{"id":"bf0c0b84-20d6-4f1e-8c8e-22c059da5e09","arxiv_id":"2502.09333","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"A non-renormalizable SU(5) model with 10S and 35S scalars claims to unify couplings above 1.4e16 GeV while generating radiative neutrino masses via leptoquark mixing and predicting a 1-10 TeV color sextet.","lead":"This paper builds a non-supersymmetric SU(5) grand unified theory with two extra scalar multiplets and generates neutrino masses through leptoquark mixing. It derives mass constraints and claims a 1-10 TeV color-sextet scalar, but that scalar's mass is placed by hand rather than predicted.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Omitted dimension-5 scalar mass operators admitted after Eq. (30) can shift the split masses that set the GUT scale, so the claimed MGUT > 1.4e16 GeV and the Mν–MD relation are not yet established.","rationale":"The central claim has two pillars: the radiative neutrino mass relation Mν ∝ M_D and the unification scale MGUT > 1.4e16 GeV. The unification calculation is driven by threshold corrections from the split multiplets of 10S and 35S, especially η2 and η3. The paper explicitly admits, immediately after Eq. (30), that dimension-5 operators giving mass to 10S and 35S 'must be included for consistency' but are not listed. Quantitatively, a generic dimension-5 scalar mass operator contributes δm² ~ v24^3/Λ ~ 4e30 GeV² for Λ = M_Pl, which would shift the 1 TeV η3 mass by fifteen orders of magnitude unless the coefficient is tuned below ~1e-24. Even if the renormalizable parameters can be readjusted to restore the intended spectrum, the omitted operators can also introduce S1*–η2 mixing that is absent at the renormalizable level, changing the neutrino mass matrix and proton decay. Thus the omitted operators directly threaten both pillars of the abstract. I considered the reader's other concern about Eq. (15); the printed fraction is ambiguous, and even a factor-of-2π error would shift the leptoquark mass bound without necessarily destroying the unification claim, so the dimension-5 omission is the more load-bearing issue. The reader's weakest assumption identifies exactly this problem, and the requested conditional revision matches what is needed: list or bound the omitted operators and recompute the claimed scales. No new evidence in the manuscript, such as machine-checked proofs or reproducible code, mitigates this gap.","tokens_in":20887,"tokens_out":15136,"duration_ms":159491,"concrete_test":"Construct the complete basis of SU(5)-invariant dimension-5 operators bilinear in {5H, 10S, 35S} and involving 24H, including 10S†10S 24H^3/Λ, 35S†35S 24H^3/Λ, and any operator mixing S1* with η2 (e.g., 35S 5H* 5H* 24H/Λ if invariant). Set Λ = M_Pl, scan coefficients over [-1,1], and recompute the split masses and two-loop unification for the scenarios of Tables 2 and 3. If keeping m_{η3} = 1 TeV requires |c| ≲ 1e-24, or if O(1) coefficients generate S1*–η2 mixing that changes Mν or the proton decay bound in Eq. (17), the central claims are not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper states after Eq. (30): 'we have not listed the dimension 5 operators giving mass to the 10S and 35S that must be included for consistency.' This is not a harmless omission. With <24H> ~ 3.6e16 GeV and cutoff Λ ≤ M_Pl, a generic operator such as 10S†10S 24H^3/Λ or 35S†35S 24H^3/Λ contributes δm² ~ v24^3/Λ ~ 4e30 GeV² after SSB, so even an O(1) coefficient moves m_{η3} from 1 TeV to ~1e15 GeV. The unification analysis in Tables 2 and 3 uses m_{η3} = 1 or 10 TeV and m_{η2} ~ 1e9–1e11 GeV as inputs to the two-loop threshold corrections; the omitted operators can change both, and therefore MGUT. They can also generate S1*–η2 mixing that the text argues vanishes at the renormalizable level (the epsilon 35 5H 5H term is zero by symmetry of the 35S), but no similar argument is given for the dimension-5 basis. Such mixing would give new contributions to neutrino mass and proton decay. Since the paper neither lists these operators nor shows that their coefficients are small, the two central claims—the leptoquark relation Mν ∝ M_D and MGUT > 1.4e16 GeV—are not yet supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a non-supersymmetric SU(5) grand unified theory whose field content is the Georgi-Glashow model plus scalar multiplets in the 10 and 35 representations, with non-renormalizable operators used to modify fermion masses. Neutrino masses are generated radiatively through the leptoquark mechanism, yielding a claimed relation between the Majorana neutrino mass matrix and the down-type quark mass matrix. From this relation the author derives an upper bound m_{S_1^*}, m_{\\widetilde R_2} ≤ 2.5×10^15 GeV, a lower bound m_{\\widetilde R_2} ≥ 2.1×10^9 GeV from proton decay, and a unification scale M_GUT ≥ 1.4×10^16 GeV, together with a predicted light color-sextet scalar η3 at 1 or 10 TeV.","tokens_in":21349,"tokens_out":9448,"duration_ms":88187,"significance":"If the claims were correct, the model would be a minimal non-supersymmetric GUT with radiative neutrino masses, a TeV-scale color sextet, and an explicit connection between neutrino and down-quark mass matrices—an attractive and nontrivial package. The paper does contain a two-loop unification analysis with threshold corrections and a transparent analytical derivation of the neutrino mass formula. However, the central quantitative claims are currently not established: there is a numerical inconsistency in the main neutrino-mass formula, an admitted omission of dimension-5 scalar-mass operators that can destroy the mass spectrum used in the unification analysis, and a 'prediction' for the η3 mass that is in fact an input. These issues affect the paper's headline results and require substantive revision.","major_comments":[{"comment":"The passage from Eq. (14) to Eq. (15) contains a numerical factor error. Using Eq. (4) with M_V = M_GUT gives v24 = M_GUT sqrt(3/(5π α_GUT)). Substituting into the coefficient of Eq. (14), the prefactor 3/(32π²) · (1/2) sqrt(5/6) v24 becomes 3 M_GUT/(64π²) · 1/sqrt(2π α_GUT). Equation (15), however, has 3 M_GUT/(64π²) · sqrt(2π)/sqrt(α_GUT), which is larger by a factor 4π. Consequently the upper bound m_{S_1^*}, m_{\\widetilde R_2} ≤ 2.5×10^15 GeV derived from Eq. (15) and any other quantitative use of this formula need to be recomputed. This is a load-bearing discrepancy, not a typographical nuance.","section":"Section 2, Eqs. (14) and (15) with Eq. (4)"},{"comment":"The text explicitly states: 'we have not listed the dimension 5 operators giving mass to the 10S and 35S that must be included for consistency.' This omission is not harmless. With <24H> ~ M_GUT ~ 10^16 GeV and cutoff Λ ≤ M_Pl, a generic operator such as 10S†10S 24H^3/Λ contributes δm² ~ v24^3/Λ ~ 10^29 GeV², which is sixteen orders of magnitude larger than m_η3 = 1–10 TeV and substantial compared to m_η2 ~ 10^9–10^11 GeV. Unless a symmetry forbids these operators or their coefficients are tuned to extreme smallness—neither of which is argued in the paper—the split masses in Eqs. (27), (29), and Tables 2–3 are not stable under the omitted operators. The unification threshold corrections, and therefore the claimed M_GUT ≥ 1.4×10^16 GeV, are not established. The same operators can also generate new baryon-number-violating couplings and additional leptoquark mixings, affecting the proton decay and neutrino mass calculations.","section":"Section 3, after Eq. (30)"},{"comment":"The abstract states as a prediction that the color sextet η3 has mass 1 TeV (10 TeV), but the body says: 'η3 prefers to be light, that is why we placed the mass of η3, which is the scale of new physics as well, at 1 (10) TeV.' The unification analysis in Tables 2 and 3 treats m_η3 as a free input and solves for m_η2 and M_GUT. For η3 to be a genuine prediction, the author must show that successful unification is possible only if m_η3 is in this range (e.g., that larger m_η3 pushes M_GUT below the proton-decay bound). As written, the headline 'prediction' is an assumption, which is a circularity in the argument.","section":"Abstract and Section 3, Tables 2–3"},{"comment":"The paper claims that the neutrino mass matrix from Eq. (14) can reproduce the observed neutrino oscillation parameters for both normal and inverted hierarchies, with couplings in the range 0.1 ≤ Y^ν, Y^D, λ_{5-10} ≤ sqrt(4π), but no explicit numerical fit is presented. The texture of M_ν in Eq. (15) is highly restricted (it is proportional to combinations of M_D and the Yukawa matrices), and it is far from obvious that the required mixing angles and mass-squared differences are attainable. A concrete point in parameter space, listing the Yukawa entries and the resulting PMNS parameters, is necessary to support this central claim.","section":"Section 2, after Eq. (16)"}],"minor_comments":[{"comment":"The word 'contrains' should be 'constrains'.","section":"Abstract"},{"comment":"The phrase 'This hiearchy holds' contains a typo: 'hiearchy' should be 'hierarchy'.","section":"Section 2"},{"comment":"The text contains 'parantheses' (should be 'parentheses') and the broken string 'MGU T' in the paragraph after Eq. (32).","section":"Section 3"},{"comment":"The use of the same symbol R_{-1/3} for the rotation matrix and for the 'b' decorated mass eigenstates is confusing; a clearer basis notation would help.","section":"Section 2, Eq. (11)"},{"comment":"The tables would be more informative if they included the values of α_GUT and the corresponding proton lifetime for each scenario, rather than only M_GUT and m_η2.","section":"Section 3, Tables 2–3"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a topic of current interest and the general construction is original, but the advertised predictions do not currently follow. The most serious problem is the omitted dimension-5 scalar-mass operators, which can shift the light η3 mass by many orders of magnitude; fixing this may require a new symmetry argument or a different model-building strategy rather than a simple numerical update. The author should also be asked to resolve the 4π discrepancy in the neutrino-mass formula and to provide an explicit neutrino-fit point. These are substantive but in principle addressable issues, hence major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read it. Short version: this is a serious new application of the leptoquark mechanism to a non-supersymmetric, non-renormalizable SU(5) model with 10S and 35S scalars, and the two-loop unification tables are real work. But the two headline numbers—m_eta3 at 1 or 10 TeV and MGUT above 1.4e16 GeV—are not yet established: one is an input, and the other depends on dimension-5 operators the authors explicitly say they omitted.\n\nWhat is new: the specific 10S+35S field content without extra fermions, the two-loop threshold analysis with split scalar multiplets, and updated bounds on the scalar leptoquark masses. The Mnu proportional to MD relation is a genuine consequence of the S1*-R2 mixing in this model, not a fitting assumption, and the lower bound on m_R2 from EW-mixing-induced proton decay is a nice application of the existing formula. The paper also credits the borrowed pieces clearly: leptoquark mechanism from [28,29], Ellis-Gaillard trick from [4].\n\nThe load-bearing soft spot is exactly what the stress-test note says. After Eq. (30) the authors state that dimension-5 operators giving mass to 10S and 35S \"must be included for consistency\" but are not listed. With v24 ~ 3.6e16 GeV and cutoff Lambda <= MPl, a generic term like 35S^dagger 35S 24H^3 / Lambda contributes delta m^2 ~ v24^3 / Lambda, at least ~4e30 GeV^2 and possibly much larger. That can move m_eta3 from 1 TeV to ~1e15 GeV, which destroys the threshold inputs used to obtain MGUT and could also generate new scalar mixings that feed back into neutrino mass and proton decay. This is a missing consistency condition, not a footnote. The authors know about it and chose not to deal with it; that choice is the main reason the central claims are conditional.\n\nMinor issues: the TeV color sextet is presented as a prediction but is set by hand (\"eta3 prefers to be light, that is why we placed it at 1 or 10 TeV\"). Also, no explicit neutrino parameter point is shown; the paper asserts that Yukawas in 0.1 to sqrt(4 pi) reproduce the oscillation data, but no texture or fit is displayed. That is a moderate gap for a model whose main observable is neutrino mass.\n\nOne reader-level red herring: Eq. (15) is not inconsistent with Eq. (14) plus Eq. (4). The prefactor converts v24 to MGUT via Eq. (4); the arithmetic works.\n\nWho gets value: GUT model builders working on radiative neutrino mass and scalar multiplets; the 35S split-mass tables and unified bounds are useful even if the model is provisional. It deserves a serious referee, and my recommendation would be major revision: list and bound the dimension-5 operators, show a neutrino fit, and stop calling an input a prediction. I would not cite it as a working model until then.","headline":"Serious new 10S+35S radiative GUT, but the TeV color sextet is an input and the omitted dimension-5 scalar mass operators can move it by fifteen orders of magnitude.","tokens_in":21924,"tokens_out":5502,"would_cite":false,"duration_ms":54060,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A non-supersymmetric SU(5) grand unified theory with scalar leptoquark mixing generates radiative Majorana neutrino masses tied to the down-type quark mass matrix and keeps the unification scale above $1.4\\times10^{16}$ GeV.","keywords":["grand unified theory","SU(5)","leptoquark mechanism","radiative neutrino mass","Majorana neutrino","proton decay","color sextet scalar","gauge coupling unification"],"falsifier":"Compute the threshold corrections from the omitted dimension-five mass operators of the $10_S$ and $35_S$, with order-one coefficients and a cutoff at the Planck scale; if they shift $B_{12}$ by more than about 1.25, the GUT scale drops below the proton-decay bound of $5.5\\times10^{15}$ GeV and the model fails.","tokens_in":20564,"feed_emoji":"⚛️","tokens_out":10150,"duration_ms":88931,"temperature":0.7,"pith_summary":"This paper constructs a grand unified theory without supersymmetry in which the only new ingredients beyond the Georgi-Glashow SU(5) model are two scalar multiplets, a 10 and a 35. Its central claim is that the mixing of the two scalar leptoquarks in these multiplets radiatively generates Majorana masses for neutrinos, and that this mechanism ties the neutrino mass matrix to that of down-type quarks. From that link, together with the requirement of perturbative couplings, the paper derives an upper bound of $2.5\\times10^{15}$ GeV on the leptoquark masses and, from the proton decay induced by leptoquark mixing, a lower bound of $2.1\\times10^9$ GeV on one of them. The same field content achieves gauge coupling unification at a scale above $1.4\\times10^{16}$ GeV, with a distinctive low-energy prediction of a color-sextet, weak isodoublet scalar at 1 or 10 TeV that has no tree-level couplings to Standard Model fermions. The paper matters because it shows that one of the simplest non-supersymmetric SU(5) extensions can simultaneously address neutrino masses, unification, and proton stability.","feed_headline":"Leptoquark loop ties neutrino masses to down quarks in SU(5)","feed_subtitle":"The non-supersymmetric model sets the unification scale above 10^16 GeV and predicts a 1 TeV color-sextet scalar.","key_machinery":"The central object is the leptoquark mixing between $S_1^*$, the color-triplet in the $5_H$, and $\\widetilde{R}_2$, the $(3,2,1/6)$ in the $10_S$, generated after electroweak symmetry breaking by the operator $\\lambda_{5-10}\\,10_S\\,5_H^*\\,5_H^*\\,24_H$. This mixing makes the scalar loop diagram that gives neutrinos their Majorana mass, and the resulting relation $M_\\nu \\propto \\lambda_{5-10}\\, M_D\\,(\\text{Yukawa combinations})$ is the paper's main identity; the paper uses it to bound the leptoquark masses and to compute the $B-L$ violating proton decay. A second key ingredient is the split-mass spectrum of the $35_S$ scalars, whose $\\eta_3$ multiplet is forced light (1--10 TeV) and whose other multiplets, together with the $10_S$ splits, adjust the running couplings so that unification occurs at a sufficiently high scale. The $\\eta_3$ is a color sextet, weak isodoublet with no tree-level fermion couplings, the model's distinctive new-physics signature.","core_discovery":"The paper establishes that the leptoquark mechanism of radiative Majorana neutrino mass, driven by electroweak mixing of the scalar leptoquarks $S_1^*$ (from the $5_H$) and $\\widetilde{R}_2$ (from the $10_S$), produces a neutrino mass matrix proportional to the down-type quark mass matrix $M_D$, up to Yukawa matrices and a loop factor. This proportionality, combined with perturbativity of the couplings, gives a common upper bound $m_{S_1^*},\\, m_{\\widetilde{R}_2} \\le 2.5\\times10^{15}$ GeV. The same mixing induces a $B-L$ violating s-channel proton decay, which forces $m_{\\widetilde{R}_2} \\ge 2.1\\times10^9$ GeV if the proton is to survive the Super-Kamiokande bounds. With the $35_S$ scalar's split multiplets, especially the light $\\eta_3$ and the heavier $\\eta_2$, the gauge couplings unify at two-loop order at a scale $M_{\\rm GUT} \\ge 1.42\\times10^{16}$ GeV, above the lower bound of $5.5\\times10^{15}$ GeV needed to avoid rapid proton decay, for all scenarios considered.","pith_inferences":["The proportionality of the neutrino mass matrix to the down-type quark mass matrix suggests that, within this framework, the atmospheric neutrino mass scale is essentially inherited from the bottom quark mass, so a precise measurement of the neutrino mixing pattern could probe the structure of the down-type Yukawa matrices beyond what the paper assumes.","The light color-sextet $\\eta_3$, despite having no tree-level fermion couplings, could be produced at colliders through its gauge and Higgs couplings, and its decay patterns would provide an indirect check of the leptoquark mixing parameters that govern proton decay.","Because the paper omits the dimension-five operators that give mass to the $10_S$ and $35_S$ scalars, a natural extension is to include them and re-run the unification analysis; if those operators are not suppressed at the Planck-scale cutoff, the claimed GUT scale window could shift or close.","The same leptoquark mechanism could be transplanted to other grand unified groups, such as SO(10), where the down-quark-neutrino connection might be constrained by additional gauge interactions and could sharpen or alter the upper bound on leptoquark masses."],"forward_implications":["The model predicts a color-sextet, weak isodoublet scalar $\\eta_3$ with a mass of 1 or 10 TeV and no tree-level couplings to Standard Model fermions, making it a concrete search target at the LHC and future colliders.","The neutrino mass matrix is, to good approximation, proportional to the down-type quark mass matrix, so the model generically predicts a strong hierarchy in neutrino masses tied to $m_b \\gg m_s \\gg m_d$ and can accommodate both normal and inverted ordering for particular choices of Yukawa couplings.","The $B-L$ violating proton decay mode induced by leptoquark mixing sets $m_{\\widetilde{R}_2} > 2.1\\times10^9$ GeV, so a lighter scalar would make the proton decay too fast; the bound tightens as the mixing grows.","Gauge coupling unification occurs at $M_{\\rm GUT}$ between $1.42\\times10^{16}$ and $4.53\\times10^{16}$ GeV in the scenarios tabulated, meaning gauge-boson-mediated proton decay is just beyond the current Super-Kamiokande limit and within reach of Hyper-Kamiokande.","The two-loop analysis fixes $\\eta_2$ at masses of order $10^9$--$10^{11}$ GeV for the chosen $\\eta_3$ masses, giving a well-defined intermediate mass scale."],"supporting_citations":[{"why":"Provides the Georgi-Glashow SU(5) model whose particle content is extended by the $10_S$ and $35_S$ scalars.","marker":"[1]"},{"why":"Supplies the nonrenormalizable operators used to repair the down-quark and charged-lepton mass ratios.","marker":"[4]"},{"why":"Gives the leptoquark-mediated neutrino mass formula that the paper adapts into its Eq. (12).","marker":"[28]"},{"why":"Is the grand-unified leptoquark mechanism construction whose mass estimates this paper refines.","marker":"[29]"},{"why":"Provides the proton decay amplitude formulas and the $B-L$ violating decay rate used for the lower bound on $m_{\\widetilde{R}_2}$.","marker":"[31]"},{"why":"Supplies the relations between weak-scale observables and effective beta coefficients used to derive the required $B_{12}$.","marker":"[32]"},{"why":"Sets the experimental lower bound on the proton lifetime that fixes the GUT scale floor.","marker":"[34]"},{"why":"Sets the proton lifetime bound used to update the lower limit on the $S_1^*$ mass.","marker":"[35]"},{"why":"Gives the upper bounds on partial proton decay rates converted into the GUT scale lower bound.","marker":"[37]"},{"why":"Provides the sum rule $m^2_{\\eta_4} = m^2_{\\eta_1} - 3m^2_{\\eta_2} + 3m^2_{\\eta_3}$ that constrains the $35_S$ split masses.","marker":"[39]"}],"fun_headline_variants":["Leptoquark loop links neutrino masses to down quarks in GUT","Leptoquark mechanism sets neutrino masses via down-quark link","SU(5) GUT with leptoquarks unifies above 10^16 GeV, predicts 1 TeV scalar","Non-renormalizable SU(5) ties neutrino mass to down quarks"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the dimension-five operators that are not written down in the paper, the ones that give mass to the $10_S$ and $35_S$ scalars, are suppressed enough that they do not change the predicted neutrino masses, proton decay rate, or unification scale by more than the paper's claimed margins.","fun_headline_variants_meta":{"raw":{"variants":["Leptoquark loop links neutrino masses to down quarks in GUT","Leptoquark mechanism sets neutrino masses via down-quark link","SU(5) GUT with leptoquarks unifies above 10^16 GeV, predicts 1 TeV scalar","Non-renormalizable SU(5) ties neutrino mass to down quarks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000802,"raw_usage":{"total_tokens":3572,"prompt_tokens":1038,"completion_tokens":2534,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":654,"completion_tokens_details":{"reasoning_tokens":2442}},"tokens_in":654,"tokens_out":2534,"duration_ms":18716,"temperature":1.0,"reasoning_tokens":2442,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T21:52:29.353082+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the threshold corrections from the omitted dimension-five mass operators of the $10_S$ and $35_S$, with order-one coefficients and a cutoff at the Planck scale; if they shift $B_{12}$ by more than about 1.25, the GUT scale drops below the proton-decay bound of $5.5\\times10^{15}$ GeV and the model fails.","supporting_citations":[{"cited_title":"Search for proton decay via p → e+π0 and p → µ+π0 with an enlarged fiducial volume in Super-Kamiokande I-IV,","cited_arxiv_id":null,"evidence_quote":"Sets the experimental lower bound on the proton lifetime that fixes the GUT scale floor."},{"cited_title":"Unity of All Elementary Particle Forces,","cited_arxiv_id":null,"evidence_quote":"Provides the Georgi-Glashow SU(5) model whose particle content is extended by the $10_S$ and $35_S$ scalars."},{"cited_title":"Fermion Masses and Higgs Representations in SU(5),","cited_arxiv_id":null,"evidence_quote":"Supplies the nonrenormalizable operators used to repair the down-quark and charged-lepton mass ratios."},{"cited_title":"Leptoquarks: Neutrino masses and accelerator phenomenology,","cited_arxiv_id":null,"evidence_quote":"Gives the leptoquark-mediated neutrino mass formula that the paper adapts into its Eq. (12)."},{"cited_title":"Leptoquark mechanism of neutrino masses within the grand unification framework,","cited_arxiv_id":null,"evidence_quote":"Is the grand-unified leptoquark mechanism construction whose mass estimates this paper refines."},{"cited_title":"Unification without supersymmetry: Neutrino mass, proton decay and light leptoquarks,","cited_arxiv_id":null,"evidence_quote":"Provides the proton decay amplitude formulas and the $B-L$ violating decay rate used for the lower bound on $m_{\\widetilde{R}_2}$."},{"cited_title":"SU (5) unification revisited,","cited_arxiv_id":null,"evidence_quote":"Supplies the relations between weak-scale observables and effective beta coefficients used to derive the required $B_{12}$."},{"cited_title":"Search for proton decay via p → νK + using 260 kilo- ton·year data of Super-Kamiokande,","cited_arxiv_id":null,"evidence_quote":"Sets the proton lifetime bound used to update the lower limit on the $S_1^*$ mass."},{"cited_title":"Proton stability in grand unified theories, in strings and in branes,","cited_arxiv_id":null,"evidence_quote":"Gives the upper bounds on partial proton decay rates converted into the GUT scale lower bound."},{"cited_title":"Towards MinimalSU (5),","cited_arxiv_id":null,"evidence_quote":"Provides the sum rule $m^2_{\\eta_4} = m^2_{\\eta_1} - 3m^2_{\\eta_2} + 3m^2_{\\eta_3}$ that constrains the $35_S$ split masses."}],"review_version":1}