{"id":"aea79685-9aee-4d7a-acc6-2a295dfc7163","arxiv_id":"2607.06333","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":8,"one_line_summary":"Forward-modeling 193 observed post-common-envelope binaries shows energy-based formalisms (α and Two-stage) match observations while the angular-momentum-based SCATTER formalism does not, with recombination energy contributing 10–40%.","lead":"This paper tests three mathematical models for how binary stars shed their outer layers during a 'common envelope' event, comparing model predictions against 193 observed post-common-envelope binaries. It finds that energy-based models work better than angular-momentum-based ones, and that recombination energy helps but only partially.","discovery_kind":"unclear","skeptic_critique":{"model":"glm-5.2","headline":"Quantitative (α_CE, f_ion) constraints rest on visual comparison with unmodeled selection effects in the super-wide regime; qualitative conclusions are more robust.","rationale":"The reader correctly identified the most load-bearing concern: the model–observation comparison is purely visual, selection effects are explicitly unmodeled, and the quantitative f_ion constraint depends on this gap. I agree with this assessment and with the CONDITIONAL verdict. The paper is honest about all limitations (§2.3.2, §4.2), which is commendable, and the qualitative conclusions — SCATTER fails, energy-based formalisms remain preferred — are defensible on grounds that do not require statistical rigor (e.g., SCATTER producing zero systems where dozens are observed). The α_CE = 0.2 value is adopted from prior calibrations to overlapping samples, introducing mild circularity, but this is standard practice when testing new formalisms against a known baseline. The Two-stage vs. α comparison is inconclusive by the paper's own admission (differences only where observations are absent, §4.3), which is honest. The specific concern that elevates this from a minor caveat to a load-bearing issue is the internal inconsistency: the paper acknowledges its model overpredicts (due to unmodeled selection), yet uses the absence of observed systems to set an upper limit on f_ion. This is the one place where the argument structure undermines its own quantitative claim. The concrete test proposed would determine whether the f_ion upper bound survives once the selection function is even approximately modeled. If it does not, the headline quantitative constraint weakens but the qualitative conclusions stand, keeping the verdict at CONDITIONAL with a note that the f_ion range is not yet robust.","tokens_in":35293,"tokens_out":2984,"duration_ms":167276,"concrete_test":"Implement a minimal UV-excess distinguishability criterion (e.g., requiring the WD luminosity to exceed a fraction of the companion flux in the near-UV, as in Davis et al. 2010 or Toonen & Nelemans 2013) and recompute the predicted super-wide PCEB population for the (α_CE=0.2, f_ion=0.4) and (α_CE=0.2, f_ion=0.6) models. If the distinguishability cut removes the predicted IK Peg-like systems at super-wide periods for f_ion=0.6, then the upper bound f_ion ≲0.4 is an artifact of the missing selection function rather than a physical constraint, and the quoted f_ion range should be widened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's qualitative conclusions are reasonably secure: SCATTER predicts zero PCEBs at P > 100 days where observations exist (Fig. 5), and predicts a HeWD:COWD ratio inconsistent with observations (Fig. 6, §4.1) — these are hard failures that do not require a statistical framework. However, the quantitative constraint that f_ion must be ≲0.4 at α_CE = 0.2 (Fig. 8, §4.2) is load-bearing for the strongest_claim and is not robust. This upper bound is derived from the absence of observed IK Peg-like systems (M_WD ≳1.1 M☉, M_MS ~1.4 M☉) at super-wide periods (P > 100 days). The paper explicitly does not model the UV-excess distinguishability criterion or survey cadence (§2.3.2: 'we have chosen to not model either due to their complexity'), and states 'we expect our model to predict more systems than what is observed if the physics is correct.' This means the model is known to overpredict; using the absence of observed systems to set an upper limit on f_ion is then internally inconsistent — the overprediction means the absence of observed IK Peg-like systems at super-wide periods could reflect selection effects rather than a genuine physical constraint. The 'necessity' of recombination energy (Fig. 7) is more robust because it concerns the model producing zero systems without recombination, not a quantitative mismatch. But the specific f_ion range (0.1–0.4) depends on the unmodeled selection function being reliable in exactly the regime where it is most uncertain.","agreement_with_reader":"agree"},"referee_report":{"model":"glm-5.2","summary":"This manuscript presents the first systematic comparison of two recently proposed common envelope (CE) formalisms—the Two-stage formalism (Hirai & Mandel 2022) and the SCATTER formalism (Di Stefano et al. 2023)—against the standard energy-based α-formalism, using forward-modelled post-common envelope binary (PCEB) populations in the Solar neighbourhood. The authors compile 193 observed WD-MS PCEBs and compare them against binary_c population synthesis predictions across orbital period and component mass space. The principal conclusions are: (1) the angular-momentum-based SCATTER formalism fails to reproduce the observed PCEB population (no wide PCEBs, incorrect HeWD:COWD ratios), (2) energy-based formalisms (α and Two-stage) remain the most descriptive, with α_CE ≈ 0.2–0.3, (3) recombination energy is necessary but only a fraction (~10–40%) can contribute, and (4) the Two-stage and α-formalisms are currently indistinguishable given observational incompleteness at intermediate periods and high companion masses. The paper also provides new polynomial fits for the Two-stage formalism's binding energy and radiative region mass parameters (Appendix A).","tokens_in":35542,"tokens_out":2596,"duration_ms":383903,"significance":"The paper addresses a timely question: whether newly proposed CE formalisms outperform the standard α-prescription when confronted with the expanded observed PCEB population. The compilation of 193 PCEBs, including the recently discovered super-wide (P > 100 d) and ultra-massive WD systems, is a valuable resource. The implementation of the Two-stage formalism in binary_c, with publicly available polynomial fits derived from Monash and MESA stellar models (Appendix A, doi:10.5281/zenodo.20117304), and the public availability of the modified binary_c code (gitlab.com/rileythai/binary_c:twostage-v2.2.4) are commendable and enable reproducibility. The qualitative conclusion that SCATTER fails to produce wide PCEBs (Fig. 5) and predicts an incorrect HeWD:COWD ratio (Fig. 6) is a robust and useful result for the community. The identification of specific observational tests that could distinguish the Two-stage from the α-formalism (sdOBA binaries from M > 2.25 M☉ donors, §4.3) provides clear direction for future work.","major_comments":[{"comment":"§4.2, Fig. 8: The quantitative constraint that f_ion ≲ 0.4 at α_CE = 0.2 is derived from the absence of observed IK Peg-like systems (M_WD ≳ 1.1 M☉, M_MS ~1.4 M☉) at super-wide periods (P > 100 days). However, §2.3.2 explicitly states that the model does not include selection effects from UV-excess distinguishability or survey cadence, and that 'we expect our model to predict more systems than what is observed if the physics is correct.' This creates an internal tension: the model is known to overpredict, so the absence of observed IK Peg-like systems at super-wide periods could reflect observational incompleteness rather than a genuine upper limit on f_ion. The paper should either (a) explicitly state that the f_ion ≲ 0.4 bound is conditional on the assumption that the super-wide Gaia sample is complete for IK Peg-like systems (which is partially addressed by the reference to Shahaf et~","section":null},{"comment":"§4.2, Fig. 8: The quantitative constraint that f_ion ≲ 0.4 at α_CE = 0.2 is derived from the absence of observed IK Peg-like systems at super-wide periods. However, §2.3.2 explicitly states that selection effects from distinguishability and survey cadence are not modelled, and that 'we expect our model to predict more systems than what is observed if the physics is correct.' This creates an internal tension: the model is acknowledged to overpredict, so the absence of observed systems could reflect incompleteness rather than a physical upper limit on f_ion. The paper should either (a) explicitly state that the f_ion ≲ 0.4 bound is conditional on the super-wide Gaia sample being complete for IK Peg-like systems (the reference to Shahaf et al. 2024 on line 'Assuming the Shahaf et al. (2024) Gaia selection... is observationally complete' partially addresses this but is stated only in passing","section":null},{"comment":"§4.2, Fig. 8: The quantitative constraint that f_ion ≲ 0.4 at α_CE = 0.2 is derived from the absence of observed IK Peg-like systems at super-wide periods. However, §2.3.2 explicitly states that selection effects from distinguishability and survey cadence are not modelled, and that 'we expect our model to predict more systems than what is observed if the physics is correct.' This creates an internal tension: the model is acknowledged to overpredict, so the absence of observed systems could reflect incompleteness rather than a physical upper limit on f_ion. The paper should either (a) explicitly state that the f_ion ≲ 0.4 bound is conditional on the super-wide Gaia sample being complete for IK Peg-like systems (the reference to Shahaf et al. 2024 completeness is stated only in passing and should be foregrounded as the load-bearing assumption), or (b) soften the claim to acknowledge that f","section":null},{"comment":"§4.2, Fig. 8: The quantitative constraint that f_ion ≲ 0.4 at α_CE = 0.2 is derived from the absence of observed IK Peg-like systems at super-wide periods. However, §2.3.2 explicitly states that selection effects from distinguishability and survey cadence are not modelled, and that 'we expect our model to predict more systems than what is observed if the physics is correct.' This creates an internal tension: the model is acknowledged to overpredict, so the absence of observed systems could reflect incompleteness rather than a physical upper limit on f_ion. The paper should either (a) explicitly state that the f_ion ≲ 0.4 bound is conditional on the super-wide Gaia sample being complete for IK Peg-like systems (the reference to Shahaf et al. 2024 completeness is stated only in passing and should be foregrounded as the load-bearing assumption), or (b) soften the quantitative claim to a lo","section":null},{"comment":"§4.2, Fig. 8: The quantitative constraint that f_ion ≲ 0.4 at α_CE = 0.2 is derived from the absence of observed IK Peg-like systems at super-wide periods. However, §2.3.2 explicitly states that selection effects from distinguishability and survey cadence are not modelled, and that 'we expect our model to predict more systems than what is observed if the physics is correct.' This creates an internal tension: the model is acknowledged to overpredict, so the absence of observed systems could reflect incompleteness rather than a physical upper limit on f_ion. The paper should either (a) explicitly state that the f_ion ≲ 0.4 bound is conditional on the super-wide Gaia sample being complete for IK Peg-like systems (the reference to Shahaf et al. 2024 completeness is stated only in passing and should be foregrounded as the load-bearing assumption), or (b) soften the quantitative claim to a lo","section":null}],"minor_comments":[{"comment":"§2.1.2, Eq. (3): The definition of q_cc is given as 'q_cc = M_core/M_2' but the text also refers to 'companion-to-core mass ratio q_cc'. This is consistent but could be confused with the more standard convention of q = M_2/M_1; a brief clarifying note would help.","section":null},{"comment":"§2.2.3, Eq. (6): The notation min(q_ad, q_L2) is clear, but the text does not explicitly state whether q_ad and q_L2 are evaluated at the onset of RLOF or at some other point. This should be specified.","section":null},{"comment":"Fig. 5: The colour bars showing 'Expected systems (count)' use different scales across panels (10^1 to 10^3 or 10^4). This is noted in the figure but makes cross-panel comparison difficult. Consider normalising or at least ensuring the reader is directed to check the scale.","section":null},{"comment":"§3.1: The statement 'We also plot non-CE stable mass transfer systems from our model in gray bins' refers to Fig. 2, but the stable MT systems are shown as a shaded region rather than 'gray bins'. Minor wording issue.","section":null},{"comment":"§4.2: 'We first assess if is recombination is necessary' — grammatical error, should read 'We first assess whether recombination is necessary'.","section":null},{"comment":"§4.1: 'the functional η predicts the orbit should shrink by a factor of 1000 when q_cc ~ 1.0' — it would be useful to show this explicitly (e.g., a small inset or annotation in Fig. 6) to help the reader understand why the functional form fails.","section":null},{"comment":"Appendix A: The polynomial fits (Eqs. A1, A2) are provided with coefficients available at a Zenodo DOI, but the manuscript does not state the mass range or evolutionary phases covered by each fit. This information is only available in the online files. A summary table of the mass grid and phases would make the appendix self-contained.","section":null},{"comment":"Table 1: The entry 'SCATTER η fitted f(q_ec), Eq. 4 Di Stefano et al. (2023)' is ambiguous in formatting; it should be clear that Eq. 4 is the authors' adopted functional form, not from Di Stefano et al. (2023) directly.","section":null},{"comment":"§2.3.2, Eq. (9): The ratio V_sph(d_max)/V_sol is described as independent of ρ_0, but the integral in the numerator is over a spherical volume while the denominator is over a cylindrical volume. The geometry of this comparison should be clarified (e.g., does the spherical volume extend beyond the cylinder?).","section":null},{"comment":"The abstract states 'Recombination energy is necessary, but only a fraction of it (~10–40%) can contribute.' The body text (§4.2) gives f_ion ~ 0.2–0.4 as the minimum required range. The abstract should clarify whether 10% is a lower bound or an approximate value.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The reader's concern about circularity (α_CE = 0.2 adopted from Zorotovic et al. 2010 / De Marco et al. 2011, which were calibrated against similar PCEB observations) is valid but not, in my assessment, a blocking issue. The paper does not claim to independently derive α_CE from first principles; it explicitly adopts the literature value and tests whether the new formalisms can match observations. The more substantive concern is the f_ion upper limit derived from unmodeled selection effects, which I have raised as a major comment. The paper is honest about this limitation (§4.2, final paragraph), which is why I judge the issue as fixable through revised framing rather than a fundamental flaw. The qualitative conclusions (SCATTER fails, energy-based formalisms preferred, recombination is necessary) are robust and do not depend on the quantitative f_ion bound. I note that this appears to be based on an Honours thesis (Acknowledgements), and the level of work is impressive for that context, though the manuscript should be evaluated on its own merits."},"author_rebuttal":{"model":"glm-5.2","summary":"The referee raises a single substantive point (repeated in the report due to apparent formatting): the f_ion ≲ 0.4 constraint in §4.2 relies on the absence of observed IK Peg-like systems at super-wide periods, but §2.3.2 acknowledges the model overpredicts systems due to unmodelled selection effects. This creates an internal tension—the absence of observed systems could reflect incompleteness rather than a physical upper limit on f_ion. The referee requests either foregrounding the completeness assumption or softening the claim. We agree this is a valid concern and will revise accordingly.","responses":[{"response":"We thank the referee for identifying this internal tension, which is a fair and important point. The referee is correct that our general statement in §2.3.2—that the model is expected to overpredict systems due to unmodelled selection effects from distinguishability and survey cadence—sits in tension with using the *absence* of observed IK Peg-like systems at super-wide periods as a quantitative upper bound on f_ion. We will resolve this in the revised manuscript in two ways. First, we will foreground the Shahaf et al. (2024) completeness assumption as the load-bearing condition for the f_ion ≲ 0.4 bound. Specifically, the super-wide PCEB sample of Yamaguchi et al. (2024a) was constructed using the Shahaf et al. (2024) Gaia astrometric selection function, which is designed to be complete for systems with MS companions in the G-type mass range (~1.2–1.4 M☉) at the relevant distances. IK Peg-like systems fall squarely within this companion-mass range, so the Shahaf et al. (2024) completeness is what makes the non-detection physically meaningful rather than a mere artifact of selection effects. We will make this reasoning explicit in §4.2 rather than leaving it as a passing reference. Second, we will add a qualifying sentence acknowledging that if the Shahaf et al. (2024) selection function is *not* complete for IK Peg-like systems specifically—for instance, if the UV-excess distinguishability criterion introduces additional incompleteness for massive-WD systems—then the f_ion ≲ 0.4 bound should be regarded as an upper limit that could be relaxed. We will also soften the language from 'f_ion can be no higher than ~0.4' to 'f_ion is constrained to be ≲0.4, conditional on the completeness of the super-wide sample for IK Peg-like systems.' These changes make the logical chain","revision_made":"yes","referee_comment":"§4.2, Fig. 8: The quantitative constraint that f_ion ≲ 0.4 at α_CE = 0.2 is derived from the absence of observed IK Peg-like systems at super-wide periods. However, §2.3.2 states that selection effects from distinguishability and survey cadence are not modelled, and that 'we expect our model to predict more systems than what is observed if the physics is correct.' This creates internal tension: the model is acknowledged to overpredict, so the absence of observed systems could reflect incompleteness rather than a physical upper limit on f_ion. The paper should either (a) explicitly state that the f_ion ≲ 0.4 bound is conditional on the super-wide Gaia sample being complete for IK Peg-like systems (the reference to Shahaf et al. 2024 completeness is stated only in passing and should be foregrounded as the load-bearing assumption), or (b) soften the quantitative claim."}],"tokens_in":35802,"tokens_out":965,"duration_ms":88701,"standing_objections":[]},"desk_editor":{"model":"glm-5.2","letter":"Bottom line: this is the first systematic confrontation of the Two-stage (Hirai & Mandel 2022) and SCATTER (Di Stefano et al. 2023) common envelope formalisms against the compiled observed PCEB population, and the qualitative conclusions are defensible. The paper finds that SCATTER fails to reproduce the observed population — no PCEBs at P > 100 days where observations exist, and a HeWD:COWD ratio inconsistent with observations — while energy-based formalisms (α and Two-stage) do reasonably well. That SCATTER fails is a hard result that does not require a statistical framework to believe. The α_CE ~ 0.2–0.3 confirmation is not new, but the systematic comparison is, and the paper is honest that this value was adopted from prior calibrations to overlapping observations (Zorotovic et al. 2010; De Marco et al. 2011). The circularity burden is real but mild — the paper does not oversell α_CE as a new measurement, and the SCATTER failure is independent of that calibration. The new polynomial parametrizations for the Two-stage formalism's convective-envelope binding energy and radiative region mass, derived from Monash and MESA models and publicly archived (Zenodo doi:10.5281/zenodo.20117304), are a concrete and reusable contribution. The binary_c code is also publicly available. These are real, reproducible deliverables. The soft spot is the quantitative f_ion constraint (0.1–0.4). The stress-test note lands here: the upper bound on f_ion at α_CE = 0.2 is derived from the absence of observed IK Peg-like systems at super-wide periods, but the paper explicitly does not model UV-excess distinguishability or survey cadence, and states the model is expected to overpredict. Using the absence of observed systems to set an upper limit when the model is known to overpredict is internally inconsistent. The 'necessity' of recombination energy (Fig. 7) is more robust — it concerns the model producing zero systems without recombination, not a quantitative mismatch. But the specific f_ion range depends on the unmodeled selection function being reliable in exactly the super-wide regime where it is most uncertain. The model–observation comparison throughout is purely visual (overlays in Figs. 5–8) with no likelihood or goodness-of-fit metric. The paper acknowledges this in §4.2. This is acceptable for a first-pass qualitative assessment but prevents the quantitative claims from being robust. The Two-stage formalism's distinguishing predictions (more intermediate-mass survivors at close periods) fall in a region with almost no observations, so the paper cannot yet distinguish it from the α-formalism. The paper says this clearly. This paper is for binary population synthesis practitioners and common envelope theorists. It provides a useful, honest first look at whether the new formalisms survive contact with observations, plus reusable parametrizations. The qualitative conclusions deserve publication; the quantitative f_ion constraint should be softened. Recommend serious peer review — the paper earns a referee's attention.","headline":"First systematic test of Two-stage and SCATTER CE formalisms against observed PCEBs; qualitative conclusions hold, quantitative f_ion constraint is soft","tokens_in":36155,"tokens_out":722,"would_cite":false,"duration_ms":108083,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["97.80.-d","97.10.Ex","97.20.Rp"],"model":"glm-5.2","headline":"Energy beats angular momentum for common envelope outcomes","keywords":["common envelope evolution","post-common envelope binaries","binary population synthesis","recombination energy","angular momentum formalism","white dwarf binaries","stellar evolution"],"falsifier":"Observation of a robust population of wide post-common envelope binaries (periods above 100 days) that the SCATTER formalism predicts but the energy-based formalisms do not, or a formal statistical analysis showing that the SCATTER formalism fits the observed population significantly better once selection effects are properly modelled.","tokens_in":35518,"feed_emoji":"","tokens_out":1323,"duration_ms":213903,"temperature":0.7,"pith_summary":"This paper tests two newer prescriptions for common envelope evolution — the Two-stage formalism (which splits the process into an energy-driven plunge followed by angular-momentum-driven mass transfer) and the SCATTER formalism (which predicts the final binary separation purely from orbital angular momentum balance) — against the standard energy-based α-formalism, by forward-modelling the expected present-day population of post-common envelope binaries in the Solar neighbourhood and comparing to 193 observed systems. The central finding is that the SCATTER formalism, which parameterises outcomes through angular momentum exchange between the envelope and the binary components, cannot reproduce the observed population under any parameter setting: it fails to predict wide binaries, overpredicts helium white dwarf systems that are not observed, and cannot match the observed ratio of white dwarf types. The authors interpret this as evidence that orbital angular momentum balance alone is fundamentally insufficient to predict common envelope outcomes. Both the standard α-formalism and the Two-stage formalism, which are energy-based, reproduce the observed population well. The paper further finds that recombination energy — energy released when ionised gas in the stellar envelope recombines — must contribute to envelope ejection, but only a fraction (roughly 10–40%) of the available recombination energy can actually participate, since a full contribution scatters ultra-massive white dwarf systems to orbital periods where they are not observed. The preferred parameter combination is α_CE ≈ 0.2–0.3 with a partial recombination contribution (f_ion ≈ 0.1–0.4). The Two-stage and α-formalisms are indistinguishable for most of the observed population; they differ only for intermediate-mass donors (above about 2.25 solar masses) at orbital periods of 1–100 days, where observations are currently sparse.","feed_headline":"Energy beats angular momentum in stellar common envelope test","feed_subtitle":"Three formalisms for predicting how close binaries form were tested against 193 observed systems. Only energy-based prescriptions survived; ","key_machinery":"The three formalisms tested are: (1) the α-formalism, which equates the envelope binding energy to a fraction α_CE of the orbital energy released during inspiral; (2) the Two-stage formalism, which splits the process into an energy-driven ejection of the convective envelope followed by angular-momentum-driven non-conservative mass transfer of the radiative layer; and (3) the SCATTER formalism, which predicts the final separation from an exponential function of the angular momentum exchanged between the envelope and each component, parameterised by η. The comparison is performed by forward-modelling a Solar neighbourhood population through binary population synthesis, weighting by birth rates","core_discovery":"The SCATTER formalism — an angular-momentum-based prescription for common envelope outcomes — fails to reproduce the observed post-common envelope binary population under any parameter value, while energy-based formalisms (the standard α-formalism and the hybrid Two-stage formalism) succeed. Recombination energy is necessary but only partially contributing (roughly 10–40%), with the preferred efficiency α_CE ≈ 0.2–0.3. No angular-momentum-only formalism tested to date matches observations, suggesting that orbital angular momentum balance alone is not predictive of common envelope outcomes.","pith_inferences":["A formal statistical framework incorporating selection effects (UV-excess distinguishability, survey cadence) could potentially overturn the conclusion that recombination energy is strictly necessary, since the claim depends on the absence of observed systems in the super-wide regime where selection effects are most uncertain.","If the SCATTER formalism's exponential sensitivity to mass ratio is the root cause of its failure, then any angular-momentum-based formalism with similar exponential dependence on mass ratio may face the same problem, suggesting a structural limitation rather than a calibration issue.","The degeneracy between α_CE and f_ion means that without independent constraints on either parameter (e.g., from hydrodynamical simulations or individual well-characterised systems), population synthesis alone cannot uniquely determine the recombination contribution."],"forward_implications":["If angular-momentum-only formalisms are fundamentally insufficient, population synthesis studies that rely on the γ-formalism or similar prescriptions may produce systematically incorrect predictions for compact object merger rates and binary populations.","The partial recombination contribution (10–40%) provides a concrete target for three-dimensional hydrodynamical simulations, which must now demonstrate why only a fraction of the recombination energy thermalises into useful work on the envelope.","The Two-stage formalism predicts a population of intermediate-mass helium-burning stars (hot subdwarfs) in close binaries from RGB donors above 2.25 solar masses that the α-formalism does not; targeted observations of such systems would distinguish the two formalisms.","The predicted but unobserved populations — PCEBs at 1–100 day periods with FGK companions, and super-wide PCEBs with M-dwarf or G-type companions — constitute specific observational targets for Gaia Data Release 4 and the Rubin Observatory.","The L2 overflow criterion for initiating common envelope in giant donors is shown to be necessary; using only dynamical instability thresholds produces unphysical populations where common envelope events occur on nearly stripped envelopes."],"fun_headline_variants":["SCATTER formalism fails observations of common envelope binaries","Energy-based formalisms survive test against 193 post-common envelope binaries","Angular momentum alone cannot predict common envelope outcomes","Recombination energy needed but only partially contributes in close binary formation","Alpha formalism at 0.2-0.3 efficiency matches observed post-common envelope systems"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The comparison between model predictions and observations is done qualitatively by visual overlay of predicted overdensities against observed points in mass–period space, without a formal statistical likelihood or goodness-of-fit metric, and without modelling the selection effects from UV-excess distinguishability or survey cadence. This means regions where the model predicts systems but none are observed cannot be statistically distinguished from observational incompleteness","fun_headline_variants_meta":{"raw":{"variants":["SCATTER formalism fails observations of common envelope binaries","Energy-based formalisms survive test against 193 post-common envelope binaries","Angular momentum alone cannot predict common envelope outcomes","Recombination energy needed but only partially contributes in close binary formation","Alpha formalism at 0.2-0.3 efficiency matches observed post-common envelope systems"]},"model":"glm-5.2","effort":"high","cost_usd":0.0,"raw_usage":{"total_tokens":648,"prompt_tokens":576,"completion_tokens":72,"prompt_tokens_details":null},"tokens_in":576,"tokens_out":72,"duration_ms":28103,"temperature":1.0,"reasoning_tokens":null,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-08T09:20:28.171616+00:00","model_set":{"reader":"glm-5.2"},"falsifier":"Observation of a robust population of wide post-common envelope binaries (periods above 100 days) that the SCATTER formalism predicts but the energy-based formalisms do not, or a formal statistical analysis showing that the SCATTER formalism fits the observed population significantly better once selection effects are properly modelled.","supporting_citations":[],"review_version":1}