{"id":"fbcde75b-ecfc-4f12-ad73-ada74e452773","arxiv_id":"2601.22077","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Exact CFT states for colliding particles that form evaporating AdS black holes are constructed, and several coarse-graining maps are shown to convert the exact pure state into mixed semiclassical Hawking radiation with partial success.","lead":"This paper asks how a perfectly reversible quantum description of a black hole can look irreversible when an observer ignores fine details of the theory. It builds explicit particle-collision states in holographic field theory and tests which averaging procedures reproduce the mixed Hawking radiation of semiclassical gravity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Small-black-hole coarse-graining rests on an unproven extrapolation of OPE-coefficient statistics (Eq. 4.17) from Δ→∞ to the c^{1/4}–c^{2/3} regime; if the variance/delta structure fails, the claimed purity e^{-S} does not follow.","rationale":"The reader's weakest-assumption identification matches my own: the small-black-hole coarse-graining argument depends on Eq. (4.17), which the authors themselves flag as an unproven extrapolation from the Δ→∞ limit. This is not a manufactured concern; it is the precise step that converts an unknown UV statistics into the e^{-S} purity of Eq. (4.20), and without that step the central claim that coarse-graining reproduces semiclassical black hole mixedness in the evaporating regime has no quantitative support. I found no internal inconsistency or obvious error in the cleaner parts of the paper: the wavepacket construction in Sec. 2.2, the spin-dimension decomposition, and the comparison of coarse-graining prescriptions in Sec. 4 are careful and explicit about their approximations. The paper also earns credit for stating the limitation directly rather than burying it. The maximum-entropy map of Sec. 4.5.1 satisfies all listed properties but is admitted to be circular, which further justifies a conditional rather than unconditional verdict. I therefore agree with CONDITIONAL and recommend no change to the reader's verdict. A direct computation of OPE statistics in the relevant dimension window, or an analytic control of subleading corrections to Eq. (2.53), would be the decisive missing check.","tokens_in":56153,"tokens_out":6363,"duration_ms":72378,"concrete_test":"Using a 2d holographic CFT with known or numerically computable heavy OPE data—e.g. the D1-D5 symmetric-orbifold point at finite c, or a random-CFT ensemble with the same light spectrum—compute C_{ϕϕa} for all primaries a with Δ_a in [c^{1/4}, c^{2/3}] within a window of width δ, and measure the empirical variance ⟨C_{ϕϕa}^2⟩, the covariances ⟨C_{ϕϕa}C_{ϕϕb}⟩ for a≠b, and the first non-Gaussian cumulant. Compare with f(Δ_a)/e^{S(Δ_a)} and with zero. If the off-diagonal covariance is not exponentially small or the variance deviates from f/e^S by more than e^{-S}, Eq. (4.17) fails and the coarse-grained purity (4.20) is unsupported. Alternatively, repeat the crossing-symmetry derivation of (2.53) retaining subleading 1/Δ corrections and check whether they dominate the e^{-S} term when Δ∼c^{2/3}.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (4.17) is the quantitative bridge between coarse-graining and semiclassical black hole purity: it asserts c_{ϕϕa}c_{ϕϕb} ≈ f(Δ_a,Δ_ϕ)δ_{ab}/e^{S(Δ_a)}. Averaging ρ_H over this gives the diagonal density matrix (4.18) and purity e^{-S} (4.20), which is the paper's match to a small evaporating AdS black hole. But the paper states explicitly (after Eq. 4.17 and around Eq. 2.53) that this form is proven only in the Δ→∞ limit and is an unproven extrapolation for Δ in the small unstable black hole range, e.g. c^{1/4}≪Δ_a≪c^{2/3} for AdS3×S3. The load-bearing content is not the smooth prefactor f but the δ_{ab}/e^{S} structure: the variance must be exponentially suppressed in the microcanonical entropy, and different operators' coefficients must be statistically uncorrelated. If, at these intermediate dimensions, off-diagonal correlations survive or the variance is not f/e^S, the averaged ρ_H is not maximally mixed in the window and the claimed semiclassical purity fails. The same pattern appears in Sec. 3.2, where h_BH(r)>h_gas(r) is assumed for all r based only on small- and large-r limits; that is secondary for the coarse-graining claim but would also need checking for the detection claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a Lorentzian AdS/CFT framework for a bathless formulation of the black hole information problem. In §2 it constructs exact CFT states (2.22) from smeared boundary operator insertions, expands them in the spin-dimension basis, and computes the wavefunction coefficients (2.44) that are claimed to describe two bulk particles colliding to form a small, unstable AdS black hole that later evaporates. In §3 it argues that boundary two-point functions distinguish black-hole states from thermal-gas states of the same ADM mass, using the geodesic approximation and a hierarchy of emblackening factors. In §4 the paper analyzes several coarse-graining maps—averaging over OPE coefficients, Hamiltonian eigenstates, energy levels, time windows, and density-matrix ensembles—and compares the resulting purities with semiclassical bulk expectations. A toy model for small evaporating black holes with a sectorized Hilbert space is developed in §4.8 and Appendix A. The central thesis is that the mixedness of the semiclassical bulk state can arise from ensemble-averaging the exact, always-unitary boundary dynamics.","tokens_in":56710,"tokens_out":6369,"duration_ms":73293,"significance":"If the results hold, this is a useful step toward connecting ensemble-averaged holography with the single-sided information problem, and it provides an explicit, tractable family of CFT states dual to black hole formation. The calculation of the wavefunction coefficients in §2.2 is clean, the geodesic inequality in §3.1 is valid under the stated staticity assumption, the comparison table in §4.7 is a genuinely useful organizing device, and the toy model in Appendix A comes with reproducible numerics. The authors are unusually transparent: they flag several steps as conjectural or as extrapolations beyond their proven range. That transparency is a strength, but it also exposes where the central claims are not yet established. In particular, the small-black-hole coarse-graining analysis—the part of the paper most relevant to the reverse information problem—rests on an OPE-statistics extrapolation that the authors themselves label unproven. The significance is therefore conditional: the framework is plausible and worth publishing only after the load-bearing assumptions are either proved, replaced, or explicitly downgraded.","major_comments":[{"comment":"The quantitative bridge between coarse-graining and semiclassical black-hole purity is Eq. (4.17), c_ϕϕa c_ϕϕb = f(Δa,Δϕ)δ_ab/e^{S(Δa)}. The text explicitly states that this form is proven only in the Δ→∞ limit and that using it for dimensions in the small unstable black-hole range (e.g. c^{1/4} ≪ Δ ≪ c^{2/3} for AdS3×S3) is an unproven extrapolation. This is not a minor technicality: the δ_ab/e^S structure is what makes the averaged ρ_H diagonal and its purity e^{-S}. If off-diagonal correlations survive or the variance is not exponentially suppressed in S at these intermediate dimensions, the claimed match with the semiclassical purity of an evaporating small black hole fails. The toy model in Appendix A uses Haar/GUE averaging rather than OPE-coefficient statistics and does not independently justify Eq. (4.17). This concern directly affects the paper's main claim about the small-black","section":"§4.1, Eq. (4.17) and §4.8"},{"comment":"The detection hierarchy for localised ten-dimensional black holes depends on the assumption h_BH(r) > h_gas(r) for all r. The paper checks only the asymptotic regimes r≪1 and r≫1 and then states 'let us assume that it holds for all r.' The geodesic length integral samples the full range of r, so an intermediate-r crossing would change the inequality between the two-point functions. In addition, the effective mass function m_BH(r) for the localised black hole at the antipodal point of the internal sphere is put in by hand rather than derived from the known localized geometry. Without either a proof or numerical verification over the full radial range, the claimed hierarchy of two-point functions (thermal gas > localised black hole > delocalised black hole) is not established. This is load-bearing for the detection claim in §3.","section":"§3.2, Eqs. (3.24)–(3.25)"},{"comment":"The maximum-entropy coarse-graining map is presented in Table 1 as satisfying all the listed properties, but the text immediately admits that the map is guaranteed to reproduce a desired density matrix or entropy curve only if that desired output is inserted as a constraint. This is circular as a constructive proposal: it does not predict the semiclassical coarse-graining, it encodes it. The table's 'Yes' entries for this row should be read as 'possible in principle, given the right input', not as an established matching between a natural boundary prescription and the bulk semiclassical state. Since this is the only map that passes all columns, the summary conclusion that a single coarse-graining can reconcile unitarity with mixed Hawking radiation is weaker than the table suggests.","section":"§4.5.1 and Table 1"},{"comment":"The replica-wormhole rescue argument is carried out by analogy with the authors' earlier random-dynamics model [87], not by a computation in the OPE-coefficient-averaged CFT state considered here. The diagrammatic discussion of ρ^n and Wick contractions is suggestive, but no replica calculation is shown for the OPE-averaging prescription, and the role of the e^{-S}-suppressed non-Gaussian corrections is only discussed qualitatively. As the authors note, such corrections can be leading order after summing over e^S states, so the claim that replica wormholes restore unitarity for the present coarse-graining maps is not demonstrated. This is secondary to the main purity comparison, but it should be flagged because the paper presents it as a resolution mechanism.","section":"§4.6"}],"minor_comments":[{"comment":"There are several typos: 'not necessariliy' in the first line, 'thermodynamicallyunstable' near Eq. (2.3), and 'funtions' in §3.2. These are harmless but should be corrected.","section":"§2.1"},{"comment":"The bipartition H = H_L ⊕ H_H is introduced as a heuristic with a tolerance parameter, and the paper acknowledges this. However, the tolerance parameter is never made precise, and the later coarse-graining results in §4.1 assume that the separation is sharp. A short discussion of how the results depend on the tolerance would help the reader assess robustness.","section":"§2.3 and §4.1"},{"comment":"The sentence 'In the previous section, it was found that f_gas ≥ f_BH for all r' is confusing: the inequality was derived in the introductory paragraph of §3, not in the previous numbered subsection. Adjusting the cross-reference would improve readability.","section":"§3.1"},{"comment":"The time-window averaging entropy curve discussion is brief and the plot is not shown. Since the subsection introduces two inequivalent time-averaging maps, a small figure comparing their purities would help the reader track the difference between them.","section":"§4.4"}],"recommendation":"major_revision","confidential_remarks":"This is a serious and well-written paper with several clean results, but the advertised small-black-hole information-problem claim rests on explicitly unproven extrapolations, especially Eq. (4.17). The paper is honest about this, but honesty does not remove the need for the claim to be supported. I recommend major revision: either prove the OPE-statistics extrapolation in the relevant range, present a different statistical model with justification, or clearly reposition the paper as a conditional framework whose main quantitative matching is for large black holes, with the small-black-hole regime as a conjectural extension. The geodesic detection claim in §3.2 also needs more than an assumed inequality over the full radial range. The toy numerics and the §2.2 construction are valuable and should be retained."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is worth a serious look. It constructs exact CFT states dual to two-particle collisions in AdS, computes the wavefunction coefficients explicitly, and then compares several coarse-graining prescriptions against semiclassical expectations. The central claim—that coarse-graining exact unitary dynamics can reproduce the mixedness of the semiclassical description—is plausible, and the paper is honest about what it does not prove.\n\nWhat is actually new: the explicit collisional state (2.22) with coefficients (2.44), the Lorentzian comparison of OPE/Hamiltonian/time-window coarse-grainings, and the two-point-function hierarchy proposal for localised black holes. The §2.2 calculation is clean: the smearing kernels and OPE expansion give a concrete state peaked at the CoM energy. The geodesic comparison in §3.1 is solid under the stated staticity assumption; f_gas ≥ f_BH implies longer boundary-anchored geodesics for the black hole. The summary table in §4.7 is genuinely useful.\n\nThe main soft spot is Eq. (4.17). The purity e^{-S} for small evaporating black holes follows from assuming the HLL OPE coefficient variance is δ_ab/e^S in the intermediate dimension range. That is proven only as Δ→∞, and the extrapolation to c^{1/4}–c^{2/3} is explicitly unproven. The authors flag it, but it makes the headline match between coarse-grained and semiclassical purity conditional. Similarly, the 10d two-point hierarchy assumes h_BH(r)>h_gas(r) for all r, checked only at small and large r. And the one coarse-graining map that satisfies all their criteria is admitted to be circular—it feeds in the desired output. None of this sinks the paper; it means the framework is a proposal with clean local calculations, not a closed argument. Also, the replica-wormhole rescue leans on their own [87]; that is a fine pointer, but not independent evidence.\n\nThe paper is for people working on AdS/CFT, quantum chaos, and the information problem. It does not resolve the paradox, but it gives a concrete sandbox and a fair comparison of ideas. It deserves a serious referee. I would send it out, expecting the authors to either justify the extrapolation or weaken the claim to a conjecture.","headline":"Useful framework paper: exact collisional states and a systematic comparison of coarse-grainings; the evaporating-BH purity claim is conditional on an extrapolation the authors flag.","tokens_in":57065,"tokens_out":3693,"would_cite":true,"duration_ms":38954,"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":"This paper claims that semiclassical black hole evaporation can be reproduced by coarse-graining the exact unitary dynamics of a pure CFT state, and constructs explicit states, probes, and averaging schemes toward that end.","keywords":["AdS/CFT","black hole information paradox","Hawking radiation","coarse-graining","ensemble averaging","OPE coefficients","small AdS black holes","two-point functions"],"falsifier":"Measure the actual variance of heavy-light-light OPE coefficients in a specific holographic CFT at dimensions in the small black hole window (c^{1/4} ≪ Δ ≪ c^{2/3}); if c_{φφa}c_{φφb} deviates from δ_{ab} f/e^{S(Δ_a)}, or if the coarse-grained purity of the colliding-particle state does not drop to e^{-S}, the central coarse-graining claim for evaporating black holes is refuted.","tokens_in":56048,"feed_emoji":"🕳️","tokens_out":8343,"duration_ms":77113,"temperature":0.7,"pith_summary":"This paper argues that the mixed-state Hawking radiation seen by a semiclassical observer is not a failure of unitarity but a coarse-grained version of an exactly pure CFT state. The authors construct explicit boundary states that describe two particles colliding in AdS to form a small, unstable black hole that later evaporates. They show that boundary two-point functions can distinguish such black holes from thermal gas of the same mass. They then compare several coarse-graining prescriptions—averaging over OPE coefficients, Hamiltonians, and time windows—and find that each reproduces some, but not all, features of the semiclassical bulk state; only a maximum-entropy ensemble matched all tested properties. The central quantitative link is a statistical formula for heavy-light-light OPE coefficients that turns the pure state into a maximally mixed state of purity e^{-S} in the black hole energy window.","feed_headline":"Coarse-graining pure CFT states yields black hole evaporation","feed_subtitle":"The exact state stays pure; averaging over unknown data produces the mixed Hawking radiation a bulk observer sees.","key_machinery":"The central objects are the smeared boundary operators Φ_{ω,e} that create localised bulk wavepackets, so |ψ(0)⟩ = N^{-1}:Φ_{ω,e_S}Φ_{ω,e_N}:|0⟩ is an exact, pure CFT state dual to a zero-impact-parameter collision. Expanded in the spin-dimension eigenbasis, its wavefunction coefficients are Gaussian-peaked at dimension 2ω with zero spin. The argument is carried by three coarse-graining mechanisms: OPE-coefficient averaging, whose key statistical identity c_{φφa}c_{φφb}=f(Δ_a,Δ_φ)δ_{ab}/e^{S(Δ_a)} makes the averaged state diagonal with purity e^{-S}; Hamiltonian-ensemble averaging, whose purity follows the spectral form factor; and the microcanonical decomposition H = ⊕_n H_BH^{(E-n)} ⊗ H_ra","core_discovery":"The paper's central claim is that mixed-state Hawking radiation is a coarse-grained image of an exactly pure CFT state, not a violation of unitarity. It constructs a state |ψ(0)⟩ = N^{-1}:ΦΦ:|0⟩ from smeared boundary operators whose evolution is dual to a trans-Planckian particle collision; at suitable ω this forms a small unstable AdS black hole that later evaporates. Coarse-graining maps—averages over OPE coefficients, Hamiltonians, and time windows—turn the pure state into a density matrix with purity 1 below the black hole threshold and e^{-S} in the black hole window; a refined toy model gives decreasing purity during evaporation.","pith_inferences":["This suggests a general dictionary: any low-energy observer's ignorance of heavy CFT data defines a specific CPTP map on the exact state, so the semiclassical bulk state is observer-dependent in a precise, calculable way.","A testable extension is to compute the variance of heavy-light-light OPE coefficients at finite Δ in a solvable large-c CFT; if the e^{-S} scaling fails in the small-black-hole window, the evaporating-black-hole purity prediction fails with it.","The two-point-function hierarchy, shown in a free matrix model, could be checked in the same strongly coupled gauge theory at finite N; agreement would tie partial deconfinement to the bulk geodesic calculation."],"forward_implications":["The exact state (2.22) is a concrete, tunable CFT representation of black hole formation: its overlaps pick out conformal dimension 2ω and zero spin, so kinematics of the bulk collision are encoded in the wavefunction coefficients (2.44).","Boundary two-point functions of simple operators can serve as a black-hole detector in the microcanonical ensemble: for fixed mass, black hole geometries give smaller two-point functions than thermal gas, with localised (and then delocalised) black holes intermediate.","Coarse-graining over OPE coefficients yields purity 1 below the black-hole threshold and e^{-S} inside it; averaging over Hamiltonian rotations gives an O(1) mixing time but a much later maximal-mixing time, so different prescriptions match the bulk only partially.","A maximum-entropy ensemble of density matrices is the only surveyed prescription that satisfies all the listed properties; the paper is explicit that this prescription works only if the desired output is fed in as input.","For small, evaporating black holes, the refined toy model predicts that coarse-grained purity falls as the black hole emits Hawking quanta, while pure radiation states remain pure—a signature that coarse-graining, not tracing out a bath, is the right notion of information loss."],"fun_headline_variants":["Coarse-Graining Pure States Mimics Black Hole Evaporation","Hawking Radiation: Coarse-Grained Image of Pure CFT","Reverse Information Problem: Unitarity via Coarse-Graining","Mixed Radiation Emerges from Coarse-Graining Pure CFT","Black Hole Information: Coarse-Graining Saves Unitarity"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the OPE-coefficient statistics c_{φφa}c_{φφb}=δ_{ab}f/e^{S(Δ_a)}, proven only at infinite conformal dimension, continue to hold for the small-black-hole dimensions (c^{1/4}≪Δ≪c^{2/3}); if that extrapolation fails, the predicted coarse-grained purity e^{-S} for an evaporating black hole does not follow.","fun_headline_variants_meta":{"raw":{"variants":["Coarse-Graining Pure States Mimics Black Hole Evaporation","Hawking Radiation: Coarse-Grained Image of Pure CFT","Reverse Information Problem: Unitarity via Coarse-Graining","Mixed Radiation Emerges from Coarse-Graining Pure CFT","Black Hole Information: Coarse-Graining Saves Unitarity"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000929,"raw_usage":{"total_tokens":3782,"prompt_tokens":680,"completion_tokens":3102,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":424,"completion_tokens_details":{"reasoning_tokens":3014}},"tokens_in":424,"tokens_out":3102,"duration_ms":20435,"temperature":1.0,"reasoning_tokens":3014,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T06:43:28.535033+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the actual variance of heavy-light-light OPE coefficients in a specific holographic CFT at dimensions in the small black hole window (c^{1/4} ≪ Δ ≪ c^{2/3}); if c_{φφa}c_{φφb} deviates from δ_{ab} f/e^{S(Δ_a)}, or if the coarse-grained purity of the colliding-particle state does not drop to e^{-S}, the central coarse-graining claim for evaporating black holes is refuted.","supporting_citations":[],"review_version":1}