{"id":"d66b080c-0433-485c-a628-5b265264eae8","arxiv_id":"2607.19904","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"In rotating Simpson-Visser black holes, repeated Penrose extraction can terminate because the evolving mass/spin leaves the two-horizon regime before the spin limit is reached, an effect controlled by the regularization parameter ξ.","lead":"This paper studies repeated Penrose energy extraction from rotating Simpson-Visser black holes—a regularized version of Kerr spacetime. It finds that for large values of the regularization parameter, the iterative process stops not because the black hole runs out of spin, but because the evolving parameters leave the two-horizon branch of the spacetime.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Termination criterion (17) is never evaluated in full: Tables 2–3 track only âmin,0,n, so the claimed geometry-induced termination may be an artifact of using the wrong spin limit.","rationale":"The reader identified the fixed-ξ assumption as the weakest point, and that is certainly a physical caveat: if ξ evolves under back-reaction, the two-horizon boundary moves and the geometry-induced termination could change or disappear. However, the paper explicitly frames the result as conditional on fixed ξ, so that concern alone does not invalidate the internal logic. A more immediate and checkable threat is that the numerical work does not appear to implement the paper’s own dynamical termination criterion, Eq. (17): the tables only list âmin,0,n. Since the central claim is that geometry terminates the process before the spin limit is reached, the comparison must use the true maximum of the three thresholds. If the omitted thresholds alter the termination step, the representative examples no longer demonstrate the claimed competition. This is an internal consistency issue, not a matter of physical interpretation, and it can be settled by directly computing the missing thresholds. I therefore do not change the reader’s CONDITIONAL verdict, but I would attach a condition that the full max criterion be verified. The fixed-ξ concern remains relevant, hence partial agreement.","tokens_in":22617,"tokens_out":10828,"duration_ms":124985,"concrete_test":"Compute âmin,i for i=1,2 from Eq. (16) at the decay radii r̂=1.2 and r̂=1.5 using the representative parameters (Ê0=1, p̂φ1=−19.434, ν=0.78345, μ0=10⁻²M0, M0=1) for the ξ0 values in Tables 2 and 3, and form max_i âmin,i at each iteration. Then re-run the termination check with Eq. (17). If max_i âmin,i = âmin,0 throughout, the red rows are valid; if not, the dynamic-termination row shifts earlier, and the claimed structural-termination cases (ξ0=0.55 and 0.88 at r̂=1.5) may actually terminate by the spin limit before crossing the two-horizon boundary.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim compares two termination mechanisms: the conventional dynamical spin limit and the geometry-induced boundary crossing. But the paper’s own dynamical limit, Eq. (17), is defined as max(âmin,0, âmin,1, âmin,2), with each âmin,i obtained from the marginal-stability condition (16). In the numerical tables, however, only the column âmin,0,n is reported; no âmin,1,n or âmin,2,n is given or even mentioned in the results. For the decisive cases — ξ0=0.55 at r̂=1.5 and ξ0=0.88 at r̂=1.5 — the blue/structural rows are identified precisely by checking that ân remains above the tabulated âmin,0,n. If the omitted thresholds âmin,1 or âmin,2 are larger than âmin,0 at those iterations, the kinematic spin limit would have been reached earlier, and the sequence would terminate dynamically rather than geometrically. The paper’s fixed-ξ assumption (§4) is a separate physical caveat and is acknowledged, but this threshold omission is an internal correctness issue: the stated termination criterion is not actually implemented in the reported numerics. The central claim therefore rests on an unverified assumption that âmin,0 is the maximum of the three thresholds for the representative parameter set.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the repetitive Penrose process (RPP) in the rotating Simpson–Visser (RSV) spacetime, assuming a fixed regularization parameter ξ while the black-hole mass M and angular momentum L evolve through successive capture of negative-energy fragments. Using the triple turning-point idealization, the authors iterate the RPP and identify two termination mechanisms: the conventional dynamical spin threshold and a new \"geometry-induced\" termination that occurs when the evolving solution leaves the two-horizon branch of the RSV parameter space. Numerical tables and figures quantify extracted energy, irreducible mass, EROI, and EUE for different ξ and decay radii, and the paper concludes that for sufficiently large ξ the geometry-induced mechanism dominates.","tokens_in":22999,"tokens_out":6055,"duration_ms":65432,"significance":"If the central claim is correct, the paper adds a conceptually new ingredient to the RPP literature: not only does the spacetime geometry modify the efficiency of energy extraction, but the very existence of additional geometric parameters can terminate the iterative sequence before the kinematic spin limit is reached. This is a clean, falsifiable extension of the RPP framework to a well-motivated regular black-hole family. The manuscript is transparent about its main assumption (fixed ξ), and the reported tables are internally consistent, e.g., ζ_n = E_extracted/(n E0). The main concern is that the paper's own stated termination criterion, Eq. (17), is not actually implemented in the reported numerics, which undercuts the central comparison between the two termination mechanisms.","major_comments":[{"comment":"The stated termination criterion is â_n < max(â_min,0, â_min,1, â_min,2), with each â_min,i obtained from Eq. (16). However, the numerical tables report only â_min,0,n. For the decisive cases — e.g., Table 2, ξ0=0.55 at r̂=1.5, where the structural termination is claimed at n=23 (â=0.930063, â_min,0=0.923448) — the conclusion that the spin limit has not yet been reached depends on â_min,0 being the largest of the three thresholds. If either â_min,1 or â_min,2 exceeds ~0.93 at that iteration, the sequence would already have terminated dynamically. The paper must either tabulate â_min,1,n and â_min,2,n for the representative parameter sets, or prove analytically that â_min,0 is always the maximum. Without this, the central claim that the termination is geometry-induced rather than dynamical is not established.","section":"§2.3, Eq. (17); Tables 2–3"},{"comment":"The structural termination condition is computed by holding ξ fixed while M decreases, so ξ̂=ξ/M increases during the evolution. The paper explicitly states this assumption, but it is load-bearing: the entire mechanism relies on the two-horizon boundary being fixed in ξ while the dynamical parameters move. No physical mechanism or conservation law is given for why the regularization parameter — sourced, according to the paper's own summary, by phantom scalar and nonlinear-electrodynamics fields — is insensitive to the absorption of negative-energy particles. If ξ varied with the back-reaction, the structural termination could be delayed, advanced, or absent. I recommend the authors add a discussion of the plausibility of this assumption, or test robustness by letting ξ evolve according to a simple model.","section":"§4, fixed-ξ assumption"},{"comment":"Fig. 1 and the surrounding text describe the termination regimes using the single threshold â_min,0, while Eq. (17) requires the maximum over three thresholds. This inconsistency is not merely notational: the phase diagram in Fig. 1 classifies the endpoint as dynamical or structural based on the â_min,0 criterion. If the maximum of the three thresholds is the actual dynamic bound, the boundary in Fig. 1 could shift. Please align the figure, the tables, and the text with the full criterion, or revise Eq. (17) if â_min,0 is intended as the operative bound.","section":"§4 and Fig. 1"}],"minor_comments":[{"comment":"The EROI is defined as ζ_n in Eq. (14), but the caption of Fig. 5 labels it \"ξnf\", which conflicts with the regularization parameter ξ. Please use ζ_{n_f} or a similar symbol.","section":"Fig. 5 caption"},{"comment":"The red/blue row coloring used to mark kinematic versus structural termination is not visible in the extracted manuscript. Please add explicit markers (e.g., bold, asterisks, or a separate column) so the termination row is unambiguous.","section":"Tables 2–3"},{"comment":"The text sometimes refers to \"the minimum-spin condition (â < â_min)\" without specifying which particle index; this is inconsistent with Eq. (17). Please standardize the notation.","section":"§4 text"},{"comment":"The appendix contains a one-sentence discussion of Table 3, but Table 3 is presented in the main body. Either move the table to the appendix or expand the discussion in the main text.","section":"Appendix / Table 3 placement"}],"recommendation":"major_revision","confidential_remarks":"The paper's central claim is potentially interesting but currently rests on an incomplete implementation of the termination criterion. The missing thresholds â_min,1 and â_min,2 are straightforward to compute with the same code, so the issue is fixable within the manuscript's scope. I would be willing to look at a revised version once this is addressed; no other fatal issues were identified."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the idea: keep ξ fixed while M and a evolve, and the RPP can leave the two-horizon branch before the usual spin limit. That structural termination is not in the cited literature, and it's a natural extension of the RPP program to a regular black hole spacetime. The authors are also honest about what the result is and isn't — they call it a limit of validity, not a fundamental end, and they state the fixed-ξ assumption explicitly. The algebra follows the established Ruffini framework and the tables are internally consistent; ζ_n = E_extracted/(nE0) checks out.\n\nThe soft spot is serious. The termination criterion in Eq. (17) is the max of three thresholds, â_min,0, â_min,1, â_min,2, but the tables only report â_min,0. For the blue rows that are supposed to show geometry-induced termination, the comparison is made against â_min,0 alone. If either of the other two thresholds is larger at those iterations, the sequence would have terminated dynamically earlier, and the central claim would be wrong for those parameters. This is not a cosmetic omission; the stated criterion is not the implemented one. The authors need to either report all three thresholds or prove that â_min,0 dominates for their parameter set.\n\nSecondary concerns are milder. The fixed-ξ assumption is physically unmotivated — no mechanism is given for why the regularizing matter is insensitive to absorbed negative-energy particles — and the paper acknowledges this but does not discuss how a varying ξ would shift the boundary. Also, the numerical work uses a single representative parameter set, so the transition at ξ ≈ 0.44 and the hierarchy of terminations are only demonstrated for that set. A scan over E0, pφ1, ν would show whether the mechanism is generic.\n\nBottom line: this is a paper for people working on repetitive Penrose processes in non-Kerr spacetimes. The idea is worth taking seriously, and the authors' own caution about scope is a good sign. But the missing thresholds are a load-bearing gap, and the claim about geometry-induced termination is not yet established by the reported numerics. I would send it to peer review — it deserves referee time — and the referees should insist on the full max criterion and ideally a wider parameter scan.","headline":"New mechanism, incomplete numerical support: the branch-crossing endpoint in RSV is plausible but the tables don't implement the paper's own termination criterion.","tokens_in":23445,"tokens_out":2871,"would_cite":true,"duration_ms":36090,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","83C15"],"pacs":["04.70.-s","04.70.Bw"],"model":"deepseek-v4-flash","headline":"The endpoint of the repetitive Penrose process in rotating Simpson–Visser black holes is governed by a competition: for large enough regularization, the evolving solution leaves the two-horizon black-hole branch before the minimum-spin limi","keywords":["repetitive Penrose process","Simpson-Visser spacetime","regular black holes","energy extraction","black bounce","minimum spin condition","irreducible mass","rotating black holes"],"falsifier":"Re-run the iterative sequence while allowing ξ to vary with the absorbed negative-energy particles (e.g., tied to M or a by a conservation law); if the evolving solution then stays within the two-horizon branch beyond the iterations reported here, the structural termination is an artifact of the fixed-ξ assumption. Alternatively, a direct check: at ξ0=0.55 and r̂=1.5, verify that the post-iteration pair (M, a) crosses M − sqrt(M^2 − a^2) while â still exceeds âmin.","tokens_in":22543,"feed_emoji":"🕳️","tokens_out":3557,"duration_ms":32972,"temperature":0.7,"pith_summary":"This paper argues that in the rotating Simpson–Visser geometry — a family that interpolates between Kerr black holes, black-bounce objects, and traversable wormholes via a regularization parameter ξ — the repeated Penrose process does not always terminate because the black hole spins down to the conventional kinematic limit. When ξ is large, the cumulative change in mass and angular momentum pushes the solution across the boundary of the two-horizon black-hole branch, so the iterative sequence ends because the assumed geometry no longer exists, not because energy extraction has been exhausted. The authors frame this as a 'geometry-induced termination' that competes with the familiar dynamical spin-threshold termination, and they trace how the number of admissible iterations, the extracted energy, and two efficiency measures all drop as ξ grows. A sympathetic reader would care because it shows the spacetime structure itself — not just particle kinematics — can set the ceiling on idealized rotational energy extraction.","feed_headline":"Regular black holes stop Penrose extraction before spin runs out","feed_subtitle":"Repeated absorption pushes the spacetime off its two-horizon branch, a geometry-induced cutoff that Kerr does not have.","key_machinery":"The rotating Simpson–Visser metric and its regularization parameter ξ: the geometry replaces r by sqrt(r^2 + ξ^2), and its two-horizon branch exists only for 0 ≤ ξ < M − sqrt(M^2 − a^2). Because ξ is held fixed while M and a are updated at each Penrose event (using the triple turning-point solution of the mass, angular-momentum, and radial-momentum conservation equations), the admissible parameter domain itself moves, letting the evolving solution cross the branch boundary before the kinematic spin limit is reached.","core_discovery":"The central claim is that, assuming the regularization parameter ξ stays fixed while the black hole mass M and spin a evolve, the endpoint of the repeated Penrose process in the rotating Simpson–Visser spacetime is set by whichever comes first: the minimum-spin threshold at which negative-energy orbits cease to exist, or the boundary at which the spacetime leaves the two-horizon regular black-hole branch. The paper shows numerically (Tables 2–3, Fig. 1) that for ξ ≳ 0.44–0.55 the structural boundary is crossed first, so the process halts even though the black hole still has extractable rotational energy; near ξ ≈ 0.9 even a single Penrose event pushes the solution off the branch.","pith_inferences":["If ξ is allowed to vary under back-reaction rather than staying fixed, the structural termination could be delayed, advanced, or replaced by a transition to the wormhole branch, so a natural extension is to couple ξ to M or a through a conservation law and re-run the sequence.","The same 'moving parameter domain' mechanism should appear in any regular black-hole family whose admissible branch depends on the pairing of evolving dynamical parameters and a fixed extra parameter — e.g., charged or de Sitter versions — making geometry-induced termination plausibly generic.","Observationally, the sharp cutoff of the iterative sequence implies that regular black holes with large ξ would show systematically lower radiative efficiency from Penrose-type extraction than Kerr, a feature that could be compared against thin-disk efficiency predictions which the paper notes are unchanged at ISCO.","The stopping point marks the limit of the two-horizon description, not of the physical spacetime; describing what happens next would require re-formulating the process on the single-horizon or wormhole branch, which the paper explicitly leaves open."],"forward_implications":["For small ξ the R-S-V evolution is qualitatively Kerr-like, but above a ξ-dependent threshold the termination is structural rather than kinematic.","The number of admissible Penrose iterations falls sharply with ξ; near the upper edge of the two-horizon regime a single decay suffices to exit the branch.","Cumulative extracted energy, final irreducible-mass growth, EROI, and EUE are all suppressed as ξ grows, largely because the sequence is cut short.","The decay radius matters: near-horizon decays give the most favorable extraction, and the optimal radius shifts inward as ξ increases.","A single Penrose event may be enough to push the spacetime out of the two-horizon branch, so the framework itself defines its own validity limit."],"fun_headline_variants":["Geometry, not spin, ends Penrose extraction","When black hole geometry halts Penrose process early","Spin limit not the only brake on Penrose process","Geometry can choke Penrose energy theft before spin runs dry"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The regularization parameter ξ is assumed to stay fixed while the black hole's mass and spin evolve under repeated particle absorption; if ξ shifts with back-reaction, the geometry-induced termination could be delayed, advanced, or absent.","fun_headline_variants_meta":{"raw":{"variants":["Geometry, not spin, ends Penrose extraction","When black hole geometry halts Penrose process early","Spin limit not the only brake on Penrose process","Geometry can choke Penrose energy theft before spin runs dry"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000122,"raw_usage":{"total_tokens":972,"prompt_tokens":824,"completion_tokens":148,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":568,"completion_tokens_details":{"reasoning_tokens":85}},"tokens_in":568,"tokens_out":148,"duration_ms":2351,"temperature":1.0,"reasoning_tokens":85,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T11:22:56.147632+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the iterative sequence while allowing ξ to vary with the absorbed negative-energy particles (e.g., tied to M or a by a conservation law); if the evolving solution then stays within the two-horizon branch beyond the iterations reported here, the structural termination is an artifact of the fixed-ξ assumption. Alternatively, a direct check: at ξ0=0.55 and r̂=1.5, verify that the post-iteration pair (M, a) crosses M − sqrt(M^2 − a^2) while â still exceeds âmin.","supporting_citations":[],"review_version":1}