{"id":"f8b8854d-ed4e-489f-bf1f-d65cf8140441","arxiv_id":"2502.07773","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A blind statistical search of Kepler, K2, and TESS multi-planet systems finds that the USP size anomaly ends at about 0.97 days and the period-ratio anomaly at about 2.09 days.","lead":"This paper uses statistical tests on 376 multi-planet systems to find where the ultra-short-period planet (USP) population ends. The size anomaly of USPs disappears near 1 day, while the orbital spacing anomaly disappears near 2 days.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 3–5 day control sample may already be shifted toward USP-like radii and period ratios, so the inferred 1-day and 2-day boundaries could be artifacts of the baseline choice rather than true astrophysical transitions.","rationale":"The reader's weakest-assumption analysis identifies the same structural vulnerability: the fixed 3–5 day control is assumed to be free of USP-like signatures. I agree this is the most load-bearing point because both claimed boundaries are defined entirely by where sliding-bin p-values cease to differ from this control. If the control is shifted, the boundaries shift. The concern is sharpened by the paper's own astrophysical discussion: the 3–5 day regime is close enough to the star that generic photoevaporation and possibly Roche-lobe effects could make its planets smaller or more detached than longer-period populations, so the control is not obviously a clean 'non-USP' baseline. The pR = 0.057 value for the proposed proto-USP bin in Table 1 shows that the 1-day size boundary sits very close to the significance threshold, making it especially sensitive to baseline contamination. The proposed concrete test—rerunning the analysis with longer-period controls and directly comparing the 3–5 day control to 5–10 day planets—would settle whether the reported PR and PP are genuine transitions or artifacts of baseline choice. This does not refute the paper's careful validation of other systematics; it identifies an assumption that is central, plausible, and testable. Since the reader already assigned CONDITIONAL with high confidence, my read does not change the verdict.","tokens_in":24162,"tokens_out":5797,"duration_ms":59148,"concrete_test":"Recompute the Section 4 moving-bin analysis with alternative control samples of 5 ≤ P1/days < 10 and 10 ≤ P1/days < 20, keeping Nbin = 30 and the same permutation-based AD procedure. Also run a direct two-sample AD test comparing the 3–5 day control's radius and period-ratio distributions to those of 5–10 day innermost planets. If PR moves above ~1.5 days, if PP moves outside 2.09 ± 0.22 days, or if the 3–5 versus 5–10 comparison rejects the null at p < 0.05, the reported boundaries are not robust to the baseline choice and the central claim should be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central result is conditional on the Section 4 assumption that USP-like size and spacing signatures 'are expected to vanish within P ≲ 3 days,' which justifies using systems with 3 ≤ P1/days < 5 as a fixed non-USP control. This assumption is asserted rather than demonstrated, and the paper's own Section 6.1 notes that photoevaporation remains potent within P ≲ 10 days and Roche-lobe overflow can persist to P ≲ 2 days. If the 3–5 day control population itself contains a modest excess of small or architecturally detached innermost planets, the moving-bin p-values in Figure 3 will cross p = 0.05 earlier than they would against a truly baseline population. The fragility is visible in Table 1: for the full sample, the 1–2 day bin has pR = 0.057, just above the significance threshold; a slightly larger or less USP-contaminated control could push this below 0.05 and move the inferred size boundary from ~1 day toward ~2 days. Because every validation in Section 5 resamples the same 3–5 day control rather than varying it, the control assumption is load-bearing and untested within the paper.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a statistical search for an empirically motivated boundary of the ultra-short-period (USP) planet population. Using 376 multi-planet systems from Kepler, K2, and TESS, the authors compare the radius and period-ratio distributions of the innermost planets with P<1 day against a 'non-USP' sample (1-5 days) using a permutation-based Anderson-Darling test with bootstrapped radii. They then compare moving bins of systems with P1<3 days against a fixed control sample with 3<=P1<5 days, locating the periods where the USP-like small-size and large-spacing signatures become statistically insignificant: PR = 0.97+0.25/-0.19 days and PP = 2.09+0.16/-0.22 days. Robustness checks include confirmed-only samples, precise radii, no giant companions, FGK hosts, and a mock detection framework for missing planets. The paper interprets these boundaries as evidence for a 1-day USP size transition and a distinct 'proto-USP' population between 1 and 2 days.","tokens_in":24404,"tokens_out":8509,"duration_ms":78361,"significance":"If the central result holds, it provides an astrophysical, rather than purely conventional, basis for the 1-day USP cutoff, and it identifies a new transitional regime at about 2 days. The paper is careful in several ways: it uses a nonparametric test tailored to tail differences, propagates radius uncertainties through bootstrap, and runs an unusually broad set of validation subsamples that all preserve the main signal. The main caveats are that the control sample is an assumed baseline rather than a demonstrated one, and that the quoted uncertainties on the transition periods are bin widths rather than statistical intervals.","major_comments":[{"comment":"The choice of the 3-5 day control sample is load-bearing and is not validated within the paper. The text calls it the 'sole assumption' that USP size/spacing signatures vanish within P<=3 days, but the only check in Section 4 compares USPs to this same control; that confirms a difference, not that the control is free of USP-like objects. Moreover, Section 6.1 states that photoevaporation remains effective within P<=10 days and Roche-lobe overflow can persist to P<=2 days, so the control may itself contain partially processed small planets. In Table 1, the full-sample pR for the 1-2 day bin is 0.057, just above the p=0.05 threshold; with a less contaminated control the pR for this bin would likely be below 0.05, moving PR from about 1 day toward about 2 days. The authors should repeat the analysis with alternative control ranges (e.g., 4-6 days) or explicitly inject a range of USP-like contamination in the control and show how PR and PP change.","section":"Section 4 and Table 1"},{"comment":"The quoted uncertainties on PR and PP are the widths of the moving bins at the crossing, not statistical uncertainties. The bootstrap procedure produces a median pR and a pP from a single permutation run, but it does not produce a distribution of crossing periods. As written, 'PR = 0.97+0.25/-0.19' can be read as a 1-sigma confidence interval, which is not what was computed. Please provide resampling-based confidence intervals (e.g., bootstrap over systems) or explicitly label these ranges as bin-width resolutions.","section":"Section 4 and Figure 3"},{"comment":"The treatment of geometric biases is explicitly qualitative and does not quantitatively bound their effect on PR. Because the sample is restricted to multi-transiting systems, a highly inclined innermost planet in a 1-5 day system could be missed by construction, and the mock-detection framework in Section 5.4.1 assumes edge-on orbits (b=0) for hypothetical planets and does not sample mutual inclinations. The paper should either implement a geometric correction or sensitivity test, or soften the claim that detection biases do not affect the identified size boundary.","section":"Section 5.4.2"}],"minor_comments":[{"comment":"The text says there are 40 USP systems with delta_Rp/Rp <= 0.20, but Table 1 lists 35; please correct the inconsistency.","section":"Section 5.1 and Table 1"},{"comment":"The phrase 'to reduced selection bias' should be 'to reduce selection bias'.","section":"Section 2"},{"comment":"The symbol eP is used for the hypothetical orbital period, which is confusing because e conventionally denotes eccentricity; consider P_hyp or similar.","section":"Section 5.4.1"},{"comment":"The sentence 'USPs only occur around ≲ 1% of stars' lacks a citation at the end; please add a reference for the occurrence rate.","section":"Section 1"},{"comment":"Verb forms such as 'Lee & Chiang (2017) posits' should be made plural or rephrased for consistency.","section":"Section 6.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is publishable if the control-sample sensitivity and uncertainty-interval issues are addressed. The text/table count discrepancy for the delta_Rp/Rp <= 0.20 subsample should be fixed. No concerns about novelty or citation fairness; the relevant literature appears well covered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth your time. This is the first blind, multi-mission moving-bin search for where USP-like behavior in radius and period ratio actually ends, and it returns quantitative answers: size differences vanish at ~0.97 days, spacing differences at ~2.09 days. That is a real step beyond the usual “USPs are small and detached” qualitative statement. The validation is thorough: confirmed-only, precise radii, no giant companions, FGK hosts, and a mock-observation scheme for undetected planets all reproduce the two transitions. The detection-bias simulation in particular is more careful than most papers in this area.\n\nThe soft spots are statistical, and they are not fatal but they are real. The quoted ± uncertainties are just the moving-bin widths, not resampling or bootstrap uncertainties on the crossing period, so they overstate precision. Multiple testing across 170 overlapping bins is uncorrected, though the authors argue—fairly—that the monotone p-value curves make the crossing largely threshold-insensitive. The bigger issue is the control sample. Everything is compared against systems with 3 ≤ P1 < 5 days, and the assumption that USP-like signatures vanish by ~3 days is asserted, not demonstrated. The stress-test note is right to point at Table 1: the 1–2 day bin has pR = 0.057, just above 0.05, so a slightly contaminated control could push the size boundary from ~1 day toward ~2 days. The paper even notes that photoevaporation still operates within 10 days, which makes the control choice less innocent than it first appears.\n\nI still think the central claim holds up in outline. The spacing transition at ~2 days is robust across every subsample, and the size transition at ~1 day, while more fragile, is consistently present even if its exact location moves. The qualitative conclusion—USPs are small and detached, proto-USPs are detached but not small—is a reasonable reading of the data. What this paper needs is an honest sensitivity analysis that varies the control sample (say 4–6 or 5–7 days) and reports resampled crossing uncertainties. Without that, the 1-day boundary is a good hypothesis, not a measured constant.\n\nWho should read it: people working on USP formation, planetary architecture, or classification schemes. It deserves a serious referee and likely publication after the control-sample test is added. If I were the editor, I would send it out.","headline":"Genuine empirical search for the USP boundary that finds a 1-day size transition and a 2-day spacing transition, but the error bars are optimistic and the 3–5 day control sample deserves a sensitivity test before the boundaries are canonized.","tokens_in":24904,"tokens_out":1928,"would_cite":true,"duration_ms":20856,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper shows that the two defining traits of ultra-short-period planets—small radius and wide companion spacing—cease to be statistically significant at 0.97 and 2.09 days respectively, giving the usual 1-day cutoff an empirical basis.","keywords":["ultra-short-period planets","USP classification boundary","period ratio","proto-USP","Anderson-Darling test","exoplanet architectures","Kepler K2 TESS","eccentric migration"],"falsifier":"Recompute $P_R$ and $P_{\\mathcal{P}}$ using a control sample drawn from longer periods, such as 5–10 days, from the same catalogs; if the inferred boundaries move by more than the quoted uncertainties or the p-value curves lose their sharp single crossings, the control-sample assumption is violated.","tokens_in":23976,"feed_emoji":"🪐","tokens_out":5644,"duration_ms":46399,"temperature":0.7,"pith_summary":"Ultra-short-period planets (USPs), worlds orbiting in under a day, are conventionally defined by a 1-day cutoff that has never been tested against data. This paper asks whether that boundary, or a different one, falls out of the observations themselves. Using 376 multi-planet systems from Kepler, K2, and TESS, it finds that the two hallmark USP signatures disappear at different periods: the tendency to be smaller than other short-period planets fades at about 0.97 days, while the tendency to be widely separated from neighboring planets persists until about 2.09 days. If the result holds, USPs are genuinely special below 1 day, and the interval from 1 to 2 days hosts a distinct proto-USP population that is detached but not especially small. The finding also gives formation theories concrete period ranges to reproduce.","feed_headline":"Ultra-short planets' odd traits end at 1 and 2 days","feed_subtitle":"Data from 376 systems pin the size transition at ~1 day and the spacing transition at ~2 days.","key_machinery":"The analysis runs a permutation-based two-sample Anderson–Darling test, which is more sensitive than the Kolmogorov–Smirnov test to tail differences, on moving bins of 30 systems with innermost period below 3 days, each compared against a fixed control sample of 177 systems with innermost periods between 3 and 5 days. Bootstrap resampling of radius uncertainties propagates into p-values for the size comparison, while the period-ratio comparison uses a single run because period uncertainties are negligible. The critical periods are defined as the last bin centers where the p-value crosses above 0.05, with the bin width adopted as the uncertainty range.","core_discovery":"On the paper's own terms, the discovery is that the USP population's two empirical signatures—reduced planet size and enlarged period ratio to the nearest companion—are real against a 3–5 day control sample, and that each signature has its own sharp transition period: $P_R = 0.97^{+0.25}_{-0.19}$ days for size and $P_{\\mathcal{P}} = 2.09^{+0.16}_{-0.22}$ days for spacing. The transitions are abrupt, roughly 2–3 orders of magnitude in p-value over less than 0.3 days, and insensitive to candidate status, radius uncertainties, giant companions, host spectral type, and simulated undetected planets. The paper interprets the 1-day size boundary as the signature of refractory mass loss and tidal decay acting on planets delivered close to the star, and the 2-day spacing boundary as the imprint of eccentric migration that strands proto-USPs in detached orbits. The authors explicitly present these results as evidence that the conventional 1-day cutoff has an astrophysical basis and that an additional 2-day boundary should be considered in future studies.","pith_inferences":["The control-sample assumption could be checked by extending the same moving-bin analysis with a control drawn from longer periods, say 5–10 days; if the inferred boundaries shift beyond the quoted uncertainties, the choice of control population is driving the result.","If the 2-day spacing transition reflects recent eccentric migration, proto-USP systems should show elevated mutual inclinations or missing non-transiting companions compared with similar-period systems that lack wide spacing; this is a testable prediction for follow-up observations.","The size and spacing boundaries may be two manifestations of a single migration-plus-mass-loss channel; correlating within individual systems whether the smallest planets are also the most detached near 1 day could distinguish formation models.","Because single-transiting USPs share the size signature but cannot be tested for the spacing transition, a joint statistical model of single- and multi-transiting systems could extend the conclusions to the full USP population, which is dominated by single-transiting configurations."],"forward_implications":["The conventional 1-day USP boundary is astrophysically meaningful: below roughly 1 day planets are statistically smaller than the 3–5 day control population, while between 1 and 2 days they are not.","A distinct proto-USP population exists at 1–2 days: planets there are not systematically small but are still widely spaced from companions, supporting a two-step formation history of eccentric migration followed by tidal decay.","Formation models must reproduce a sharp spacing transition near 2 days, not just the pile-up below 1 day, so the 2-day boundary becomes a new constraint for dynamical simulations.","If applied jointly, the two boundaries suggest a classification scheme where USPs are both small and detached, proto-USPs are detached but not small, and planets beyond 2 days are neither.","The 2-day transition provides a target for future transit surveys to enlarge the proto-USP sample and test whether the spacing boundary persists with better statistics."],"supporting_citations":[{"why":"Establishes the conventional P<1 day USP definition and occurrence statistics that the paper sets out to test.","marker":"Sanchis-Ojeda et al. (2014)"},{"why":"Documents the architectural detachment of USPs, one of the two signatures whose persistence the paper measures.","marker":"Steffen & Farr (2013)"},{"why":"Supplies the vetted Kepler multi-planet catalog that dominates the sample and provides refined radii and period measurements.","marker":"Lissauer et al. (2024)"},{"why":"Provides the equilibrium-tide formation model whose predicted 2-day detachment scale the paper compares against.","marker":"Lee & Chiang (2017)"},{"why":"Provides the low-e migration mechanism the paper favors and simulated period ratios that match the observed 2-day transition.","marker":"Pu & Lai (2019)"},{"why":"Provides the high-eccentricity secular-chaos migration model and its predicted period-ratio distributions for USPs and proto-USPs.","marker":"Petrovich et al. (2019)"},{"why":"Defines the proto-USP regime and supplies host-age comparisons used to argue for migration followed by tidal decay.","marker":"Schmidt et al. (2024)"},{"why":"Documents large mutual inclinations for planets with P less than about 2 days, used in the geometric-bias validation and formation discussion.","marker":"Dai et al. (2018)"}],"fun_headline_variants":["USP quirks vanish at 1 and 2 days","Data pin USP size drop ~1 day, spacing ~2 days","376 systems show USP size and spacing cutoffs","Ultra-short planets: two distinct transition periods","USP size dips at 1 day, spacing gap at 2 days"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The control sample of systems with innermost periods between 3 and 5 days is assumed to contain none of the small-size or wide-spacing USP signatures, so a failure to reject the null against that control marks the end of the USP regime.","fun_headline_variants_meta":{"raw":{"variants":["USP quirks vanish at 1 and 2 days","Data pin USP size drop ~1 day, spacing ~2 days","376 systems show USP size and spacing cutoffs","Ultra-short planets: two distinct transition periods","USP size dips at 1 day, spacing gap at 2 days"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000219,"raw_usage":{"total_tokens":1541,"prompt_tokens":1144,"completion_tokens":397,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":760,"completion_tokens_details":{"reasoning_tokens":312}},"tokens_in":760,"tokens_out":397,"duration_ms":4241,"temperature":1.0,"reasoning_tokens":312,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T11:36:43.354020+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute $P_R$ and $P_{\\mathcal{P}}$ using a control sample drawn from longer periods, such as 5–10 days, from the same catalogs; if the inferred boundaries move by more than the quoted uncertainties or the p-value curves lose their sharp single crossings, the control-sample assumption is violated.","supporting_citations":[{"cited_title":"H., & Farr, W","cited_arxiv_id":null,"evidence_quote":"Documents the architectural detachment of USPs, one of the two signatures whose persistence the paper measures."},{"cited_title":"J., Rowe, J","cited_arxiv_id":null,"evidence_quote":"Supplies the vetted Kepler multi-planet catalog that dominates the sample and provides refined radii and period measurements."},{"cited_title":"J., & Chiang, E","cited_arxiv_id":null,"evidence_quote":"Provides the equilibrium-tide formation model whose predicted 2-day detachment scale the paper compares against."},{"cited_title":"2019, AJ, 157, 180","cited_arxiv_id":null,"evidence_quote":"Provides the high-eccentricity secular-chaos migration model and its predicted period-ratio distributions for USPs and proto-USPs."},{"cited_title":"P., Schlaufman, K","cited_arxiv_id":null,"evidence_quote":"Defines the proto-USP regime and supplies host-age comparisons used to argue for migration followed by tidal decay."}],"review_version":1}