{"id":"00df13a4-6cef-4cb7-a9b6-e11fb750ef31","arxiv_id":"2607.08384","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"With CMB+BAO mass-sum bounds only A1/A2 two-zero textures survive; viable one-zero textures (via flow matching) predict distinct Σmi, ⟨mee⟩, and δCP patterns, realizable by non-invertible selection rules.","lead":"Updated neutrino mass-matrix texture zeros with NuFIT 6.0 and DESI cosmology leave only A-series two-zero textures under the tightest mass-sum bound, while one-zero textures still allow several patterns with distinct CP and 0νββ predictions. The work also shows how non-invertible selection rules can generate those one-zero patterns.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the reader's already-noted best-fit fixing of oscillation inputs.","rationale":"The paper's strongest claim is a clean, data-driven update of the texture-zero program. The two-zero analysis is fully analytic and reproducible from the published equations; the one-zero results are cross-checked by both flow matching and the triangle-inequality method of Sec. 3.2, which agree on the allowed patterns and on the characteristic δCP clustering for H1/H2 (IO). The non-invertible constructions are secondary and do not affect the phenomenological tables. The only material limitation is the incomplete propagation of oscillation-parameter uncertainties already flagged by the reader; that limitation does not overturn the viability conclusions under present data. Hence the CONDITIONAL verdict (pending code release and fuller error propagation) stands without adjustment.","tokens_in":27263,"tokens_out":476,"duration_ms":4800,"concrete_test":"Re-solve the two-zero algebraic condition (Eq. 2.13) for A1/A2 while sampling θ12, θ13, Δm²21, Δm²31 from the NuFIT 6.0 covariance (or 3σ box); if any sampled point drives Σmi above the CMB+BAO upper edge for the entire 3σ θ23 interval, the 'only A1/A2 remain' claim weakens.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (only A1/A2 two-zero textures survive CMB+BAO; several one-zero textures remain viable with distinct predictions) rests on standard algebraic constraints from vanishing matrix entries plus external NuFIT/cosmology bounds. The reader's weakest assumption (fixing θ12, θ13, Δm² to NuFIT 6.0 best-fits in Secs. 2.1 and 3.2) is real but secondary: the two-zero solutions are continuous in those inputs, the one-zero analytical inequalities (Eq. 3.10) and flow-matching samples already scan θ23/δCP over 3σ ranges, and the surviving A-series textures sit well inside the allowed mass-sum window. No internal inconsistency or hidden assumption that would reverse the viability tables is apparent.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper re-examines two-zero and one-zero textures (and, in appendices, the corresponding minors) of the Majorana neutrino mass matrix against NuFIT 6.0 oscillation parameters, Planck/ACT/DESI cosmological bounds on Σmi, the KATRIN kinematic limit, and current 0νββ limits. For two-zero textures the standard algebraic relations (Eqs. 2.7–2.22) are solved after fixing θ12, θ13 and the mass-squared differences to NuFIT best-fit values; under the CMB-only sum bound several textures (A1, A2 and the B-series for NO; B1, B3, C for IO) remain viable, while the stronger CMB+BAO bound leaves only A1 and A2 (NO). One-zero textures are explored with conditional flow matching (Sec. 3.1) and cross-checked by triangle-inequality analytics (Eq. 3.10, Sec. 3.2–3.3); several structures survive and yield distinct ranges for Σmi, meff_νe, ⟨mee⟩ and δCP (Tables 7–9). A short model-building section shows how the surviving one-zero patterns can arise from non-invertible selection rules obtained by Z2 or Z3 gauging of cyclic groups.","tokens_in":27510,"tokens_out":1124,"duration_ms":10771,"significance":"The work supplies a timely, comprehensive update of the classic two-zero texture classification under the latest DESI BAO+CMB mass-sum bounds and extends the analysis to one-zero textures with a modern generative-AI sampler that is validated against analytic inequalities. The resulting viability tables and the characteristic δCP islands of the B-series (and of H1, H2 in IO) are concrete, experimentally testable predictions that can be confronted by next-generation 0νββ experiments and by improved cosmological measurements. The non-invertible-selection-rule constructions further connect the phenomenological classification to a concrete ultraviolet origin. These features make the paper a useful reference for both model builders and experimentalists.","major_comments":[{"comment":"Secs. 2.1 and 3.2 fix θ12, θ13 and the mass-squared differences to NuFIT 6.0 central values when solving the two-zero algebraic constraints and when constructing the one-zero triangle inequalities. While the surviving A-series textures lie comfortably inside the allowed mass-sum window and the one-zero flow-matching samples already scan θ23/δCP over 3σ ranges, a quantitative estimate of how the 3σ correlations among the fixed inputs shift the viability boundaries (especially for the B-series under the CMB-only cut) is missing. A short sensitivity check or a Monte-Carlo variation of the fixed parameters would make the robustness of Tables 3 and 7 fully transparent.","section":null},{"comment":"The flow-matching pipeline (Sec. 3.1.1) employs a transformer with fixed hyperparameters and a multi-round fine-tuning schedule whose χ² thresholds are structure-dependent. Although the final samples are required to satisfy χ² < 45 on the five NuFIT observables and are cross-checked by the analytic inequalities, no ablation or comparison with a simpler sampler (e.g., nested sampling or a plain MCMC) is provided. A brief demonstration that the reported viable regions are stable under reasonable changes of network architecture or fine-tuning schedule would strengthen confidence that the exclusions in Table 7 are not artifacts of the generative model.","section":null}],"minor_comments":[{"comment":"Table 3 and the surrounding text use both “CMB” and “CMB+BAO”; a single consistent acronym (e.g., “Planck+ACT+DESI”) would avoid ambiguity with the pure CMB bound of Eq. (2.23).","section":null},{"comment":"In Figs. 1–2 and 13–19 the green/yellow bands for δCP are taken from the NuFIT 3σ ranges, yet the red prediction curves sometimes extend outside those bands; a short sentence clarifying that the curves are pure texture predictions (not constrained by the δCP measurement) would help the reader.","section":null},{"comment":"Appendix B, Table 12: the caption still says “texture” in a few places where “minor” is intended; likewise Table 14 header.","section":null},{"comment":"Sec. 4.1, Eq. (4.4): the fusion rule is written without multiplicities; a parenthetical remark that multiplicities are suppressed (as later noted for the Z3 case) would improve clarity.","section":null},{"comment":"References [36] and [37] cite DESI and KATRIN results that appeared after the NuFIT 6.0 release; a brief note on whether the oscillation parameters remain consistent with those newer data sets would be useful.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is a solid, incremental update that fits well in a standard hep-ph journal. The two major points are easily addressable and do not threaten the central claim. I see no novelty or citation issues that would require editorial attention."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This is a careful, usable update of the texture-zero program. Under the DESI BAO+CMB mass-sum cut only the two-zero A1 and A2 patterns remain viable in normal ordering; several one-zero textures still work and give concrete ranges for Σmi, meff_νe, ⟨mee⟩ and δCP (Tables 3, 7–9). That is the headline result model builders will actually use.\n\nWhat is new is the combination: a full two-zero re-analysis with NuFIT 6.0 and the latest cosmology, a first comprehensive flow-matching scan of all one-zero textures (with χ² filtering and fine-tuning), and explicit class assignments that realize the G- and H-series from Z2-gauging of Z5 and Z3-gauging of Z7. The two-zero algebra is standard and correctly applied; the one-zero ML results are cross-checked against the triangle-inequality analytics in Sec. 3.2–3.3 and agree on the preferred δCP islands for H1/H2 in inverted ordering. Circularity is low—viability is judged against external NuFIT, Planck/ACT/DESI, KATRIN and 0νββ limits, not fitted to the same quantities used as labels.\n\nSoft spots are real but secondary. Fixing θ12, θ13 and the Δm² to NuFIT best-fits when solving the two-zero equations and the one-zero inequalities is a simplification; the solutions are continuous in those inputs and the surviving A-series sit comfortably inside the mass-sum window, so the viability tables are unlikely to flip. No code or training data for the flow-matching pipeline is released, which limits independent checks of the generative step. The two-zero part is incremental relative to recent Asai et al. updates; the non-invertible constructions are useful but secondary.\n\nThis is for people who build or constrain neutrino mass matrices and for experimentalists planning 0νββ and long-baseline runs. The math, data handling and citation pattern look solid. I would send it to peer review; a referee can ask for fuller uncertainty propagation and code release without the paper needing to be rewritten. Worth engaging if you work on textures or non-invertible flavor.","headline":"Clean update of texture zeros under NuFIT 6.0 + DESI: only A1/A2 two-zeros survive CMB+BAO; one-zero scan with flow matching plus non-invertible constructions is the real addition.","tokens_in":28155,"tokens_out":590,"would_cite":true,"duration_ms":6062,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Stronger cosmological mass bounds leave only two two-zero neutrino textures viable; one-zero patterns still work and give distinct, testable predictions.","keywords":["neutrino mass matrix","texture zeros","two-zero textures","one-zero textures","cosmological mass sum","neutrinoless double-beta decay","flow matching","non-invertible selection rules"],"falsifier":"A future determination of δ23 and δCP that falls outside the narrow bands predicted by A1 or A2 (or outside the δCP ≈ π/2, 3π/2 islands preferred by the B-series and by H1/H2 inverted-ordering one-zero textures), or a cosmological mass-sum bound tighter than the A-series predictions, would rule out the surviving patterns.","tokens_in":28153,"feed_emoji":"⚛️","tokens_out":748,"duration_ms":6961,"temperature":0.7,"pith_summary":"The paper re-examines every one-zero and two-zero pattern in the neutrino mass matrix against the newest oscillation data, the cosmological upper limit on the sum of neutrino masses, the laboratory bound on the electron-neutrino mass, and the non-observation of neutrinoless double-beta decay. With only the older CMB mass-sum bound, several two-zero textures (especially the B-series) survive and force the Dirac CP phase near π/2 or 3π/2 while predicting sizable effective Majorana masses that future double-beta experiments can reach. Once the tighter CMB+BAO limit is imposed, only the two A-series textures remain allowed for normal ordering. The authors therefore turn to the less restrictive one-zero textures, using flow-matching generative networks together with analytic inequalities to map the still-viable patterns. Those patterns yield characteristic windows for the mass sum, the effective electron-neutrino mass, the Majorana mass, and the CP phase. Finally they show that the surviving one-zero zeros can be generated by non-invertible selection rules that ordinary group symmetries cannot produce.","feed_headline":"Only two two-zero neutrino textures survive tighter mass bounds","feed_subtitle":"One-zero patterns remain allowed and give distinct, testable ranges for CP phase and double-beta rates","key_machinery":"The two-zero algebraic relations that fix mass ratios and Majorana phases once four oscillation parameters are set to NuFIT best-fit values, together with flow-matching generative sampling of the eleven-parameter one-zero mass matrices constrained by the same data and by cosmological mass-sum inequalities.","core_discovery":"Under the DESI BAO+CMB bound on the sum of neutrino masses, the only two-zero textures still compatible with data are A1 and A2 in normal ordering; several one-zero textures remain allowed and produce distinct, experimentally accessible ranges for Σmi, meff_νe, ⟨mee⟩ and δCP.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Only A1 and A2 two-zero textures survive DESI BAO+CMB mass bounds","Tighter sum-of-masses limit rules out all but A-series two-zero textures","One-zero neutrino textures still allowed with distinct Σm and δCP ranges","Flow matching isolates viable one-zero patterns under current data","B-series two-zero textures excluded once CMB+BAO bound is imposed"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The analysis freezes the three best-measured oscillation parameters and the two mass-squared differences at their NuFIT central values instead of scanning their full correlated uncertainties.","fun_headline_variants_meta":{"raw":{"variants":["Only A1 and A2 two-zero textures survive DESI BAO+CMB mass bounds","Tighter sum-of-masses limit rules out all but A-series two-zero textures","One-zero neutrino textures still allowed with distinct Σm and δCP ranges","Flow matching isolates viable one-zero patterns under current data","B-series two-zero textures excluded once CMB+BAO bound is imposed"]},"model":"grok-4.5","effort":"low","cost_usd":0.005378,"raw_usage":{"total_tokens":1463,"prompt_tokens":802,"num_sources_used":0,"completion_tokens":90,"cost_in_usd_ticks":53780000,"prompt_tokens_details":{"text_tokens":802,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":571,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":802,"tokens_out":90,"duration_ms":4735,"temperature":1.0,"reasoning_tokens":571,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T08:19:22.815935+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A future determination of δ23 and δCP that falls outside the narrow bands predicted by A1 or A2 (or outside the δCP ≈ π/2, 3π/2 islands preferred by the B-series and by H1/H2 inverted-ordering one-zero textures), or a cosmological mass-sum bound tighter than the A-series predictions, would rule out the surviving patterns.","supporting_citations":[],"review_version":1}