{"id":"f80f43eb-eb59-4c4d-b8f8-4f3cad1b2caa","arxiv_id":"2505.13349","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Entangled holographic states below the Hawking-Page temperature stay classically connected through Euclidean spacetime regions, extending ER-EPR to cases where Lorentzian wormholes are unstable.","lead":"This short essay argues that in holographic spacetimes, entangled states whose energy is too low to form a black hole remain connected through regions with Euclidean signature, not through Lorentzian wormholes. The idea extends the ER-EPR proposal to low temperatures, where the usual Einstein-Rosen bridge is unstable.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The necessity of Euclidean regions is not proven: below the Hawking–Page temperature, small black holes still exist as two-sided Lorentzian saddles with ER bridges, so thermodynamic instability does not remove Lorentzian connectivity.","rationale":"The reader's weakest_assumption identifies exactly this step, and I agree. The central claim is interpretively appealing, but the inference from nonzero correlators to Euclidean regions depends on the premise that no Lorentzian ER bridge exists at low temperature. That premise is false if subdominant black-hole saddles are included. The suggested test distinguishes the two alternatives by checking which bulk saddle actually reproduces the quoted formula. Since this issue is already the basis of the CONDITIONAL verdict, no further adjustment is needed.","tokens_in":4612,"tokens_out":14894,"duration_ms":159785,"concrete_test":"Evaluate the two-sided scalar correlator at β>2π in the small-BTZ (or small AdS-Schwarzschild) saddle using the Skenderis–van Rees real-time AdS/CFT prescription, and compare it term-by-term with the formula displayed in Section 4. If this Lorentzian two-sided saddle already reproduces the k-sum formula, the nonzero correlator does not require Euclidean regions, and the Euclidean-region conclusion fails. If, instead, the matching requires the purely Euclidean saddle with ML→0, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central proof hinges on the claim in Section 4 that at low temperature 'the black holes are unstable' and therefore the TFD state cannot be dual to a two-sided Lorentzian black hole; nonzero two-sided correlators are then taken to force curves through Euclidean regions. This step conflates canonical-ensemble dominance with the existence of a bulk solution. The Hawking–Page transition says which Euclidean saddle dominates Z(β)=Tr e^{-βH}, not which saddles appear in the Hartle–Hawking wavefunction of the pure TFD state (4.1). Small AdS black holes exist below the transition (e.g., BTZ black holes for all β, or AdS_{d+1} Schwarzschild above its minimum temperature), and each admits the usual maximally extended two-sided Lorentzian geometry with an Einstein–Rosen bridge. Thermodynamic instability does not remove this saddle, nor the geodesics connecting the two boundaries. Thus the dichotomy of Section 3 (Lorentzian ER bridge or Euclidean region) is incomplete: the nonzero correlator can be mediated by the unstable but existing Lorentzian black hole. The displayed k-sum formula is the standard eternal-black-hole/real-time result and does not discriminate between the two mediations. Without an independent argument that the low-temperature state has no two-sided Lorentzian saddle at all, the central claim that Euclidean regions are necessary is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that in holography, entangled states whose Lorentzian Einstein-Rosen bridges are thermodynamically unstable must instead be dual to geometries containing Euclidean-signature regions. The argument uses the thermofield double state (4.1), the geodesic approximation to boundary correlators (2.1)-(2.2), and a Hartle-Hawking wavefunction decomposition M = M- ∪ ML ∪ M+ to claim that below the Hawking-Page temperature nonzero two-sided correlators force curves connecting the two boundaries to traverse Euclidean regions. The paper presents this as an extension of ER-EPR to regimes where wormholes are unstable.","tokens_in":4937,"tokens_out":4267,"duration_ms":44824,"significance":"If the central claim were correct, it would generalize ER-EPR beyond stable Lorentzian wormholes and give a phase-transition interpretation of signature change in holography. The paper draws on well-established real-time AdS/CFT tools, and the framing using geodesic probes of emergent geometry is a useful way to think about connectivity. However, the argument fails at a load-bearing point: it ignores the existence of small, thermodynamically unstable AdS black holes that are nevertheless valid two-sided Lorentzian solutions with Einstein-Rosen bridges. The quoted correlator formula is standard and does not select Euclidean mediation. The proposed scenario is interesting as a conjecture, but the paper does not establish necessity of Euclidean regions.","major_comments":[{"comment":"The dichotomy stated in Section 3, 'there are only the following two possibilities' (Lorentzian ER bridge or Euclidean region), is incomplete. Below the Hawking-Page temperature, small AdS black holes still exist as Lorentzian two-sided geometries with ER bridges; the Hawking-Page transition concerns which Euclidean saddle dominates the canonical partition function Z(β)=Tr e^{-βH}, not whether a two-sided Lorentzian solution exists. For example, BTZ black holes exist for every inverse temperature β, and higher-dimensional Schwarzschild-AdS solutions exist above a minimum temperature. These unstable black holes admit the usual maximally extended Lorentzian geometry with geodesics connecting the two boundaries. Thus the correlator (2.1) can be mediated by an unstable but existing Lorentzian bridge, and the inference that Euclidean regions are required does not follow.","section":"Section 3"},{"comment":"The key step in Section 4 is the assertion that when 'the black holes are unstable, the argument above cannot work.' This conflates canonical-ensemble dominance with the existence of a bulk saddle for the pure TFD state (4.1). The TFD state is a pure state in H1⊗H2, and its Hartle-Hawking wavefunction receives contributions from all saddles, including the two-sided Lorentzian black hole, regardless of whether that black hole dominates the thermal partition function of a single CFT. Thermodynamic instability does not delete the Lorentzian saddle, nor the geodesics that connect the two boundaries. Therefore the conclusion 'This proves our claim' is unsupported.","section":"Section 4"},{"comment":"The displayed formula for ⟨Ψβ|O(t1,φ1)O(t2,φ2)|Ψβ⟩ is quoted without derivation and does not discriminate between Lorentzian and Euclidean mediation. This formula is the standard two-sided thermal correlator for the eternal black hole; in the BTZ case its geodesic interpretation includes geodesics that pass through the Lorentzian horizon and connect the two asymptotic regions. The sum over k can be understood as a sum over image geodesics around the black hole, not necessarily as paths that must probe Euclidean regions. The claim that 'the main contribution comes from the geodesic paths that probe the Euclidean regions' is therefore not established by the formula.","section":"Section 4, displayed correlator formula"}],"minor_comments":[{"comment":"In the abstract, 'regimes whether wormholes' should read 'regimes where wormholes', and 'entangled structure of the dual state persists' repeats 'state' twice in the same sentence.","section":"Abstract"},{"comment":"The notation for the TFD state contains a rendering error: 'flflΨβfi' should be displayed as |Ψβ⟩, and the bra-ket notation in ⟨Ψβ|Ψβ⟩ uses the wrong angle-bracket glyphs.","section":"Section 4"},{"comment":"The caption says 'spacial slice' and 'entaglement'; these should be 'spatial slice' and 'entanglement'.","section":"Figure 1 caption"},{"comment":"The text refers to 'l.h.s.(1)' and 'r.h.s of this equation' where the equation is numbered (2.1); the referencing should be consistent.","section":"Section 2"},{"comment":"There is a typo 'Eclidean' in the sentence 'geometrically connected to through an Eclidean region'; it should be 'Euclidean', and the phrase 'connected to through' should be 'connected through'.","section":"Discussion"},{"comment":"Reference [12] begins with a stray bracket '] J. M. Maldacena'; this should be cleaned up.","section":"References"}],"recommendation":"reject","confidential_remarks":"This is an essay for a gravity-research prize, so the level of rigor expected is lower than for a full research paper. Nevertheless, the central logical step in Section 4 is not just under-derived; it rests on a false premise, namely that thermodynamic instability removes the two-sided Lorentzian black-hole saddle. The existence of unstable small AdS black holes is textbook material and is even implicit in the cited Hawking-Page reference. I do not see a way to repair the argument without substantially changing the claim from 'Euclidean regions are necessary' to 'Euclidean saddles contribute at low temperature', which would no longer support the paper's main thesis as stated. If the editors are willing to publish speculative essays with a weakened, conjectural framing, a major revision might be negotiable, but as it stands the manuscript's central claim is not established."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is an essay with a good nose for a real issue, but the load-bearing step is broken. The author wants to extend ER-EPR to low temperatures by claiming that once the black hole is unstable, the two-sided Lorentzian geometry is unavailable and the dual state must be connected through Euclidean regions. The problem is that Hawking-Page instability does not mean the Lorentzian saddle disappears. Small AdS black holes, including BTZ for any beta, exist below the transition temperature and carry the usual maximally extended two-sided geometry with an Einstein-Rosen bridge. Thermodynamic instability affects which saddle dominates the canonical ensemble, not which saddles exist in the path integral or in a Hartle-Hawking construction of the pure TFD state. So the Section 3 dichotomy (Lorentzian ER bridge or Euclidean region) is incomplete, and the quoted nonzero two-point function can be mediated by the unstable Lorentzian black hole. The central claim of the abstract, that Euclidean regions are necessary, is therefore unsupported as written.\n\nWhat is genuinely new is the interpretive step: connecting the known real-time AdS/CFT result that two-sided correlators get contributions from geodesics running through Euclidean caps to the ER-EPR picture, and framing signature change as a phase transition. That is a legitimate and interesting idea, and the essay is honest about the fact that the underlying technology comes from [15,16,17,18]. The prose is clear and the intent is transparent. The citation pattern is fine; the author cites the real-time literature and his own prior work where appropriate.\n\nThe soft spots beyond the main one: the correlator formula is quoted, not derived, but for an essay that is acceptable. The distinction between 'unstable' and 'nonexistent' is the real issue. If the author instead considered the genuinely black-hole-free regime (T below the minimum AdS-Schwarzschild temperature in d>2), the argument would have more room to breathe, but the current text does not isolate that regime.\n\nWho is this for? Readers interested in ER-EPR, signature change, and the real-time AdS/CFT prescription. It deserves a serious referee, but one who will insist on fixing the dichotomy. My own verdict is skeptical on the main claim unless it is revised.","headline":"A likeable essay with a broken central step: the claimed necessity of Euclidean regions rests on confusing thermodynamic instability with nonexistence of the Lorentzian saddle.","tokens_in":5374,"tokens_out":4315,"would_cite":false,"duration_ms":45311,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["04.60.-m","04.70.-s","11.25.Tq"],"model":"deepseek-v4-flash","headline":"The paper argues that entangled holographic states stay classically connected through Euclidean spacetime regions when wormhole bridges would be unstable.","keywords":["AdS/CFT correspondence","entanglement and geometry","ER-EPR conjecture","thermofield double state","Euclidean wormholes","signature change","AdS thermal phase transition","holographic two-point functions"],"falsifier":"A direct large-$N$ computation of the two-point function below the transition that keeps the unstable two-sided black hole in the path integral would settle the question: if that saddle alone gives the nonzero correlator, Euclidean regions are not required. Conversely, a full computation of the mutual information between the two boundary theories that finds it vanishing below the transition would contradict the proposed Euclidean connectivity.","tokens_in":4429,"feed_emoji":"🔗","tokens_out":9714,"duration_ms":95111,"temperature":0.7,"pith_summary":"The paper argues that in holographic duality, an entangled state of two boundary theories is always dual to a classically connected bulk spacetime, and that when a Lorentzian wormhole cannot support the connection, the bulk must contain a Euclidean-signature region. The argument starts from the bulk two-point function written as a sum over continuous curves between the two boundaries: a nonzero correlator for causally disconnected points forces such curves to exist, and if no stable two-sided black hole is available they cannot be timelike everywhere. Applied to the thermal field double state below the AdS thermal phase-transition temperature, this says the two boundaries remain connected, but by curves that pass through an Euclidean segment rather than through a wormhole throat. The proposal therefore extends the entanglement-wormhole correspondence to low-temperature regimes where wormhole bridges are unstable, treating signature change as a phase of the emergent geometry.","feed_headline":"When wormholes fail, entangled spacetimes turn Euclidean","feed_subtitle":"Holographic argument: entanglement keeps boundaries connected even where wormholes are unstable.","key_machinery":"The load-bearing object is the bulk two-point function expressed as a path sum over continuous curves, $\\langle\\Psi|O(x)O(y)|\\Psi\\rangle = \\int_{\\gamma \\subset M} [D\\gamma]\\, e^{i m l[\\gamma(x,y)]}$, which turns the existence of boundary entanglement into a statement about geometric connectivity. The second ingredient is the glued spacetime $\\mathcal{M} = \\mathcal{M}_- \\cup \\mathcal{M}_L \\cup \\mathcal{M}_+$: a Euclidean saddle, a Lorentzian middle slice, and its time reverse, glued along common surfaces. When the Lorentzian slice shrinks away, the geometry is Euclidean AdS with period $\\beta$, and this is the configuration that computes the low-temperature correlator. The sum over geodesic paths, with winding number $k$, is what exposes the Euclidean bridge: the closed form of the correlator contains terms $\\cos[(t_2-t_1)+i\\beta(k-\\tfrac12)]-\\cos(\\phi_2-\\phi_1)$, whose imaginary time separations are the signature of curves probing Euclidean regions.","core_discovery":"The central claim is that the dual of an entangled state is a classically connected geometry, and that when the entangled structure cannot be supported by a stable two-sided black hole, the connecting curves must pass through a Euclidean-signature region. Concretely, the author considers the thermal field double state $|\\Psi_\\beta\\rangle = \\sum_n e^{-\\beta E_n/2} Z^{-1/2} |E_n\\rangle_1 \\otimes |E_n\\rangle_2$ and the bulk two-point function $\\langle\\Psi_\\beta|O(t_1,\\phi_1)O(t_2,\\phi_2)|\\Psi_\\beta\\rangle$. The correlator is nonzero for boundary points on the two causally independent conformal boundaries, so by the curve-sum interpretation there must be continuous bulk paths joining them. At high temperature these paths traverse the two-sided black hole; at low temperature, where that black hole is unstable, the computation instead uses a geometry built from Euclidean saddles glued to an interpolating Lorentzian piece, $\\mathcal{M} = \\mathcal{M}_- \\cup \\mathcal{M}_L \\cup \\mathcal{M}_+$, and the connecting geodesics run through the Euclidean part. The conclusion is that the dual of the low-temperature thermal field double state contains an Euclidean region whose role is to preserve exactly the connectivity that entanglement requires.","pith_inferences":["The paper does not say so explicitly, but the same argument would predict that mutual information between the two boundaries stays nonzero at arbitrarily low temperature, since classical connectivity via Euclidean regions should maintain some amount of boundary correlation; a direct large-$N$ mutual-information calculation below the transition would test this.","An extension the author leaves implicit is that any entangled pure state with a well-defined Euclidean saddle construction, not just the thermal field double, would develop Euclidean regions whenever no stable Lorentzian horizon exists, making instanton-like geometries a generic symptom of entanglement rather than a thermal artifact.","One could probe the Euclidean bridge in the dual picture by scattering bulk probes between the two boundaries: geodesic lengths would acquire imaginary components characteristic of Euclidean traversal, showing up as phases in two-point functions at low temperature."],"forward_implications":["Below the AdS thermal phase-transition temperature, the thermal field double state still has a classically connected bulk dual; the connecting curves pass through a Euclidean region instead of a two-sided black hole.","The correspondence between entanglement and bulk connectivity acquires two geometric phases: a Lorentzian wormhole phase at high temperature and a Euclidean-bridge phase at low temperature.","Thermal correlators in the low-temperature entangled state are explicitly computable by cutting the Euclidean circle, inserting real-time intervals, and summing over winding geodesics; the shortest Euclidean path dominates.","If the Lorentzian segment shrinks completely, the construction reduces to the standard Euclidean thermal AdS, reproducing previously known thermal correlators."],"supporting_citations":[{"why":"Supplies the premise that nonzero correlators between causally disconnected boundary points imply classically connected bulk curves.","marker":"[3]"},{"why":"Provides the holographic propagator as a sum over bulk curves used as the basic connectivity criterion.","marker":"[5]"},{"why":"Extends the geodesic-propagator method to black hole backgrounds, grounding the paper's equation (2.1).","marker":"[6]"},{"why":"States the correspondence between wormholes and entangled states that the paper generalizes to low temperatures.","marker":"[7]"},{"why":"Constructs the eternal black hole dual of the thermal state and computes two-sided correlators at high temperature.","marker":"[12]"},{"why":"Establishes the thermal phase transition in AdS and the low-temperature Euclidean thermal correlators used as the baseline.","marker":"[14]"},{"why":"Gives the real-time gauge/gravity duality prescription for gluing Euclidean and Lorentzian saddles used to compute the low-temperature correlator.","marker":"[16]"}],"fun_headline_variants":["Euclidean signature preserves entanglement when wormholes fail","Spacetime flips to Euclidean to keep entanglement connected","Wormhole instability triggers signature change in holography","Entangled states need Euclidean geometry when wormholes die","Holographic dual turns Euclidean when wormholes destabilize"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that below the thermal phase-transition temperature the two-sided black hole stops being the correct bulk description of the entangled thermal state; if that unstable black hole still contributes to the actual quantum state, the Lorentzian wormhole connection might survive without any Euclidean region.","fun_headline_variants_meta":{"raw":{"variants":["Euclidean signature preserves entanglement when wormholes fail","Spacetime flips to Euclidean to keep entanglement connected","Wormhole instability triggers signature change in holography","Entangled states need Euclidean geometry when wormholes die","Holographic dual turns Euclidean when wormholes destabilize"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000546,"raw_usage":{"total_tokens":2572,"prompt_tokens":868,"completion_tokens":1704,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":484,"completion_tokens_details":{"reasoning_tokens":1625}},"tokens_in":484,"tokens_out":1704,"duration_ms":13557,"temperature":1.0,"reasoning_tokens":1625,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:14:34.507607+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct large-$N$ computation of the two-point function below the transition that keeps the unstable two-sided black hole in the path integral would settle the question: if that saddle alone gives the nonzero correlator, Euclidean regions are not required. Conversely, a full computation of the mutual information between the two boundary theories that finds it vanishing below the transition would contradict the proposed Euclidean connectivity.","supporting_citations":[{"cited_title":"Balasubramanian, S","cited_arxiv_id":null,"evidence_quote":"Provides the holographic propagator as a sum over bulk curves used as the basic connectivity criterion."}],"review_version":1}