopic gap is absent.","supporting_citations":[{"cited_title":"state-dependent","cited_arxiv_id":null,"evidence_quote":"introduced the idea that the reconstructable region is the intersection of entanglement wedges, which the paper formalizes as the reconstruction wedge."}],"review_version":1}