{"id":"3494b11f-03ae-466b-a959-151aa05b9410","arxiv_id":"2607.11641","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Timelike entanglement and subregion complexity detect the cap–horizon transition of localized AdS3×S3×T4 black poles via fixed-boundary-interval Lorentzian branch selection, effects absent in BTZ and large-r limits.","lead":"This paper computes two time-based holographic probes—timelike entanglement and subregion complexity—in a black hole whose horizon is localized on an internal sphere rather than spread uniformly. The calculations show these probes can detect the localized cap–horizon transition, an effect invisible to ordinary BTZ and to the large-radius approximation.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.5","headline":"The dual map (reduced θ0-branch then full-θ lift + fixed-T min of Re A or C) is assumed, not derived; if wrong, the reported cap–horizon sensitivity does not follow.","rationale":"The reader correctly isolates the dual map as the weakest assumption. The bulk calculation is carefully executed: non-monotonic time maps, fixed-T selection, large-r analytic limits, and Appendix A’s local log enhancement are all internally consistent under the stated prescription. No internal contradiction or numerical artifact is evident that would overturn the geometric effect once the map is granted. The concern is therefore not that the numerics are wrong, but that the map itself is an untested extrapolation from spatial RT and from homogeneous black holes. That keeps the verdict Conditional (high confidence on bulk consistency, medium correctness risk on the dual interpretation) and does not warrant a move to Reject or Accept. The proposed test is a direct, finite check of whether the θ0-freeze step is essential to the reported transition-region tracking.","tokens_in":47677,"tokens_out":818,"duration_ms":7430,"concrete_test":"Recompute the fixed-T selection of §3.4 and §4.4 with a fully θ-dependent reduced metric (i.e., allow the branch kernels Ktim, Ksp themselves to depend on the integration variable θ, or extremize the ten-dimensional area/volume functional without freezing the profile at a single θ0). If the selected (r0*,θ0*) still track θ⋆ and move inward with T, the dual-map assumption is robust; if the selected saddles leave the transition region or the multi-branch structure disappears, the headline claim weakens.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The strongest claim is that, after fixed-boundary-interval selection, selected Lorentzian branches for both TEE and timelike complexity move inward and become sensitive to the black-pole cap–horizon transition (Abstract; §§3.4–3.5, 4.4–4.5, 5). That claim rests entirely on the localized lifting prescription of Ref. [6] adapted to Lorentzian branches: solve the reduced (t,r) problem at a single angular label θ0 using F(r;θ0), H(r;θ0) (eqs. 2.22–2.23, 3.14), then lift area/volume by integrating the full Ky(r,θ), G(r,θ) over physical θ (eqs. 3.60–3.62, 4.1–4.5), and select by minimizing Re(Afull_tEE) or Clift_T at fixed T (eqs. 3.64, 3.107; 4.8, 4.72). The paper never derives this dual map from a CFT or from a first-principles bulk variational principle for timelike regions; it is imported from the spatial RT construction of [6] and from Lorentzian branch work in BTZ/AdS-Schwarzschild. If the correct bulk dual instead extremizes a fully ten-dimensional Lorentzian surface (or a different angular weighting), the non-monotonic T(r0,θ0) map and the subsequent selection toward θ⋆ need not be the physical saddles, and the claimed sensitivity to the localized transition region would not follow. Large-r checks and Appendix A only confirm internal consistency of this particular prescription.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper computes holographic timelike entanglement entropy (complex lifted area) and timelike subregion complexity (real finite renormalized volume) for the black-pole solution of AdS3×S3×T4. Both observables are built from the same Lorentzian spacelike/timelike branch geometry. The authors adapt the localized lifting prescription of Ref. [6]: reduced (t,r) branches are solved at an angular label θ0 using F(r;θ0), H(r;θ0), then the area/volume is lifted by integrating the full Ky(r,θ), G(r,θ) over the physical angle θ. Large-r analytics recover short-interval BTZ-like formulae (log + iπ/2 for TEE; T² log for complexity). In the exact geometry the time map T(r0,θ0) becomes non-monotonic, so saddles are selected only after fixing the boundary interval and minimizing Re(A) or the finite volume. Selected branches move inward toward the cap–horizon transition θ⋆ as T grows—effects absent in BTZ and the large-r limit. Appendix A supplies a local logarithmic mechanism for the Tmax enhancement near θ⋆.","tokens_in":48118,"tokens_out":1178,"duration_ms":10342,"significance":"If the dual map is accepted, the work supplies a concrete, complementary pair of Lorentzian probes that detect internal-sphere localization beyond the BTZ uplift and the asymptotic regime. Strengths include closed-form large-r hypergeometric integrals, controlled UV subtractions, an explicit BTZ benchmark for the volume prescription, and a transparent local analysis (Appendix A) of the transition-region enhancement. The fixed-boundary multi-branch selection is a necessary and carefully implemented technical step once non-monotonicity appears. The results are therefore a useful extension of the recent timelike-entanglement and subregion-complexity literature to genuinely ten-dimensional localized black holes, provided the imported lifting prescription is regarded as the correct holographic dual.","major_comments":[{"comment":"The central claim (Abstract; §§3.4–3.5, 4.4–4.5, 5) that selected branches become sensitive to the cap–horizon transition rests entirely on the localized lifting prescription imported from the spatial RT construction of Ref. [6] and adapted to Lorentzian branches (eqs. 2.22–2.23, 3.14, 3.60–3.62, 4.1–4.5). The paper never derives this dual map from a CFT calculation or from a first-principles ten-dimensional variational principle for timelike regions. A short discussion of why the reduced-θ0-then-full-θ-lift is preferred over a fully ten-dimensional extremal surface (or an alternative angular weighting), and of how the conclusions would change if that map failed, is needed for the claim to be load-bearing.","section":null},{"comment":"Numerical results for TEE and complexity are presented at different energy fractions (xE=0.2 in §3 vs xE=0.6 in §4). Because θ⋆, ℓ1 and ℓ2 depend on xE through τ (eqs. 2.10, 2.16), a direct comparison of the two selected saddles is not immediate. Either a common xE should be used for the main figures, or an explicit cross-check at one shared value should be added so that the claimed complementarity of the two observables is demonstrated under identical geometric parameters.","section":null}],"minor_comments":[{"comment":"Notation for the compact-space factor N=(2π)^6 V4 is introduced repeatedly (eqs. 3.38, 3.59, 4.2); a single definition in §2 would reduce clutter.","section":null},{"comment":"Figures 8 and 19 are dense multi-panel grids; a clearer legend or a single summary panel of selected (θ∗₀,r∗₀) versus T would improve readability.","section":null},{"comment":"The unit choice Q1=Q5=Ry=1 (eq. 2.17) is stated, but a brief remark that all plotted lengths are in these units would help readers comparing with other D1-D5 literature.","section":null},{"comment":"A few typographical inconsistencies appear (e.g., “LocalizedAdS” in the title line, occasional missing spaces around ×). A light copy-edit pass would suffice.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is technically careful and the large-r/Appendix-A analytics are solid. The only real risk is that the dual map is an unexamined import; once the authors add a short justification paragraph the paper is suitable for a solid hep-th journal. Scope and novelty are appropriate."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The punchline is simple: this is careful bulk work that takes the existing Lorentzian branch construction for timelike entanglement and subregion complexity and runs it on the Bena et al. black-pole geometry. What is new is the quantitative result that, once you fix the boundary interval, the selected saddles move inward and become sensitive to the cap–horizon transition on the internal S3—something absent in BTZ and in the large-r limit.\n\nThey do the technical parts well. Branch equations are clean, large-r limits recover the expected short-interval formulae (log + iπ/2 for TEE; T^{2} log for complexity) with closed hypergeometric expressions, UV subtractions are standard and consistent, and Appendix A gives a local logarithmic enhancement that actually explains why Tmax peaks near θ⋆. The fixed-boundary selection is necessary once the time map becomes non-monotonic, and they implement it carefully for both observables. Citation pattern is appropriate; self-citation is limited to the geometry they use.\n\nThe soft spot is real but proportionate: the dual map itself (solve reduced (t,r) at a single θ0, then lift over physical θ, then minimize Re A or finite C at fixed T) is imported from the spatial RT prescription of [6] and from BTZ/AdS-Schwarzschild Lorentzian work. It is not derived from a CFT calculation or a first-principles 10d variational principle for these timelike regions. If that map is wrong, the reported sensitivity to the transition region does not follow. Large-r checks and Appendix A only confirm internal consistency of this particular prescription. Minor practical notes: different xE for the two observables, complexity restricted to the exterior patch, no code. None of these sink the calculation.\n\nThis is for specialists in AdS3 holography, D1-D5, and holographic complexity/entanglement who want a concrete Lorentzian diagnostic of internal-sphere localization. The math and numerics look solid on their own terms. I would send it to peer review; a referee should press on the dual-map assumption and ask for a clearer statement of what would falsify the selection rule, but the paper deserves that conversation.","headline":"Solid computational holography: first systematic Lorentzian-branch application to the black pole, with a clean geometric effect (selected saddles track the cap–horizon transition) that is internally consistent but rests on an imported dual map.","tokens_in":48769,"tokens_out":546,"would_cite":true,"duration_ms":6599,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Timelike holographic probes of a black pole feel the internal sphere's cap-horizon split, not just the asymptotic BTZ geometry.","keywords":["timelike entanglement entropy","timelike subregion complexity","localized black holes","black pole","AdS3 × S3 × T4","holographic duality","cap-horizon transition"],"falsifier":"Compute the same fixed-boundary-interval branches in the exact black pole and check whether, as the boundary interval grows, the selected turning points and angular labels still migrate toward the cap–horizon transition; if they remain asymptotic or show no angular preference, the central claim fails.","tokens_in":48511,"feed_emoji":"🕳️","tokens_out":650,"duration_ms":5591,"temperature":0.7,"pith_summary":"The paper asks whether Lorentzian holographic probes can see localization of a black-hole horizon on an internal sphere, something that ordinary BTZ geometry erases. It studies two related observables—timelike entanglement entropy (a complex lifted area) and timelike subregion complexity (a real renormalized volume)—in the black-pole solution of asymptotic AdS3\times S3\times T4. Both are built from the same spacelike-plus-timelike bulk branches. In the large-radius limit the angular dependence drops out and one recovers the familiar short-interval BTZ-like behaviour. In the exact geometry the map from bulk turning point to boundary time interval becomes non-monotonic, so one must first fix the boundary interval and only then minimize. Once that is done, larger intervals force the selected branches inward toward the angular transition between the smooth cap and the localized horizon. The claim is that these timelike probes therefore register ten-dimensional localization effects that neither pure BTZ nor the asymptotic expansion can see.","feed_headline":"Timelike probes feel a black pole's internal sphere split","feed_subtitle":"Selected bulk branches move to the cap-horizon transition that BTZ erases","key_machinery":"Localized lifting of Lorentzian branches: solve the reduced (t,r) branch problem at a single angular label θ0, then lift the area or volume by integrating the full black-pole warp factors Ky(r,θ) and G(r,θ) over the physical internal angle θ, and select the physical saddle only among branches that share the same boundary time interval.","core_discovery":"In the exact black-pole geometry, after fixed-boundary-interval selection, the selected Lorentzian branches for both timelike entanglement entropy and timelike subregion complexity move inward and become sensitive to the localized cap–horizon transition region on the internal sphere—features absent in BTZ and in the leading large-r description.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Timelike branches sense black-pole cap-horizon transition BTZ erases","Exact black poles expose sphere transition via fixed-interval branches","Selected Lorentzian probes move inward to localized cap-horizon region","Timelike EE and complexity detect sphere effects missing from BTZ","Fixed-boundary selection pulls branches into black-pole sphere structure"],"cache_read_input_tokens":32896,"weakest_assumption_plain":"The dual map is assumed to be the reduced-branch-plus-ten-dimensional-lift prescription, with the physical answer given by minimizing the real lifted area or the finite volume at fixed boundary interval.","fun_headline_variants_meta":{"raw":{"variants":["Timelike branches sense black-pole cap-horizon transition BTZ erases","Exact black poles expose sphere transition via fixed-interval branches","Selected Lorentzian probes move inward to localized cap-horizon region","Timelike EE and complexity detect sphere effects missing from BTZ","Fixed-boundary selection pulls branches into black-pole sphere structure"]},"model":"grok-4.5","effort":"low","cost_usd":0.004766,"raw_usage":{"total_tokens":1375,"prompt_tokens":775,"num_sources_used":0,"completion_tokens":90,"cost_in_usd_ticks":47660000,"prompt_tokens_details":{"text_tokens":775,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":510,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":775,"tokens_out":90,"duration_ms":4496,"temperature":1.0,"reasoning_tokens":510,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T04:10:27.317553+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Compute the same fixed-boundary-interval branches in the exact black pole and check whether, as the boundary interval grows, the selected turning points and angular labels still migrate toward the cap–horizon transition; if they remain asymptotic or show no angular preference, the central claim fails.","supporting_citations":[],"review_version":1}