{"id":"159e22ec-0623-4ed5-8db6-3bafcd261974","arxiv_id":"2501.15024","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For holography with a finite ETW-brane cutoff, entanglement wedge nesting requires the two intervals' RT surfaces to be spacelike separated, a condition stronger than spacelike separation of the intervals themselves.","lead":"This paper derives restrictions on where two intervals can sit when one is on a brane that cuts off AdS, so that a property called entanglement wedge nesting is not violated. The authors show that mere spacelike separation in the bulk is not enough at finite cutoff, and they probe the same issue in a BTZ black hole.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The EWN-violation claim rests on Eq. (2.24), where the connected wedge is defined by fiat as an intersection of spacelike-separated sets; if the physical cutoff wedge is instead the restricted-maximin or replica wedge, the derived bounds do not constrain physical EWN.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing concern: the connected wedge in Eq. (2.24) is postulated rather than derived, and the paper's EWN bounds constrain that prescription. I agree with this assessment. The paper is otherwise careful: the analytic derivations in the appendices are detailed, the parameter-free inequalities are internally coherent, and the numerical scans support the stated phase-dominance claims. The concern is not that the paper contradicts itself, but that the physical interpretation of the central claim depends on an unvalidated identification of the entanglement wedge in cutoff holography. Because the paper explicitly acknowledges that restricted maximin produces different RT surfaces precisely when EWN is violated, the result is best understood as a sharp constraint on the naive RT prescription rather than an established property of the physical cutoff theory. A boundary replica calculation in a solvable BCFT2 would settle whether the naive RT area is the correct physical entropy in the relevant regime; absent that check, the conditional verdict is appropriate. I therefore recommend keeping the reader's CONDITIONAL verdict unchanged.","tokens_in":66106,"tokens_out":8338,"duration_ms":90854,"concrete_test":"Perform a boundary replica computation of S(A∪B) in a solvable BCFT2 with the same interval layout as Figure 11, for parameters in the claimed EWN-violating region, and compare the result with both the naive connected RT area used in the paper and the restricted-maximin area. If the replica answer matches restricted maximin wherever the two prescriptions differ, the EWN violation is an artifact of the assumed RT formula; if it matches the naive RT area, the violation is a genuine property of the cutoff theory.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that EWN can be violated for spacelike-separated A and B depends on identifying the connected entanglement wedge as W_E(A∪B) = SL+_AdS3(χ1) ∩ SL-_AdS3(χ2) ∩ Mphys, Eq. (2.24). This region is introduced by postulate rather than derived from a boundary replica computation or from a first-principles construction of the entanglement wedge in cutoff holography. In standard AdS/CFT the entanglement wedge is the domain of dependence of a partial Cauchy slice bounded by the boundary subregion and its RT surface; here the paper postulates that such a slice Σ_A∪B exists and that its domain of dependence equals the intersection in Eq. (2.24). The necessary and sufficient condition for EWN, Eq. (3.12), is therefore a constraint on this specific prescription. The paper itself concedes in Section 3.5 that the naive RT prescription and restricted maximin agree only when EWN is respected and disagree exactly in the parameter region where the claimed violation occurs. Consequently, the result can be read as showing that the naive RT prescription violates EWN, not necessarily that the physical entanglement wedges of the cutoff theory violate EWN. This is a scope limitation rather than an internal inconsistency, but it is load-bearing because every quantitative bound in Section 3 and the BTZ interpretation in Section 4 are claims about the object defined in Eq. (2.24).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies entanglement wedge nesting (EWN) in AdS3 with a finite cutoff implemented by an end-of-the-world (ETW) brane. It considers two constant-time intervals, A on the asymptotic boundary and B on the brane, constructs RT surfaces and associated entanglement wedges, and derives the condition |Δt| < min{Δt_A,EWN, Δt_2,EWN} (Eq. 3.12) as necessary and sufficient for EWN in the connected phase. It interprets this condition as the requirement that all RT surfaces involved are spacelike separated, argues that bulk spacelike separation of A and B is not sufficient for EWN, and contrasts the prescription with the restricted maximin construction of arXiv:2008.07022. The second part repeats the analysis for a two-sided planar BTZ black hole with an ETW brane in one exterior, obtaining constraints on the Kruskal-time parameter that prevent connected RT surfaces from crossing the τ = ±π/2 singularities.","tokens_in":66441,"tokens_out":5677,"duration_ms":56594,"significance":"If the prescription is accepted, the paper provides explicit, analytically derived constraints on a simple holographic model at finite cutoff, with useful limiting checks (θ0 → π/2 reproduces standard holography) and a clean geometric reinterpretation of EWN in terms of spacelike separation of all RT surfaces. The appendices contain substantial derivations, and the comparison with restricted maximin is valuable: it sharpens what is prescription-dependent versus what is a genuine property of cutoff holography. The BTZ result also gives a concrete bulk reason to discard connected RT surfaces through the singularities, complementing earlier work on DGP constraints. However, the central EWN-violation claim is load-bearing and, as discussed in the major comments, currently applies only to the paper's own connected-wedge prescription rather than to an independently defined physical entanglement wedge.","major_comments":[{"comment":"The connected entanglement wedge is introduced by postulate rather than derived. The text states that 'we can postulate the existence of a specific partial Cauchy slice Σ_{A∪B}' and identify its domain of dependence with SL+_AdS3(χ1) ∩ SL-_AdS3(χ2) ∩ Mphys. In standard AdS/CFT this identification follows from subregion duality or from a replica/maximin construction; here no such justification is given for the cutoff setup. Every bound in Section 3, including the central Eq. (3.12), is a constraint on this prescription. Since the paper itself argues in §3.5 that restricted maximin satisfies EWN by construction and disagrees with the naive RT prescription precisely in the claimed violation region, the abstract's statement that 'EWN can be violated' should be rephrased as 'the naive RT/EW prescription violates EWN' unless Eq. (2.24) is derived from a boundary construction or otherwise justified as the physical entanglement wedge.","section":"§2.4.3, Eq. (2.24)"},{"comment":"There is a circularity issue in the definition of W_E(A∪B) and the bound Δt_2,EWN. The construction of the connected wedge as a smooth tube is introduced 'as long as χ1 and χ2 are spacelike separated from each other,' and the paper later shows that |Δt| < Δt_2,EWN is precisely the condition for χ1 and χ2 to be spacelike separated. Thus the regime in which EWN is claimed to be violated (|Δt| ≥ Δt_2,EWN) is outside the domain where Eq. (2.24) is a well-defined domain of dependence. The paper partially acknowledges this in §3.3, but the violation claim still relies on extending the prescription beyond its regime of validity. The authors should either define W_E(A∪B) independently in that regime, or explicitly state that EWN is only defined when the connected wedge exists, in which case the 'violation' is not a violation of a physical nesting property but a breakdown of the prescription.","section":"§3.3 and §2.4.3"},{"comment":"The nontriviality of the EWN constraint depends on the claim that the connected phase dominates before the EWN bound is reached, i.e., Δt_EWN − Δt_con > 0 for 2a− > ℓ*. This statement is supported by numerical scanning (Figures 16 and 17) rather than by an analytic proof. Since the paper's main conclusion is that spacelike-separated A and B can violate EWN, this phase-dominance assertion is load-bearing. An analytic proof, or at least a crisp analytic characterization of the parameter region where the connected phase dominates, would considerably strengthen the paper; as it stands, a skeptic cannot verify the claim beyond the sampled parameters.","section":"§3.2 and Appendix B.3"}],"minor_comments":[{"comment":"The expression 'tBr∩C+ ≈ 2.695 = b2 − b1/2 − 0.305' is ambiguous and dimensionally inconsistent as written; it should be t_{Br∩C+} ≈ 2.695 ≈ (b2 − b1)/2 − 0.305, with the understanding that the numerical value depends on the chosen parameters.","section":"§2.4.3, Eq. (2.27)"},{"comment":"The table entries such as '|Δt| → Δt_2,EWN' would be clearer if they specified whether the approach is from below or from above, since the phase at the bound is not continuous in the parameter regimes discussed.","section":"§3.2, Table 1"},{"comment":"The color-coded regions in Figure 11 are described in the text, but the figure itself lacks a legend; adding one would help the reader map the discussion of where the naive and restricted maximin surfaces agree.","section":"§3.5, Figure 11"}],"recommendation":"major_revision","confidential_remarks":"The paper is a serious technical contribution and the derivations appear internally consistent, but the stated conclusion goes beyond what the construction justifies. The referee report focuses on the fact that Eq. (2.24) is a postulate and that the violation regime lies outside the domain where the connected wedge is a well-defined domain of dependence. This is fixable by a substantial reframing of the claims, which is why I recommend major revision rather than rejection. The paper would also benefit from an analytic treatment of the phase-dominance question in §3.2."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth a serious referee. The new analytic result is Eq. (3.12): for a boundary interval A and a brane interval B in the connected phase, EWN holds iff |Δt| < min{Δt_A,EWN, Δt_2,EWN}, and this is equivalent to demanding that all candidate RT and wedge-building surfaces are spacelike separated. That derivation, spread over Section 3 and Appendix B, is careful and internally consistent. The BTZ section gives a clean corollary: EWN in the connected phase rules out connected RT surfaces that cross τ = ±π/2, which ties naturally to the concerns in [60]. The comparison with restricted maximin is also handled honestly, including a useful phase diagram (Fig. 11) showing where the two prescriptions agree and disagree.\n\nThe soft spot is exactly where the stress test lands, and the paper itself acknowledges part of it in Section 3.5. The connected wedge W_E(A∪B) is not derived; it is identified by postulate with SL+ ∩ SL− ∩ M_phys in Eq. (2.24), treating the set of points spacelike separated from each RT segment toward the other as the domain of dependence of a partial Cauchy slice. The paper does not derive that region from a replica computation or from restricted maximin. So the EWN bound constrains this specific prescription. Restricted maximin satisfies EWN by construction and disagrees with the naive RT surfaces precisely in the parameter region where the violation occurs, as the paper states explicitly. The correct reading is therefore: within the naive RT prescription, EWN fails; whether that failure is a property of the physical entanglement wedges of cutoff holography remains open. This is a scope limitation, not an internal inconsistency, and it does not undermine the algebra.\n\nA smaller gap: some phase-dominance statements in Section 3.2 rest on numerical scans rather than complete analytic proofs. That is minor relative to the main bound, since the central inequality is derived rather than fitted, and no free parameters or prior results are leaned on.\n\nWho is this for? People working on double holography, surface/state correspondence, and restricted maximin will want to know this bound and the exact region of disagreement between prescriptions. I would bring it to a reading group and would cite it, with the prescription caveat attached. Send it to peer review. A good referee should press for either a sharper justification of Eq. (2.24) or a clearer framing of it as defining the prescription, and should ask the author to prove or explicitly flag the numerical phase claims.","headline":"Careful analytic paper that derives a concrete EWN bound for the naive RT prescription on an ETW-brane cutoff; worth refereeing, but the physical punchline is conditional on the prescription choice made in Eq. (2.24).","tokens_in":66906,"tokens_out":2160,"would_cite":true,"duration_ms":23337,"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":"Entanglement wedge nesting can fail when one region lives on a finite cutoff, even if the two regions are spacelike separated through the bulk.","keywords":["entanglement wedge nesting","end-of-the-world brane","cutoff holography","holographic entanglement entropy","AdS3/CFT2","BTZ black hole","restricted maximin","double holography"],"falsifier":"Take the paper's AdS3 parameters with 2a− > ℓ* so the connected phase dominates near the bound, and choose |Δt| between min{Δt_A,EWN, Δt_2,EWN} and Δt_c. Compute the entanglement entropy and wedges directly from the dual BCFT2 state, including boundary degrees of freedom, rather than from the postulated wedge; if the boundary computation gives the connected-phase entropy but still satisfies WE(A) ∪ WE(B) ⊆ WE(A ∪ B), the prescription in Eq. (2.24) is the incorrect entanglement wedge.","tokens_in":65900,"feed_emoji":"🕳️","tokens_out":7210,"duration_ms":62200,"temperature":0.7,"pith_summary":"This paper tries to establish that in AdS3 holography with a finite cutoff implemented by a subcritical end-of-the-world (ETW) brane, entanglement wedge nesting can fail even when the two chosen regions A (on the conformal boundary) and B (on the brane) are spacelike separated through the bulk. In the connected phase the nesting condition WE(A) ∪ WE(B) ⊆ WE(A ∪ B) is shown to hold if and only if |Δt| < min{Δt_A,EWN, Δt_2,EWN}, and this bound is exactly the condition that all RT surfaces involved are mutually spacelike separated. The same reasoning in a two-sided planar BTZ black hole with an ETW brane forbids connected RT surfaces that cross the Kruskal singularities at τ = ±π/2. If the claim is right, spacelike separation of subregions is not enough to make them independent in cutoff holography; the RT surfaces themselves must be spacelike separated, which is a precise geometric signature of the non-locality of the cutoff theory.","feed_headline":"Nesting fails for spacelike-separated regions in cutoff AdS3","feed_subtitle":"Entanglement wedges nest only when their RT surfaces are mutually spacelike, a strictly stronger condition than region separation.","key_machinery":"The load-bearing construction is the connected entanglement wedge WE(A ∪ B) = SL+_AdS3(χ1) ∩ SL-_AdS3(χ2) ∩ Mphys (Eq. 2.24), defined as the intersection of the sets of points spacelike separated from each RT segment toward the other, restricted to the physical spacetime in front of the brane. For a brane interval B the RT surface is extended behind the brane to a virtual boundary interval, giving WE(B) = WE(Vir(B)) ∩ Mphys. The argument is carried by the equivalence between entanglement wedge nesting and mutual spacelike separation of all RT surfaces χdis(A), χdis(B), χ1, χ2, expressed through the two computable bounds Δt_A,EWN and Δt_2,EWN whose minimum is the EWN threshold.","core_discovery":"The central discovery is that the naive RT prescription for a brane interval B and a boundary interval A violates entanglement wedge nesting in the connected phase unless the time separation obeys |Δt| < min{Δt_A,EWN, Δt_2,EWN}. The first bound comes from requiring χdis(A) and χdis(B) to be spacelike separated; the second from requiring the two connected segments χ1 and χ2 to be spacelike separated. This is strictly stronger than requiring A and B to be spacelike separated through the bulk, and the paper shows explicitly that EWN can be violated while A and B remain spacelike separated. In the BTZ example the analogous nesting condition, in the limit of large intervals, translates into c− ≤ ct ≤ c+, which geometrically prevents the connected RT surface from touching the τ = ±π/2 singularities. The paper concludes that in holography at a cutoff, the entanglement wedges WE(A) and WE(B) must themselves be spacelike separated, and that the region of parameter space where this fails is precisely where restricted maximin and naive RT surfaces disagree.","pith_inferences":["A testable diagnostic suggested by the result: in any cutoff-holography model, treat two cutoff subregions as independent only when their associated extremal surfaces are mutually spacelike separated, not merely when the regions are spacelike separated.","One extension would be to check whether EWN violations always originate in arbitrarily small neighborhoods of the RT endpoints, as the paper observes for these examples; if so, higher-dimensional EWN conditions could be derived from local data near entangling surfaces.","When Neumann boundary conditions put dynamical gravity on the brane, the bound can be translated into constraints on brane gravitational couplings, since those couplings shift where RT surfaces end on the brane and thereby move B relative to A.","The observation that the wedge intersection with the brane grows when far-away regions are included suggests a concrete IR/UV split: IR information on the cutoff is stored locally, UV information non-locally, a structure one could look for in solvable T¯T-deformed models."],"forward_implications":["In the connected phase, EWN is equivalent to |Δt| < min{Δt_A,EWN, Δt_2,EWN}; any connected configuration with larger time separation violates nesting.","Spacelike separation of the subregions through the bulk is not sufficient; one must require the entanglement wedges themselves to be spacelike separated, equivalently all RT surfaces mutually spacelike.","The restricted maximin prescription and the naive RT prescription agree exactly where EWN is respected; outside that region restricted maximin produces time-dependent RT profiles even in static geometries, signaling that the subregions are not independent.","In the two-sided planar BTZ setup, the EWN condition disallows connected RT surfaces that cross the Kruskal singularities at τ = ±π/2, reinforcing earlier constraints on such surfaces.","In the conformal-boundary limit θ0 → π/2 the bound reduces to standard holography, where spacelike separation of A and B is sufficient for EWN."],"supporting_citations":[{"why":"Supplies the restricted maximin prescription whose EWN guarantees and RT surfaces are compared with the naive prescription.","marker":"[1]"},{"why":"Establishes the geodesic shortcuts between brane and boundary that motivate the non-locality interpretation.","marker":"[37]"},{"why":"Introduces the ETW brane action and double-holography cutoff model used throughout.","marker":"[25]"},{"why":"Provides evidence that subregion entropies on the brane obey the RT formula, justifying the paper's starting point.","marker":"[29]"},{"why":"Grounds the strong subadditivity and maximin framework that restricted maximin builds on.","marker":"[45]"},{"why":"Previous analysis of the same BTZ brane setup giving reasons to discard RT surfaces crossing the τ = ±π/2 singularities.","marker":"[60]"}],"fun_headline_variants":["Entanglement nesting requires spacelike-separated wedges in cutoff AdS3","EWN fails unless wedges are mutually spacelike in cutoff holography","Cutoff AdS3: nesting forces spacelike separation of RT surfaces","Naive RT breaks entanglement wedge nesting in cutoff AdS3","Need spacelike wedges: EWN violation in finite-cutoff holography"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The connected-phase entanglement wedge is identified, by postulate, as the set of points spacelike separated from each RT segment toward the other (Eq. 2.24), rather than derived from a boundary replica or from the restricted maximin construction; if the true entanglement wedge in cutoff holography follows a different prescription, the derived EWN violation need not describe physical entanglement.","fun_headline_variants_meta":{"raw":{"variants":["Entanglement nesting requires spacelike-separated wedges in cutoff AdS3","EWN fails unless wedges are mutually spacelike in cutoff holography","Cutoff AdS3: nesting forces spacelike separation of RT surfaces","Naive RT breaks entanglement wedge nesting in cutoff AdS3","Need spacelike wedges: EWN violation in finite-cutoff holography"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000344,"raw_usage":{"total_tokens":1967,"prompt_tokens":1102,"completion_tokens":865,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":718,"completion_tokens_details":{"reasoning_tokens":766}},"tokens_in":718,"tokens_out":865,"duration_ms":20234,"temperature":1.0,"reasoning_tokens":766,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:41:58.095715+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the paper's AdS3 parameters with 2a− > ℓ* so the connected phase dominates near the bound, and choose |Δt| between min{Δt_A,EWN, Δt_2,EWN} and Δt_c. Compute the entanglement entropy and wedges directly from the dual BCFT2 state, including boundary degrees of freedom, rather than from the postulated wedge; if the boundary computation gives the connected-phase entropy but still satisfies WE(A) ∪ WE(B) ⊆ WE(A ∪ B), the prescription in Eq. (2.24) is the incorrect entanglement wedge.","supporting_citations":[],"review_version":1}