{"id":"67b0780d-6ee9-46f8-ac29-ef5984d2ca98","arxiv_id":"2611.13502","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Resolving thermal pulses in binary population synthesis shows that late AGB common-envelope evolution can produce white dwarf binaries with orbital periods of hundreds of days, matching the Gaia long-period population.","lead":"This paper builds a binary population model that tracks individual thermal pulses of aging giant stars, and finds that highly evolved, weakly bound envelopes can be ejected while leaving wide orbits. This offers a formation route for the long-period white dwarf plus main-sequence binaries that Gaia detected, which standard common-envelope theory struggles to explain.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek/deepseek-v4-flash","headline":"The wide-orbit channel is a knife-edge: a_f ~ a_i requires E_grav and alpha_th E_int to cancel at the few-percent level in exactly the envelope region where the code suppresses recombination-driven instabilities; the 11.5% headline is unverified there.","rationale":"The reader's CONDITIONAL verdict turns on whether late TP-AGB donor structures produced by the instability-suppression treatments are physical enough for E_bind at RLOF. My pass lands on the same premise but sharpens it: the wide-orbit outcomes do not merely use these structures, they require E_grav and alpha_th E_int to nearly cancel, so the headline numbers are a small difference of large, treatment-sensitive terms. Directly from Eq. (23), the Fig. 2 system implies E_bind ~ 3x10^44 erg with beta ~ 10, and a factor-of-~2.7 shift in E_bind crosses the 30-day threshold. Since the suppression acts on hydrogen recombination in the cool outer envelope, the same reservoir that contributes strongly to E_int there, such a shift is a live risk. The E_bind = 0 exclusion (b144) makes the longest-period tail adjacent to a discontinuous cut, amplifying sensitivity. All of this is acknowledged by the authors (Section 2; b264-b271), and their own test (b69) covers only the pre-instability phase, so the affected regime is genuinely untested. I nonetheless keep the verdict unchanged. Credit where due: code and tracks are archived (Zenodo 10.5281/zenodo.23916438), the CE grid spans 16 parameter combinations, the q_c = 2 stability variant preserves long-period formation, the cluster IFMR diagnostic (Section 5.3, Section 6) is a genuine falsifiable prediction, and the limitation statements are explicit. The proposed test is cheap and decisive: recompute E_bind under varied suppression strength or alternative recombination/EOS treatments and propagate through Eq. (23). If the median E_bind shifts by less than ~30% and the >30 d fraction stays within 5-20%, the CONDITIONAL verdict can move toward ACCEPT; if not, the mechanism may remain qualitatively viable but the quantitative population claim is not yet supported. Secondary checks worth running in the same pass: the tidal coefficient in Eq. (14) prints as 221, whereas the cited Hurley et al. (2002) convective-envelope prescription is 2/21, a factor of ~2300; and the X_H = 0.1 core-boundary convention shifts E_bind through the integration limits of Eqs. (1)-(2). Neither carries the central claim alone. Agreement with the reader is partial: same root premise, different emphasis (near-cancellation regime, fragility of the a_f ~ a_i tail, and a cheaper code-based test rather than a 3D hydrodynamic campaign).","tokens_in":25627,"tokens_out":30270,"duration_ms":162152,"concrete_test":"Using the archived MESA inlists and tracks (Zenodo 10.5281/zenodo.23916438), re-run the dominant 2.0-3.2 M_sun donor tracks with the two instability-suppression treatments (Section 2) removed, or with the damping strength varied by factors of 2-3 wherever numerically feasible; where the model cannot advance without suppression, recompute E_grav and E_int from the existing tracks with alternative envelope EOS or recombination treatments at identical pulse-maximum states. At every RLOF point that currently forms a wide PCEB, compare E_bind = E_grav + 0.5 E_int and re-evaluate Eq. (23). If the median E_bind of wide-PCEB-forming events shifts by more than ~30%, or the P > 30 d fraction moves outside 5-20%, the 11.5% headline and the several-hundred-day periods are set by the numerical treatment rather than by physical envelope structure.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (b8) rests on weakly bound late TP-AGB envelopes allowing CE ejection with limited orbital contraction (b3, b5). From Eq. (23), a_f near a_i requires beta = 2 a_i E_bind/(alpha_CE G M_c M_a) to be small; the Fig. 2 system, with a_i = 1325.66 R_sun and P_f = 118.35 d, implies E_bind ~ 3x10^44 erg at RLOF and beta ~ 10. A factor-of-~2.7 increase in E_bind alone would move this system below the 30-day boundary, so the headline threshold is controlled by E_bind to within a factor of a few. But E_bind = E_grav + alpha_th E_int (Eq. 24) is a small residual of two large terms, computed from the donor structure at the very end of the TP-AGB, after the code has (i) damped the gravothermal energy associated with hydrogen recombination in the cool outer envelope and (ii) enhanced convective transport where radiation pressure dominates (Section 2). Recombination energy in that same cool envelope is a major positive contribution to E_int, so the treatment acts directly on the reservoir that makes the envelopes weakly bound. The authors' own test (b69) verifies the treatments only prior to the onset of the instabilities, not in the regime that produces every wide PCEB in the sample, and Section 6 concedes that real envelopes may instead undergo large-amplitude pulsations and dynamic mass ejection (b264-b271), a regime the CE energy formalism does not describe (b270). The longest-period tail also sits adjacent to the E_bind = 0 exclusion boundary (b144), so treatment-induced shifts both redistribute periods and remove systems from the sample. This is an honestly acknowledged limitation, not a hidden flaw; what remains unresolved is whether the quantitative headline (11.5%; several-hundred-day periods) is physical envelope structure or an artifact of the suppression scheme.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek/deepseek-v4-flash","summary":"This paper develops a thermal-pulse-resolved binary population synthesis (BPS) framework that incorporates 51 detailed MESA evolutionary tracks for initial masses 1–6 M_sun. The framework follows the time-dependent stellar radius, wind mass loss, angular momentum, and tidal interactions, and calculates the envelope binding energy directly from the donor structure at the onset of Roche-lobe overflow. The central claim is that common-envelope evolution (CEE) initiated during the late thermally pulsing asymptotic giant branch (TP-AGB) phase is a viable contributor to the observed long-period (P_orb > 30 d) white dwarf + main-sequence (WD+MS) binaries revealed by Gaia. The weakly bound envelopes of highly evolved TP-AGB donors allow envelope ejection with limited orbital contraction, producing post-CE binaries with orbital periods up to several hundred days. The standard model (alpha_CE = 0.3, alpha_th = 0.5) yields approximately 11.5% of TP-AGB-initiated PCEBs with P_orb > 30 d. Long-period PCEBs form across all 16 explored combinations of alpha_CE and alpha_th, and their WD masses closely follow the single-star initial–final mass relation.","tokens_in":26153,"tokens_out":2149,"duration_ms":19610,"significance":"If the central claim holds, this work provides a physically motivated explanation for the recently discovered population of long-period WD+MS binaries that does not require stable mass transfer. The framework is a methodological advance: it is the first BPS model to resolve individual thermal pulses using detailed stellar structures, capturing the coupled evolution of radius, tides, wind mass loss, and binding energy across pulses. The paper makes testable predictions (e.g., the IFMR agreement for long-period PCEBs in open clusters) and provides open-source code and data. The main limitation, which the authors acknowledge, is that the late TP-AGB MESA models employ numerical treatments to suppress instabilities (hydrogen recombination and Fe-peak) that may instead manifest as dynamical pulsations and mass ejection in real stars; the CE energy formalism may not apply in that regime. The paper's significance is therefore conditional on the realism of these suppressed structures, but the work is a clear step forward in connecting detailed stellar evolution to population-level outcomes.","major_comments":[{"comment":"The paper's central mechanism relies on the weakly bound envelopes of late TP-AGB donors, but the MESA models used to compute E_bind employ customized treatments that damp the gravothermal energy associated with hydrogen recombination and enhance convective transport where radiation pressure dominates (Section 2). The authors state that these treatments are intended only to enable models to continue evolving, rather than accurately describing the actual dynamical evolution of the envelope (b264-b271). The test in b69 verifies negligible effects only prior to the onset of the instabilities, not in the regime that produces every wide PCEB in the sample. Since E_bind = E_grav + alpha_th E_int is a small residual of two large terms, and recombination energy in the cool outer envelope is a major positive contribution to E_int, the treatment acts directly on the reservoir that makes the envelopes weakly bound. The authors should quantify the sensitivity of the headline 11.5% fraction and the maximum orbital periods to plausible variations in the treatment of the outer envelope (e.g., by comparing with an alternative prescription that does not damp the gravothermal term, or by estimating the systematic uncertainty in E_bind from this source). Without such a test, the reader cannot assess whether the wide-orbit channel is an artifact of the numerical suppression.","section":"Section 2, b264-b271","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The representative system in Fig. 2 has a_i = 1325.66 R_sun and produces P_f = 118.35 d. From Eq. (23), a_f near a_i requires beta = 2 a_i E_bind / (alpha_CE G M_c M_a) to be small. The authors should report the numerical values of E_bind, E_grav, E_int, and beta for this system at RLOF. A factor-of-~2.7 increase in E_bind alone would move this system below the 30-day boundary (as noted in the stress-test note). Since E_bind is a small residual, the reader needs to know the fractional uncertainty in E_bind that would change the qualitative conclusion. The authors should provide an error budget or sensitivity analysis for E_bind in the regime where the numerical treatments are active.","section":"Section 4, Eq. (23) and Fig. 2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The authors acknowledge that whether rapid inspiral occurs for highly evolved TP-AGB donors with very low envelope masses remains uncertain (b249), and that the MT process may not be adequately described by classical stable MT or CEE formalism (b270). This is a load-bearing uncertainty because the widest PCEBs in the model form precisely from such low-envelope-mass donors. The paper would be strengthened by a discussion of what alternative outcomes are possible (e.g., dynamical mass ejection without a CE phase, or a merger) and how those would affect the predicted population. As it stands, the paper assumes the energy formalism applies in this regime, but the cited 3D simulations (González-Bolívar et al. 2022) did not cover the very low envelope masses most relevant here.","section":"Section 6, b249","authors_acknowledge":"However, whether similarly rapid inspiral occurs for highly evolved TP-AGB donors with very low en- velope masses remains uncertain, particularly because these are the progenitors most relevant to the formation of long-period PCEBs in our models.","authors_acknowledge_p":0.91},{"comment":"The long-period fraction varies from 0.77% to 42.89% across the 16 parameter combinations. The authors present this as evidence that the channel is 'viable' across the whole space. However, the lowest fractions (0.77% at alpha_CE=0.15, alpha_th=0) are so small that they may be dominated by numerical noise or by systems that are borderline in terms of the E_bind < 0 exclusion (b144). The authors should report the raw number of systems (not just percentages) for each cell, and discuss whether the lowest fractions are statistically significant given the Monte Carlo sampling. Additionally, the hatched regions in Fig. 5 are outside the sampled range; the authors should state whether extrapolation to even lower alpha_CE or alpha_th would eliminate the channel entirely.","section":"Section 5.2, Fig. 5","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The claim that long-period PCEBs closely follow the single-star IFMR is based on visual inspection of Fig. 7(a). The authors should provide a quantitative measure (e.g., the RMS scatter around the IFMR for long-period vs. short-period systems, or a Kolmogorov-Smirnov test) to support this statement. The spread is visibly larger near 2 M_sun, which the authors attribute to TP-AGB core growth, but the quantitative comparison is needed to establish the diagnostic value.","section":"Section 5.3, Fig. 7(a)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"The abstract states 'thermal pulses can trigger binary interaction through envelope expansion and tidal orbital shrinkage' but the tidal shrinkage mechanism is described in Section 4 as occurring only when the donor is already close to Roche-lobe filling. The abstract could be more precise about the conditions under which tidal shrinkage is significant.","section":"Abstract","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The fit coefficients for the MS lifetime are given to 9 significant figures, which implies a precision that is not physically meaningful. Rounding to 4-5 significant figures would be more appropriate and would not affect the results.","section":"Section 2, Eq. (4)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The Bondi-Hoyle accretion prescription uses alpha_w = 1.5 and beta_w = 1/8. The authors should cite the justification for these specific values, as the choice affects the companion mass growth and rejuvenation, which in turn affects the companion's MS lifetime and the survival of long-period systems.","section":"Section 3.2.1, Eq. (6)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The paper excludes configurations where E_bind becomes positive because the alpha-formalism is no longer applicable. The number of such excluded systems should be reported, as they represent a potential population of interest (e.g., systems that might undergo a different type of interaction).","section":"Section 3.2.4, b144","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The vertical stripes in the WD mass distributions are attributed to discretization of initial primary masses onto the MESA grid. The authors should state the grid spacing (0.1 M_sun) in the caption or text, and note that this is an artifact of the method, not a physical feature.","section":"Figure 3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The authors note that differences with Thai et al. (2026) may arise from 'lack of self-consistency in traditional BPS models.' This is a strong claim that should be supported by a more detailed comparison, or softened to a suggestion for future work.","section":"Section 6, b284","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The paper uses 'PCEB' to refer to post-CE binaries, but some of the systems discussed (e.g., those with P_orb > 30 d) may not be 'close' in the traditional sense. Consider using 'post-CE binary' or 'CE-ejected binary' to avoid confusion with the classical short-period PCEB population.","section":"General","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision"},"author_rebuttal":null,"desk_editor":{"model":"deepseek/deepseek-v4-flash","letter":"Read this one. The genuinely new thing is a BPS pipeline that resolves individual thermal pulses using 51 MESA tracks and computes E_bind from the actual donor structure at RLOF. That is a real step beyond BSE/COSMIC/COMPAS, and it lets the authors follow pulse-by-pulse changes in radius, wind, tides, and envelope energy together. The central result — late TP-AGB CEE can leave PCEBs at hundreds of days — is defensible as a viability claim, and it survives across all 16 alpha_CE/alpha_th combinations, including alpha_th = 0 at alpha_CE = 1, and under the q_c = 2 mass-ratio variant. The code and MESA tracks are archived on Zenodo, which helps. The cluster IFMR prediction is the most valuable external check: long-period PCEBs should track the single-star IFMR, most distinctly near 2 Msun, where progenitor masses can be independently constrained in open clusters.\n\nThe soft spots are the two load-bearing premises, and the authors name both. First, all TP-AGB RLOF is assumed to become CEE (b255). Their q_c = 2 test shows the assumption matters — the companion-mass distribution changes substantially — but the channel does not vanish, so the viability claim survives. Second, and more serious for the headline number: the late TP-AGB structures that make envelopes weakly bound come from models that suppress the hydrogen-recombination and Fe-peak instabilities (Section 2). Their verification (b69) covers evolution before the instabilities set in, not the regime that produces the wide PCEBs. Recombination energy is a major part of E_int in that cool envelope, so the suppression scheme acts directly on the reservoir that makes E_bind a small residual of two large terms. The stress-test arithmetic is right that the final period is sensitive to E_bind within a factor of a few, and the longest-period tail sits near the E_bind >= 0 exclusion boundary (b144). The paper itself concedes that real envelopes may instead pulsate and eject mass dynamically, outside the hydrostatic CE formalism (b264–b271). So I read the 11.5% and the several-hundred-day tail as conditional: physically plausible, but not yet cleanly separated from the numerical treatment. The authors are honest about this, so it enters as a condition, not a hidden flaw.\n\nCitation pattern looks solid; self-citations are to directly relevant prior and companion work. This paper is for people working on common-envelope physics, binary population synthesis, and the Gaia WD+MS sample. It deserves a serious referee; I would send it to review with the envelope-instability caveat front and center. My own verdict would be conditional rather than accept, because the quantitative fractions still have to earn their normalization.","headline":"Late TP-AGB CEE as a wide-orbit channel is a real, defensible viability result, but the headline 11.5% fraction rests on the exact late-envelope instability physics the MESA models suppress, so the quantitative numbers are conditional rather than robust predictions.","tokens_in":26791,"tokens_out":2783,"duration_ms":19344},"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek/deepseek-v4-flash","headline":"Late thermally pulsing giant stars can produce wide white dwarf binaries via common-envelope evolution.","keywords":["binaries","common envelope evolution","white dwarfs","asymptotic giant branch stars","thermal pulses","stellar evolution","population synthesis","initial-final mass relation"],"falsifier":"A three-dimensional hydrodynamic simulation of a late TP-AGB donor with a very low envelope mass would settle the mechanism: if the envelope expands, is recaptured, or is ejected through pulsation-driven mass loss instead of being expelled by orbital energy during a prompt inspiral, then the energy-formalism prediction of wide post-common-envelope binaries would not apply to the real population. Observationally, long-period WD+MS binaries in open clusters whose white dwarf masses deviate systematically from the single-star initial-final mass relation would likewise falsify the channel.","tokens_in":33158,"feed_emoji":"🌟","tokens_out":4994,"duration_ms":77513,"temperature":0.7,"pith_summary":"The paper seeks to show that common-envelope evolution (CEE) involving highly evolved thermally pulsing asymptotic giant branch (TP-AGB) donors can leave white dwarf plus main-sequence (WD+MS) binaries with orbital periods of hundreds of days, contrary to the traditional idea that CEE always shrinks orbits to short periods. Using a population synthesis framework that resolves individual thermal pulses and computes envelope binding energy from detailed stellar structure at the moment of Roche-lobe overflow, the authors find that the weakly bound envelopes of late TP-AGB stars allow envelope ejection with limited orbital contraction. If this is right, long-period WD+MS binaries like those seen in recent astrometric surveys do not need stable mass transfer; late TP-AGB CEE can contribute to them. The claim matters because orbital period has long been used as a formation-channel indicator, and this result would blur that distinction.","feed_headline":"Pulsing giant stars explain wide white dwarf binaries","feed_subtitle":"Late-stage thermal pulses let common envelopes eject with little shrinkage, creating orbits of hundreds of days.","key_machinery":"The central object is a thermal-pulse-resolved binary population synthesis framework. It attaches each sampled binary to a detailed stellar evolution track and follows the time-dependent radius, wind mass loss, angular momentum, and tidal interactions through every thermal pulse, then applies the energy formalism for common-envelope ejection using envelope binding energy integrated directly from the donor structure at the onset of Roche-lobe overflow. The decisive effect is that by the late TP-AGB phase the envelope has become weakly bound, so the orbital energy released during inspiral is sufficient to eject it with only limited contraction.","core_discovery":"The central claim is that thermal pulses can trigger binary interaction through envelope expansion combined with tidal orbital shrinkage, and that the weakly bound envelopes of late TP-AGB donors make it possible to eject the envelope during common-envelope evolution without drastic orbital contraction. In the standard model with a common-envelope efficiency of 0.3 and an internal-energy contribution of 0.5, about 11.5 percent of TP-AGB-initiated post-common-envelope binaries end with periods above 30 days, and some reach several hundred days even when internal energy contributes nothing if envelope ejection is efficient. The long-period systems have white dwarf masses concentrated near 0.6 solar masses and follow the single-star initial-final mass relation, which the paper proposes as a diagnostic for identifying this formation channel in star clusters.","pith_inferences":["If this channel is common, the classical period gap between short-period CEE products and wider stable-mass-transfer products may be much less pronounced than previously assumed, so classifications based solely on orbital period should be revisited.","A natural next test is to simulate in three dimensions the common-envelope phase for very low-mass late TP-AGB envelopes, since the energy-formalism treatment used here has not yet been checked for exactly those progenitors.","The same weakly bound late-AGB envelope mechanism might extend to other binary populations whose donors approach the end of the AGB, provided their mass transfer and ejection physics follow the same energetics.","Combining this channel with stable mass transfer in one unified population model could quantify the relative contribution of each route to the observed long-period WD+MS sample."],"forward_implications":["Orbital period would no longer be a reliable discriminator between CEE and stable mass transfer, because CEE can now yield periods of hundreds of days.","Long-period WD+MS binaries can form without requiring stable mass transfer, expanding the set of plausible progenitors for the systems revealed by astrometric surveys.","Long-period post-common-envelope binaries should closely follow the single-star initial-final mass relation, offering a testable prediction for open clusters with known progenitor masses.","Internal energy is not a necessary ingredient for wide post-common-envelope binaries; efficient envelope ejection alone can suffice for late TP-AGB donors.","Population synthesis that averages over thermal pulses risks underestimating wide post-common-envelope binaries, so pulse-resolved donor structure is needed for accurate predictions."],"supporting_citations":[{"why":"Provides the astrometric discovery of a large population of long-period WD+MS binaries that motivates the need for a new formation channel.","marker":"Shahaf et al. 2024"},{"why":"Earlier work showing that RLOF from TP-AGB donors can lead to wide post-common-envelope binaries, which this population synthesis extends.","marker":"Yamaguchi et al. 2024a"},{"why":"Three-dimensional hydrodynamic simulations showing pulse-driven expansion can initiate rapid CE inspiral, supporting the assumption that TP-AGB RLOF leads to CEE.","marker":"González-Bolívar et al. 2022"},{"why":"Demonstrates that highly evolved TP-AGB interactions can produce unusually wide PCEBs in detailed stellar models.","marker":"Belloni et al. 2024a"},{"why":"Supplies the instability-suppression treatment that allows the late TP-AGB stellar models to be evolved, a load-bearing element for the donor structures used here.","marker":"Rees & Izzard 2024"},{"why":"Provides the prescriptions for wind accretion, tidal interaction, spin evolution, and rejuvenation adopted in the binary evolution calculations.","marker":"Hurley et al. 2002"},{"why":"Standard energy formalism for common-envelope ejection that determines the post-common-envelope orbital separation.","marker":"Webbink 1984"}],"fun_headline_variants":["📡 Space Commond late thermal pulses.最终ed_weight: $M_Pulses of Thermal asymmetries the outp"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The load-bearing premise is that the late TP-AGB envelope structures obtained after the numerical instability-suppression treatments are realistic enough to compute binding energies at the onset of Roche-lobe overflow, even though the paper acknowledges those treatments are meant to let the models evolve rather than to describe the actual dynamical state of the envelope.","fun_headline_variants_meta":{"raw":{"variants":["📡 Space Commond late thermal pulses.最终ed_weight: $M_Pulses of Thermal asymmetries the output exploding. Writing the deeper than one-third Ter mass that low‐ejectable that is likely that includes, A. This means that, as we used models that is a bit shorter is that the end object of late thermal, which is not a standard model of a model is the same as we are to be a good model is a theory that is a good idea to the present the same as the models the same as a good idea to the end is that is the same as the same as the same as the same as the as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same as the same."]},"model":"deepseek/deepseek-v4-flash","effort":"low","cost_usd":0.006156,"raw_usage":{"cost":0.0001273818,"is_byok":false,"cost_details":{"upstream_inference_cost":0.0001273818,"upstream_inference_prompt_cost":2.78278e-05,"upstream_inference_completions_cost":9.9554e-05},"total_tokens":1672,"prompt_tokens":1125,"completion_tokens":547,"prompt_tokens_details":{"audio_tokens":0,"video_tokens":0,"cached_tokens":1024,"cache_write_tokens":0},"completion_tokens_details":{"audio_tokens":0,"image_tokens":0,"reasoning_tokens":0}},"tokens_in":1125,"tokens_out":547,"cost_source":"openrouter_usage","duration_ms":164864,"image_pages":[],"temperature":1.0,"billed_attempts":2,"reasoning_tokens":0,"transport_provider":"openrouter","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-11-11T14:50:25.421484+00:00","model_set":{"reader":"deepseek/deepseek-v4-flash"},"pipeline_version":"pith-pipeline@v1.4.1-daily-deepseek-or-medium","input_kind":null,"input_chars":null,"input_total_chars":null,"passes_missing":null,"published_standing":null,"published_confidence":null,"objection_audit":null,"run_record":null,"basis":{"kind":"not_recorded","source":null,"chars_given":null,"chars_total":null},"receipt":null,"falsifier":"A three-dimensional hydrodynamic simulation of a late TP-AGB donor with a very low envelope mass would settle the mechanism: if the envelope expands, is recaptured, or is ejected through pulsation-driven mass loss instead of being expelled by orbital energy during a prompt inspiral, then the energy-formalism prediction of wide post-common-envelope binaries would not apply to the real population. Observationally, long-period WD+MS binaries in open clusters whose white dwarf masses deviate systematically from the single-star initial-final mass relation would likewise falsify the channel.","supporting_citations":[],"lane_accuracy":{"status":"not yet measured","lane":{"model":"deepseek/deepseek-v4-flash","input_kind":null},"url":"https://pith.science/accuracy"},"review_version":1}