{"id":"bd143681-43f2-4d42-a427-17f35d66290a","arxiv_id":"2607.06677","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"Direct waves in filtered Schwarzschild ringdown are the anti-causal filter-pole contribution sourced by near-horizon trajectory dynamics and do not vanish.","lead":"This paper derives the 'direct wave' seen in black-hole ringdown from the causal structure of the filtered Green's function in Schwarzschild spacetime. It shows the signal is a real, non-vanishing near-horizon effect, giving a first-principles basis for using it as a probe of horizon dynamics in gravitational-wave data.","discovery_kind":"first_principles","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper's strongest claim is cleanly supported by the causal decomposition (Sec. II, Eq. 12) and by the explicit numerical match of the anti-causal integral (Eq. 15) to the filtered waveform (Fig. 3). The vanishing-arc step is the most delicate analytic ingredient, but it is not unique to this work and is corroborated by the same residual that already quantifies how completely the anti-causal piece accounts for the signal. The discussion correctly limits the scope to linear Schwarzschild and sketches the path to Kerr/NR without overclaiming. No further load-bearing flaw that would move the verdict away from ACCEPT was found; the concrete arc check is a useful verification rather than a expected failure mode.","tokens_in":11246,"tokens_out":499,"duration_ms":11257,"concrete_test":"Independently recompute the filtered Green's function integral (Eq. 6) for a representative source radius and retarded-time window by direct numerical quadrature along a large semicircle in the LHP/UHP (or by high-frequency asymptotic estimates of the integrand) and verify that the arc contribution is smaller than the ~0.1% residual already reported in Fig. 3; if it is not, re-evaluate whether the isolation of Eq. 15 remains clean.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the filtered direct wave is the anti-causal contribution (Eq. 15) of the filtered Green's function and does not vanish. The reader's weakest assumption (vanishing large-arc contributions, dotted contours in Fig. 1) is load-bearing for the contour decomposition, but it is inherited from the same prior analyses [57–61] that already underpin the prompt-response calculation [61] and is standard for these retarded Green's functions. The paper's own numerical evidence (Fig. 3) independently shows that the anti-causal integral alone reproduces the filtered Zerilli waveform to ~0.1% residual for the ISCO plunge (and is stated to hold for eccentric plunges), so even a residual arc contribution would have to be tiny to affect the claim. No internal inconsistency or untested regime that would reverse the non-vanishing result is apparent within the stated linear Schwarzschild + point-particle setting.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper derives a first-principles foundation for the 'direct wave' component of black-hole ringdown in Schwarzschild spacetime. Starting from the sourced Zerilli equation, the authors apply a rational filter that removes a prescribed set of QNMs and analyze the causal structure of the filtered Green's function via contour deformations in the complex frequency plane. They obtain a three-window decomposition (anti-causal, prompt, and tail; Eq. 12) and show that the filtered waveform for plunging point particles is dominated by the anti-causal contribution (Eq. 15), which is sourced by the near-horizon trajectory segment. For an ISCO plunge, this piece alone reproduces the filtered Zerilli waveform to ~0.1% residual (Fig. 3). An integration-by-parts reduction recovers the instantaneous frequency ω_G of Oshita et al., while clarifying that the direct wave is an accumulated anti-causal effect rather than a light-cone contribution subject to the cancellation argued in Kuntz et al. Horizon-mode contributions from individual filter poles cancel collectively, so the signal is controlled by near-horizon source dynamics.","tokens_in":11452,"tokens_out":895,"duration_ms":11089,"significance":"If correct, the result places the direct-wave interpretation of filtered NR and GW250114 waveforms on a firm theoretical footing within linear Schwarzschild perturbation theory, and cleanly separates it from both ordinary QNMs and the vanishing light-cone modes of Ref. [56]. Strengths include a transparent contour analysis that reuses standard Green's-function machinery, an explicit integral formula (Eq. 15) that can be checked independently, a high-precision numerical match for the ISCO plunge, and a controlled phase-rescaling test (Fig. 5) that links the signal to near-horizon orbital motion. The work is complementary to QNM spectroscopy and supplies a concrete bridge from filtered waveforms to horizon-proximate source dynamics.","major_comments":[],"minor_comments":[{"comment":"The vanishing of the large-arc contributions (dotted contours in Fig. 1) is load-bearing for isolating the anti-causal piece. A short appendix or paragraph summarizing the estimates from Refs. [57–61] (or a brief self-contained argument for the filtered case) would make the paper more self-contained.","section":null},{"comment":"Section III states that the anti-causal dominance holds for eccentric plunges, but only the ISCO case is shown. A single additional panel or a brief quantitative residual for one eccentric trajectory would strengthen the claim.","section":null},{"comment":"In the reduction from Eq. (17) to (18)–(19), the dropped higher-order corrections are mentioned only in a footnote. A short estimate of their size near the horizon would clarify the domain of validity of ω_G.","section":null},{"comment":"Figure 4 shows individual anti-causal poles decaying as e^{-κ u} while their sum does not; a sentence quantifying the degree of cancellation (e.g., relative residual at late u) would help the reader.","section":null},{"comment":"Notation: the same symbol R is used for the particle trajectory and for homogeneous radial solutions (R_in, R_up, R_down). Distinct symbols would reduce occasional ambiguity in Sec. III.","section":null},{"comment":"The discussion of the NR/close-limit interpretation (Sec. IV) is suggestive but qualitative. Framing it more clearly as an outlook rather than a derived claim would avoid over-reading the linear point-particle results.","section":null}],"recommendation":"accept","confidential_remarks":"The manuscript is short, technically clean, and directly addresses a timely controversy (Oshita et al. vs. Kuntz et al.). I see no load-bearing error within the stated linear Schwarzschild + point-particle setting. The main limitation is scope (Schwarzschild only; NR connection is interpretive), which the authors already flag; that is appropriate for a foundations paper and does not warrant major revision. Fit for a letters-style or short-article venue in gr-qc is good."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This paper does the job it claims: it supplies the missing causal Green’s-function foundation for the “direct wave” that Oshita et al. and Lu et al. saw after rational filtering. The new piece is the three-window decomposition of the filtered Green’s function (Eq. 12) and the explicit anti-causal integral (Eq. 15) that samples the near-horizon trajectory segment. For an ISCO plunge the anti-causal piece alone reproduces the filtered Zerilli waveform to ~0.1% residual (Fig. 3); prompt + tail are negligible. That is the result that settles the non-vanishing question against the Kuntz et al. cancellation argument for light-cone/horizon modes.\n\nWhat works well is the bookkeeping. Contour deformations, filter poles, and the reduction to the instantaneous frequency ω_G recover the earlier heuristic without pretending it was rigorous. The phase-rescaling test (Fig. 5) cleanly shows the signal tracks near-horizon source motion. Citations are appropriate; the authors’ own prior filter and Green’s-function papers are used as machinery, not as a circular substitute for the new identification. The discussion correctly limits the claim to linear Schwarzschild + point particles and sketches the Kerr/NR path without over-selling.\n\nSoft spots are real but secondary. The vanishing of the large arcs is inherited from the same prior contour analyses that already support the prompt-response calculation; the numerical match in Fig. 3 makes a residual arc contribution hard to hide. No code is released, and the model is still linear point-particle, so the jump to comparable-mass NR remains interpretive. Neither undercuts the central claim inside the stated setting.\n\nThis is for people who already care about ringdown spectroscopy, rational filters, or near-horizon signatures. It is not a broad-audience paper, but it is the right theoretical foundation for the residual cycles already seen in NR and candidate events. I would send it to peer review without hesitation; a serious referee will tighten the arc discussion and the Kerr outlook, not reverse the non-vanishing result. Worth reading and, for anyone working on filtered ringdown, worth citing.","headline":"Clean first-principles derivation that the direct wave is the non-vanishing anti-causal filter-pole integral, not a light-cone artifact, and it matches the filtered waveform to ~0.1%.","tokens_in":12052,"tokens_out":537,"would_cite":true,"duration_ms":6206,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Direct waves in black-hole ringdown come from the anti-causal near-horizon source, not from light-cone or horizon modes, and do not vanish in Schwarzschild.","keywords":["black-hole ringdown","direct waves","Green's function","quasinormal modes","rational filters","Schwarzschild","near-horizon dynamics","Zerilli equation"],"falsifier":"Compute the same rationally filtered Zerilli waveform for a plunging particle and check whether the anti-causal integral alone still matches the full filtered signal to ~0.1 percent, or whether the residual grows once the large-arc assumption is relaxed or the contour is evaluated differently.","tokens_in":12146,"feed_emoji":"🕳️","tokens_out":887,"duration_ms":9452,"temperature":0.7,"pith_summary":"After a black-hole merger, the ringdown signal is usually described by quasinormal modes, but filtered waveforms still show several decaying oscillatory cycles near the strain peak, called direct waves. Earlier work linked those cycles to source motion near the horizon, yet lacked a first-principles derivation, and a recent argument suggested they might vanish in Schwarzschild. This paper derives them from the causal structure of the filtered Green's function for the Zerilli equation. It shows that the filter introduces an anti-causal piece sourced by the trajectory segment that has already plunged toward the future horizon; that piece alone reproduces the filtered waveform for plunging particles to about 0.1 percent residual, while prompt response and tail contribute negligibly. The resulting signal is controlled by the near-horizon orbital phase and radial infall, not by a pure horizon mode or an instantaneous light-cone contribution. The result supplies a theoretical basis for reading near-horizon dynamics out of filtered ringdown, complementary to spectroscopy of quasinormal modes.","feed_headline":"Direct waves track near-horizon plunge, not horizon modes","feed_subtitle":"Anti-causal Green's function piece alone matches filtered Schwarzschild ringdown to 0.1%","key_machinery":"Causal decomposition of the filtered Green's function into anti-causal (upper-half-plane filter poles for u < -r*), prompt, and tail windows; the anti-causal integral (Eq. 15) over the near-horizon segment is what produces the direct wave.","core_discovery":"The direct wave does not vanish in Schwarzschild spacetime. It is exactly the anti-causal contribution of the rationally filtered Green's function, an integral over the near-horizon trajectory segment of the source, and that contribution alone accounts for the filtered Zerilli waveform of plunging particles; its instantaneous frequency and decay are set by the source's near-horizon phase and radial velocity.","pith_inferences":["If the anti-causal construction survives in Kerr, filtered NR ringdowns of real mergers could be used to constrain near-horizon plunge kinematics without relying on an effective-one-body picture.","Collective cancellation of individual horizon-mode poles may be a general feature of unit-modulus rational filters, so similar rearrangements could appear whenever QNMs are filtered from other linear wave equations.","The same contour split might isolate prompt-response and tail pieces cleanly enough to test whether nonlinearities after common-horizon formation still leave a clean anti-causal imprint."],"forward_implications":["Direct waves remain available as a probe of near-horizon source dynamics even in non-spinning black holes.","They should not be modeled as pure horizon modes; their frequency and decay track the plunge trajectory.","The same anti-causal mechanism can be extended to Kerr and to residual post-merger distortions treated as effective sources on a remnant black hole.","Horizon signatures enter the observable only gradually through source redshift and frame-dragging, not as isolated horizon-mode rings."],"fun_headline_variants":["Direct waves arise from near-horizon source dynamics in Schwarzschild","Anti-causal Green's function alone yields the direct wave in ringdown","Direct wave tracks near-horizon plunge trajectory, not QNMs","Non-vanishing direct waves probe horizon-source dynamics via Green's function","Filtered Schwarzschild ringdown matches anti-causal near-horizon integral"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The large-arc pieces of the complex-frequency contours vanish, so the filtered waveform is fully determined by the anti-causal poles, the small arc, and the branch cuts.","fun_headline_variants_meta":{"raw":{"variants":["Direct waves arise from near-horizon source dynamics in Schwarzschild","Anti-causal Green's function alone yields the direct wave in ringdown","Direct wave tracks near-horizon plunge trajectory, not QNMs","Non-vanishing direct waves probe horizon-source dynamics via Green's function","Filtered Schwarzschild ringdown matches anti-causal near-horizon integral"]},"model":"grok-4.5","effort":"low","cost_usd":0.006524,"raw_usage":{"total_tokens":1586,"prompt_tokens":652,"num_sources_used":0,"completion_tokens":93,"cost_in_usd_ticks":65240000,"prompt_tokens_details":{"text_tokens":652,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":841,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":652,"tokens_out":93,"duration_ms":14442,"temperature":1.0,"reasoning_tokens":841,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T23:33:53.601432+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Compute the same rationally filtered Zerilli waveform for a plunging particle and check whether the anti-causal integral alone still matches the full filtered signal to ~0.1 percent, or whether the residual grows once the large-arc assumption is relaxed or the contour is evaluated differently.","supporting_citations":[],"review_version":1}