{"id":"d0b94034-f3db-4950-83f9-d7a65a4a95bc","arxiv_id":"1908.08387","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"Planck-scale corrections to a Co-bimaximal neutrino mass matrix are reported to predict neutrino masses of 10^-5 to 10^-3 eV, but the calculations contain internal contradictions.","lead":"This paper calculates how quantum-gravity effects at the Planck scale would alter neutrino masses and mixing under the Co-bimaximal pattern, yielding tiny neutrino masses above the GUT scale. A generalist might read it to see whether Planck-scale physics can leave an observable imprint in neutrino oscillations, but the paper's numbers contradict themselves.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's claimed Planck-scale shift of Δ21 relies on a 2 eV degenerate mass, but the output masses near 10^-4 eV make the same correction negligible; the central prediction is not self-consistently derived.","rationale":"The paper's central claim is that Planck-scale terms add a dimension-5 operator correction that shifts Δ21 into the experimentally allowed region for Co-bimaximal mixing. The argument has two load-bearing pillars: (i) the zeroth-order masses are nearly degenerate with a common mass near 2 eV, making the correction terms in Eq. (14) of order 10^-5 eV^2; and (ii) the output masses are computed from Eqs. (19)-(21) using the modified angle θ'12. The first pillar is directly contradicted by the paper's own outputs: if the final masses are about 10^-4 eV, then the same correction is negligible and no meaningful shift in Δ21 occurs. The second pillar is independently problematic because Eqs. (19)-(21) neither reproduce Δ21 = m_2^2 - m_1^2 nor match the tabulated masses when the stated inputs are used. I do not see a reinterpretation of phases or normalizations that rescues the central claim. The reader's REJECT verdict with high confidence is consistent with these mechanical checks. I found no machine-checked proof, reproducible code, or independent numerical artifact that would support the tables. The most honest assessment is that the internal inconsistency is decisive.","tokens_in":6260,"tokens_out":5925,"duration_ms":57453,"concrete_test":"Recompute the section-3 calculation literally: fix U for Co-bimaximal angles θ13 = 10°, θ23 = 45°, θ12 = 34°, δ = ±π/2, fix M_1 = M_2 = M_3 = 2 eV, and take λ as the 3×3 all-ones matrix. Compute m = μ U^T λ U with μ = 2.5×10^-6 eV, then evaluate Eq. (14): Δ'21 = Δ21 + 2(M_1 Re(m_11) - M_2 Re(m_22)), and also the first-order masses M_i + Re(m_ii). If Δ'21 is not in the experimental range, or if the corrected masses are not near 2 eV, the claimed mechanism fails. Separately, plug Δ'21 = 8×10^-5 eV^2 and θ12 = 34° into Eq. (20); if the result does not match Table 1, the mass-extraction equations are inconsistent with the stated inputs.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3 assumes a common degenerate mass of 2 eV, and this is the only reason the perturbation term in Eq. (14) is non-negligible. With m_ii ≈ μ = v^2/M_pl = 2.5×10^-6 eV and M_i ≈ 2 eV, the correction 2(M_i Re(m_ii) - M_j Re(m_jj)) is about 1×10^-5 eV^2, a meaningful fraction of Δ21 = 8×10^-5 eV^2. But the masses reported in Tables 1-2 and quoted in the abstract are m'_i ≈ 10^-5 to 10^-4 eV. For m ~ 10^-4 eV the same correction is about 5×10^-10 eV^2, four orders of magnitude below Δ21, so the claimed shift cannot occur. The paper never evaluates Δ'21 from Eq. (14); instead it obtains masses from Eqs. (19)-(21), which are numerically incompatible with the stated Δ21: with θ12 = 34°, Eq. (20) gives m'_2 = sqrt(cos^2(θ12) Δ'21) ≈ 0.007 eV if Δ'21 = 8×10^-5 eV^2, not the table's 10^-4 eV. Additionally, Eqs. (1)-(3) imply m_2^2 - m_1^2 = cos(2θ12) Δ21, not Δ21. Thus the central numerical claim rests on an internally contradictory use of the degenerate-mass assumption.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that Planck-scale effects, encoded in a dimension-5 SU(2)_L x U(1)-invariant operator with a flavor-blind coupling matrix, perturb a zeroth-order neutrino mass matrix that has Co-bimaximal mixing. Assuming a common degenerate neutrino mass of 2 eV just above the electroweak scale, the author claims that the modified mass-squared difference Delta'_21 is shifted by an amount large enough to be consistent with solar neutrino data, and obtains modified neutrino masses above the GUT scale. The central numerical claims are the ranges m'_1 ~ 0.00001-0.00003 eV, m'_2 ~ 0.00008-0.00012 eV, and m'_3 ~ 0.000207-0.000320 eV stated in the abstract and conclusions, with detailed values in Tables 1 and 2.","tokens_in":6700,"tokens_out":4615,"duration_ms":42984,"significance":"If the central claim were correct, the paper would demonstrate that quantum-gravitational corrections can leave a measurable imprint on the neutrino mass spectrum, specifically on Delta_21, without spoiling the smallness of Delta_31. The conceptual setup, treating the Weinberg-type operator as a perturbation of a GUT-scale mass matrix, is a standard and potentially interesting framework. However, the manuscript's numerical results are internally inconsistent: the defining equations do not reproduce the claimed mass differences, the abstract and tables disagree by a factor of 10 for m'_3, and the 2 eV degeneracy assumption is contradicted by the output masses. The proposed prediction is therefore not established, and the main claim cannot be accepted as presented.","major_comments":[{"comment":"Equations (1) and (2) do not satisfy the defining relation m_2^2 - m_1^2 = Delta_21. Substituting them gives m_2^2 - m_1^2 = [(cos^4(theta12) - sin^4(theta12))/cos^2(theta12)] Delta_21 = cos(2 theta12) Delta_21, which equals Delta_21 only for theta12 = 0. Thus the paper's starting point for absolute mass extraction is algebraically incorrect, and any masses derived from these formulas are not reliable.","section":"§1, Eqs. (1)-(3)"},{"comment":"The abstract and conclusions state m'_3 ~ 0.000207-0.000320 eV, while Tables 1 and 2 list m'_3 in the range 0.00246-0.00320 eV. This factor-of-10 discrepancy is unexplained and leaves the paper's central prediction ambiguous. The table values are also not obtained from the stated formulas: for theta12 = 34 deg, Eq. (20) gives m'_2 = sqrt(cos^2(theta12) Delta'_21) ~ 0.007 eV, not the tabulated ~0.0001 eV, and Eq. (21) gives an even larger m'_3.","section":"Abstract and Conclusions vs. Tables 1-2"},{"comment":"The paper assumes a common degenerate mass of 2 eV just above the electroweak scale, and this assumption is what makes the Planck-scale correction in Eq. (14), of order 2 M_i Re(m_ii) ~ 1e-5 eV^2, comparable to Delta_21 = 8e-5 eV^2. But the masses actually reported in Tables 1 and 2 are of order 1e-4 eV. If the true masses were 1e-4 eV, the same correction would be about 5e-10 eV^2, four orders of magnitude below Delta_21, so the claimed Planck-scale shift would be negligible. The paper never evaluates Delta'_21 from Eq. (14); it instead substitutes the experimental Delta_21 into Eqs. (19)-(21), so the central 'large shift' claim is not self-consistently derived.","section":"§3, degenerate-mass assumption and Eq. (14)"},{"comment":"The final masses are essentially rearrangements of the experimental inputs Delta_21 and Delta_32, not independent predictions. Equation (20) is m'_2^2 = [cos^4(theta12)/cos^2(theta12)] Delta'_21, and Eq. (21) adds Delta'_32; using the stated inputs with theta12 = 34 deg yields m'_2 ~ 7.4e-3 eV and m'_3 ~ 4.4e-2 eV, in strong disagreement with the tabulated values. The paper also does not report any value of Delta'_21 obtained from Eq. (14), so the claim that the correction brings Delta'_21 into the experimentally accepted region is unsupported.","section":"§3, Eqs. (19)-(21)"}],"minor_comments":[{"comment":"There are numerous typographical errors, including 'non-reormalizable', 'phenemenon', 'Supper-Kmaiokande', and the equation label 'Eq. (4.0)'; a careful proofread is needed.","section":"Throughout"},{"comment":"Units are missing for m'_2 in the abstract, and m'_3 is written as '0.000207eV-000320eV' without the leading zero; the notation should be made uniform.","section":"Abstract and Tables"},{"comment":"No uncertainties or experimental error bars are quoted for Delta_21, Delta_31, theta12, or theta13, so it is impossible to assess whether the predicted mass ranges are statistically consistent with the input data.","section":"Numerical results"},{"comment":"The captions say the tables list 'the modified neutrino mass square difference term', but the columns contain mass eigenvalues in eV; the captions and column headers should describe the content accurately.","section":"Tables 1 and 2 captions"},{"comment":"Reference [6] is cited for the CHOOZ bound on theta13, but the bibliographic details appear incorrect or incomplete; all references should be checked against the original sources.","section":"References"}],"recommendation":"reject","confidential_remarks":"The manuscript contains load-bearing algebraic errors and internal contradictions that undermine the central numerical claim. The most serious issue is the inconsistency between the 2 eV degeneracy assumption and the output masses of order 1e-4 eV, which invalidates the claimed Planck-scale correction to Delta_21. I do not see a path to repair this within the scope of the present text."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, quick take on 1908.08387. The paper applies an existing perturbation formalism (from Koranga's earlier papers) to Ma's Co-bimaximal mixing pattern, claiming that Planck-scale effects shift Δ21 into the experimental range for a 2 eV degenerate neutrino mass. That is a legitimate exercise, but the numbers do not hold up.\n\nWhat's new: not much. The mechanism is recycled from refs [12-14]; the Co-bimaximal zeroth-order mixing is from Ma [18]. Applying an old calculation to a different mixing pattern is routine. No new derivation, no new data, no error analysis. The paper is readable and honest in its citations.\n\nThe soft spots are load-bearing. Eqs. (1)-(3) are supposed to give absolute masses from Δ21, but they imply m2^2 - m1^2 = (cos2θ12/cos^2θ12) Δ21 ≈ 0.55 Δ21, not Δ21. So the mass formulas are wrong from the start. More seriously, the abstract and Table 1 disagree on m3' by a factor of 10: abstract says 0.000207-0.000320 eV, tables list 0.00246-0.00320 eV. The conclusions repeat the abstract. That is an internal inconsistency a referee would catch immediately.\n\nThe central claim fails on its own logic. Section 3 assumes a common degenerate mass of 2 eV to make the perturbation term in Eq. (14) non-negligible (~10^-5 eV^2). But the masses finally reported are ~10^-4 eV; for those masses the same correction is ~10^-10 eV^2, four orders of magnitude too small. The paper never actually evaluates Δ'21 from Eq. (14) and shows the shift. It just uses Eqs. (19)-(21), which are rearrangements of the input Δ21, and reports masses that do not even reproduce Δ21 = 8×10^-5 eV^2: with θ12 = 34°, Eq. (20) gives m2' ≈ 0.007 eV, not the table's 10^-4 eV. So the claimed prediction is not self-consistently derived.\n\nWho is this for? Only someone studying Planck-scale corrections to neutrino mass matrices from this specific author. It is not a serious contribution to quantum gravity or neutrino physics as it stands. I would desk reject it; it does not deserve referee time. If the author fixes the algebra and actually evaluates Eq. (14), it might be a marginal phenomenological note, but this version is not worth spending referees' time on.","headline":"The paper's Planck-scale shift of Δ21 relies on a 2 eV degenerate mass that its own output masses contradict; the algebra and tables are internally inconsistent.","tokens_in":7127,"tokens_out":3592,"would_cite":false,"duration_ms":30668,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["14.60.Pq","04.60.-m"],"model":"deepseek-v4-flash","headline":"Planck-scale corrections to the neutrino mass matrix shift the solar splitting into the accepted range and set absolute masses near $10^{-4}$ eV.","keywords":["neutrino masses","neutrino mixing","Co-bimaximal mixing","dimension-five operator","Planck-scale corrections","quantum gravity","solar mass-squared difference","degenerate neutrinos"],"falsifier":"A tritium $\\beta$-decay endpoint measurement that pushes the upper bound on the effective electron-neutrino mass below about $1$ eV would remove the $2$ eV degeneracy and shrink the Planck-scale shift below the size needed to move $\\Delta_{21}$; that measurement would settle whether the predicted spectrum can survive.","tokens_in":6105,"feed_emoji":"🌌","tokens_out":16204,"duration_ms":130997,"temperature":0.7,"pith_summary":"The paper aims to show that Planck-scale quantum gravity, encoded in a dimension-five neutrino–Higgs operator, can leave a measurable mark on neutrino oscillation: starting from a Co-bimaximal mixing pattern and nearly degenerate masses just above the electroweak scale, the correction shifts the solar mass-squared difference into the experimentally accepted range and fixes the absolute neutrino masses above the grand-unified-theory (GUT) scale. With a common degenerate mass of $2\\,\\text{eV}$, the predicted spectrum is $m_1'\\simeq0.00001\\text{--}0.00003$ eV, $m_2'\\simeq0.00008\\text{--}0.00012$ eV, and $m_3'\\simeq0.000207\\text{--}0.000320$ eV. This matters because absolute neutrino masses are otherwise hard to predict, and quantum-gravity corrections are usually dismissed as far too small to affect oscillation experiments. If the claim is correct, the solar sector is where Planck-scale physics first becomes observable.","feed_headline":"Quantum gravity corrections predict neutrino masses near 0.0001 eV","feed_subtitle":"A Planck-scale dimension-5 term shifts the solar splitting into the accepted range without moving the atmospheric one.","key_machinery":"The load-bearing object is the effective dimension-five operator $L_{\\rm grav}=\\frac{\\lambda_{\\alpha\\beta}}{M_{\\rm pl}}(\\psi_{A\\alpha}\\epsilon\\psi_C)C^{-1}_{ab}(\\psi_{B\\beta}\\epsilon\\psi_D)+h.c.$, which after electroweak symmetry breaking becomes the neutrino mass term $\\mu\\lambda$ with $\\mu=v^2/M_{\\rm pl}=2.5\\times10^{-6}\\,\\text{eV}$; assuming flavor blindness makes $\\lambda$ a matrix of ones. The argument then runs through two perturbative formulas: the first-order shift in mass-squared differences, $\\Delta M'^2_{ij}=\\Delta M^2_{ij}+2(M_i\\operatorname{Re}(m_{ii})-M_j\\operatorname{Re}(m_{jj}))$, and the correction $\\delta\\theta_{ij}$ to the mixing matrix, both controlled by $m=\\mu U^t\\lambda U$. These corrected quantities are inserted into Eqs. (19)–(21) to produce the predicted absolute masses.","core_discovery":"The central discovery is a predicted spectrum, not a measurement: when the flavor-blind Planck-scale mass matrix $\\mu\\lambda$ with $\\mu=v^2/M_{\\rm pl}=2.5\\times10^{-6}\\,\\text{eV}$ is added as a perturbation to the GUT-scale Co-bimaximal mass matrix, the modified eigenvalues above the GUT scale fall in the ranges $m_1'\\simeq0.00001\\text{--}0.00003$ eV, $m_2'\\simeq0.00008\\text{--}0.00012$ eV, and $m_3'\\simeq0.000207\\text{--}0.000320$ eV. The perturbation shifts the solar splitting by an amount comparable to $\\Delta_{21}\\simeq8\\times10^{-5}\\,\\text{eV}^2$, so the final $\\Delta'_{21}$ remains inside the experimentally accepted region, while the atmospheric splitting $\\Delta_{31}$ changes negligibly. This happens for the Co-bimaximal texture defined by $\\theta_{13}\\neq0$ (about $10^\\circ$), $\\theta_{23}=\\pi/4$, $\\tan^2\\theta_{12}=(1-3\\sin^2\\theta_{13})/2$ (about $34^\\circ$), and Dirac phase $\\delta=\\pm\\pi/2$, with the input masses assumed nearly degenerate at $2\\,\\text{eV}$.","pith_inferences":["A natural next step the paper does not take is to run the same perturbation with a non-degenerate starting spectrum ($m_1\\simeq0$, $m_2\\simeq\\sqrt{\\Delta_{21}}$, $m_3\\simeq\\sqrt{\\Delta_{31}}$); the Planck-scale terms would then be roughly two orders of magnitude too small to shift $\\Delta_{21}$, which would show that the near-degeneracy at $2\\,\\text{eV}$, not the Co-bimaximal texture alone, does t","The abstract and conclusions quote $m_3'$ around $0.0002\\text{--}0.0003$ eV, while the table entries for $m_3'$ are around $0.0025\\text{--}0.0032$ eV; reconciling this numerical spread would clarify which range is the paper's prediction.","The same flavor-blind perturbation could be applied to other zeroth-order textures, such as tribimaximal or bimaximal mixing, to see whether the selective shift of $\\theta_{12}$ is generic or specific to Co-bimaximal mixing."],"forward_implications":["If the prediction is right, Planck-scale physics shows up first in the solar sector: $\\Delta'_{21}$ shifts enough to stay inside the accepted oscillation region while $\\Delta'_{31}$ is essentially unchanged.","The absolute mass scale above the GUT scale becomes fixed near $10^{-4}$ eV for all three states, a range that future beta-decay and cosmological probes of the neutrino mass sum can confront.","Because the correction is flavor blind, the conclusion does not depend on the detailed GUT-scale physics that generates the zeroth-order matrix, as long as all Planck-scale couplings are of order one.","Majorana phases $a_1$ and $a_2$ scan the allowed ranges in Tables 1 and 2, so the prediction can in principle be sharpened once neutrinoless double-beta decay constrains those phases."],"supporting_citations":[{"why":"Supplies the dimension-five neutrino–Higgs operator whose electroweak symmetry breaking creates the Planck-scale mass correction.","marker":"[11]"},{"why":"Defines the Co-bimaximal mixing pattern with θ13≠0, θ23=π/4, tan²θ12=(1−3 sin²θ13)/2, and δ=±π/2, the zeroth-order input for the calculation.","marker":"[18]"},{"why":"Provides the tritium beta-decay upper bound near 2 eV that motivates the nearly degenerate common mass.","marker":"[15]"},{"why":"Gives the measured solar mass-squared difference Δ21=0.00008 eV² used as input.","marker":"[17]"},{"why":"Gives the measured atmospheric mass-squared difference Δ31=0.002 eV² used as input.","marker":"[16]"},{"why":"Provides the earlier perturbative framework for how Planck-scale corrections change neutrino mixing angles.","marker":"[13]"},{"why":"Supplies the first-order formulas for modified mass-squared differences and mixing corrections used in Eqs. (14) and (15).","marker":"[10]"},{"why":"Supplies the hermitian correction matrix δθ that encodes the first-order change in the mixing matrix.","marker":"[12]"},{"why":"Establishes the experimentally accepted region into which the corrected Δ'21 is claimed to fall.","marker":"[19]"}],"fun_headline_variants":["Quantum gravity predicts neutrino masses near 0.0001 eV","Planck-scale term sets neutrino spectrum in predicted range","Co-bimaximal mixings yield masses from quantum gravity","Quantum gravity fixes solar splitting without moving atmospheric","Dimension-5 operator from Planck scale pins neutrino masses"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that just above the electroweak scale the three neutrino masses are nearly degenerate at a common mass of about $2\\,\\text{eV}$, because only then do the Planck-scale correction terms (about $10^{-5}\\,\\text{eV}^2$) become comparable to the solar splitting $\\Delta_{21}\\simeq8\\times10^{-5}\\,\\text{eV}^2$.","fun_headline_variants_meta":{"raw":{"variants":["Quantum gravity predicts neutrino masses near 0.0001 eV","Planck-scale term sets neutrino spectrum in predicted range","Co-bimaximal mixings yield masses from quantum gravity","Quantum gravity fixes solar splitting without moving atmospheric","Dimension-5 operator from Planck scale pins neutrino masses"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000589,"raw_usage":{"total_tokens":2836,"prompt_tokens":1092,"completion_tokens":1744,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":708,"completion_tokens_details":{"reasoning_tokens":1666}},"tokens_in":708,"tokens_out":1744,"duration_ms":14879,"temperature":1.0,"reasoning_tokens":1666,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:46:45.991228+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A tritium $\\beta$-decay endpoint measurement that pushes the upper bound on the effective electron-neutrino mass below about $1$ eV would remove the $2$ eV degeneracy and shrink the Planck-scale shift below the size needed to move $\\Delta_{21}$; that measurement would settle whether the predicted spectrum can survive.","supporting_citations":[{"cited_title":"Weinberg, Phys.Rev.Lett","cited_arxiv_id":null,"evidence_quote":"Supplies the dimension-five neutrino–Higgs operator whose electroweak symmetry breaking creates the Planck-scale mass correction."},{"cited_title":"B755 (2016) ,348-350","cited_arxiv_id":null,"evidence_quote":"Defines the Co-bimaximal mixing pattern with θ13≠0, θ23=π/4, tan²θ12=(1−3 sin²θ13)/2, and δ=±π/2, the zeroth-order input for the calculation."},{"cited_title":"Kraus etal., Eur.Phys.J","cited_arxiv_id":null,"evidence_quote":"Provides the tritium beta-decay upper bound near 2 eV that motivates the nearly degenerate common mass."},{"cited_title":"Araki etal., Phys","cited_arxiv_id":null,"evidence_quote":"Gives the measured solar mass-squared difference Δ21=0.00008 eV² used as input."},{"cited_title":"hosaka etal., Phys","cited_arxiv_id":null,"evidence_quote":"Gives the measured atmospheric mass-squared difference Δ31=0.002 eV² used as input."},{"cited_title":"Uma Sankar,Phys.Lett.B665, 63 (2008)","cited_arxiv_id":null,"evidence_quote":"Provides the earlier perturbative framework for how Planck-scale corrections change neutrino mixing angles."},{"cited_title":"Vissani etal., Phys.Lett","cited_arxiv_id":null,"evidence_quote":"Supplies the first-order formulas for modified mass-squared differences and mixing corrections used in Eqs. (14) and (15)."},{"cited_title":"Uma Sankar, Fi zika B18:219-226,2009","cited_arxiv_id":null,"evidence_quote":"Supplies the hermitian correction matrix δθ that encodes the first-order change in the mixing matrix."},{"cited_title":"56 (2017) no.1 1, 3508-3513 10","cited_arxiv_id":null,"evidence_quote":"Establishes the experimentally accepted region into which the corrected Δ'21 is claimed to fall."}],"review_version":1}