{"id":"11f96e93-b451-4ea8-a212-7bc34bf18c23","arxiv_id":"2608.10312","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The CKM angles, the unitarity triangle, and the neutrino mass ratio are claimed to lie on an eighteenth-power lattice of one parameter, with the leptonic CP phase predicted near 296 degrees.","lead":"This paper reports that the measured quark and neutrino mixing angles can be written as small integer powers of a single number, and that the unitarity triangles fall on a 7.5-degree grid, like a clock. If the pattern is real, it predicts the unmeasured neutrino CP phase to be near 296 degrees, which DUNE and Hyper-Kamiokande can test.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The eighteenths lattice is anchored to the exclusive-leaning |Vub|=0.00373; if the inclusive value near 4.1e-3 is correct, the sinθ_d exponent moves from 17.05 to about 17.4 and the pattern fails.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing point, and the manuscript itself confirms it in Sec. III: the lattice placement of sinθ_d is stated to be hostage to the unresolved inclusive/exclusive |Vub| tension. This is the most load-bearing concern because every subsequent claim in the multiplicative structure—the eighteenths exponents, m2/m3=ε^{19/18}, tanβ≃√ε, and the Table IV estimators—is defined relative to ε=|Vub|^{3/10}. If the inclusive determination of |Vub| is correct, the cleanest exponent placement moves from 0.05 to roughly 0.4 lattice units away from the integer, and the three-angle joint placement probability ceases to be the reported 0.10. The paper is honest about this, and its self-reported p-values are not in dispute; the issue is that the central pattern is not robust to a currently unresolved experimental choice. The lepton-sector prediction is less directly affected because it uses only the π/24 angular lattice, but the combined coherent structure of the paper leans on the quark-side anchor. The verdict CONDITIONAL already reflects this dependence, so no change is needed; if the inclusive value is confirmed, the verdict should move toward REJECT, and if the exclusive side is confirmed, the pattern becomes more credible.","tokens_in":23047,"tokens_out":9684,"duration_ms":105630,"concrete_test":"Recompute the exact FX inversion (Eqs. 3–4) and Table III using the PDG inclusive averages |Vub|=(4.13±0.26)×10^-3 and |Vcb|=(42.16±0.51)×10^-3 from Ref. [10], including their covariance, while keeping |Vus| and |Vtd/Vts| fixed. Then compare the three fitted exponents 18 ln sinθ_i / ln ε to the integers 26, 17, and 34. If the sinθ_d exponent moves from 17.05 to ≥17.3, or if any of the three distances-to-integer exceeds 0.3, the integer-eighteenths claim fails under the inclusive input; if it remains within 0.1 of 17 with all distances ≤0.25, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the FX angles are integer eighteenth powers of one parameter is not robust to the unresolved inclusive/exclusive |Vub| tension, because the parameter is defined as ε=|Vub|^{3/10} (Eq. 5) and every exponent in Table III is measured relative to it. The paper adopts the exclusive-leaning |Vub|=0.00373±0.00012, which yields fitted exponents (25.77, 17.05, 34.23) for (sinθ_u, sinθ_d, sinθ), with distances 0.23, 0.05, and 0.23 from the integers 26, 17, and 34. Sec. III itself states that inclusive values near 4.1×10^-3 would give ε≈0.193, outside the estimator band, and move the sinθ_d placement from 17.05 to about 17.4. Since sinθ_d is fixed by |Vtd/Vts| and is independent of |Vub|, this shift is pure ε-dependence: a roughly 10% upward change in |Vub| removes the cleanest of the three placements. The cross-sector relations m2/m3=ε^{19/18} and tanβ≃√ε inherit the same anchor, so the failure is not confined to one angle. The p-values of Sec. V are computed under the adopted input and do not include the input-selection uncertainty. The paper's explicit caveat is accurate: the claim is hostage to this tension.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes two commensurate empirical structures in the measured CKM and PMNS data. Multiplicatively, it claims that the three Fritzsch–Xing angles satisfy sinθ_u = ε^{26/18}, sinθ_d = ε^{17/18}, and sinθ = ε^{34/18} with the single hierarchy parameter ε = |V_ub|^{3/10} = 0.1869, and that the FX phase is maximal, φ_FX ≈ 92.3° ≈ π/2. Additively, it claims that the unitarity-triangle angles are quantized on the π/24 lattice, (α, β, γ) = (90°, 22.5°, 67.5°), with a leptonic analog predicting δ_CP ≈ 296° in the upper atmospheric octant or 244° in the lower octant. Additional relations tie the neutrino mass ratio m_2/m_3 to ε^{19/18}, express the PMNS first row in powers of r = m_2/m_3, and give a geometric completion m_1 = m_2^2/m_3. The analysis is explicitly confined to the parameterization level, with no dynamical input.","tokens_in":23314,"tokens_out":7744,"duration_ms":78440,"significance":"If the patterns survive, they would provide a strikingly compact encoding of flavor parameters and would focus model building on specific exponent and angle assignments; the leptonic δ_CP prediction and the mass-ratio relations are concrete and testable at DUNE, Hyper-Kamiokande, and JUNO. The paper has notable strengths: the FX inversion is exact and clearly presented; the Monte Carlo error propagation and the complete reporting of fitted exponents, distances, and order-one coefficients make the analysis reproducible; the chance-probability accounting is explicit; and the text is unusually candid about its own limitations, including the anchor dependence on |V_ub|. The main reservation is that the central pattern is a post-hoc fit: the denominator 18, the anchor exponent 3/10, the π/24 unit, and the choice of PMNS triangle were all selected after inspecting the same data, and the reported p-values do not correct for these choices. The paper itself concedes that the retrodictive agreement is only suggestive and that the case rests on prospective measurements, which tempers but does not remove the concern.","major_comments":[{"comment":"The integer eighteenths pattern is anchored to the exclusive-leaning value |V_ub| = 0.00373 ± 0.00012 through ε = |V_ub|^{3/10}, while sinθ_d is fixed by |V_td/V_ts| and is essentially independent of |V_ub|. The paper itself notes that an inclusive |V_ub| near 4.1×10^{-3} would give ε ≈ 0.193 and move the sinθ_d exponent from 17.05 to about 17.4. This is not a peripheral uncertainty: the assignment sinθ_d = ε^{17/18} is the cleanest placement in Table V, it is the only odd numerator that forces the denominator 18, it underpins the 5σ rejection of the ninths lattice in Sec. III, and it produces the exponent difference 26/18 − 17/18 = 1/2 underlying tanβ = √ε in Sec. VIII. With inclusive input, that placement fails and the derived β theorem shifts. Because the abstract and Sec. XI present the eighteenths pattern as a property of the measured data, the claims need to be explicitly conditional on the |V_ub| determination, with a dedicated sensitivity analysis across the inclusive–exclusive range and revised versions of Tables IV and V and the Sec. V p-values under both choices.","section":"Sec. III, Eq. (5) and Tables I, III, V"},{"comment":"The reported chance probabilities, p ≈ 0.10 for the three angle exponents and p ≈ 0.04 for the two triangle angles, condition on the lattice structure already being chosen: the denominator 18, the anchor exponent 3/10, the FX parameterization, the π/24 unit, and the (1,3) PMNS triangle were all selected after inspecting the same data. The paper acknowledges the denominator look-elsewhere effect only in passing, noting that a skeptic granting trials over denominators would dilute the probabilities toward tens of percent; that admission already shows that p = 0.10 is not the probability that the pattern arises by chance. The abstract's promise to quantify the chance probability should be revised to state clearly that these numbers are conditional on the model-selection choices, or explicit trials factors should be given.","section":"Sec. V"},{"comment":"The '23° theorem' tanβ ≃ √ε is not an independent confirmation of the framework. It follows algebraically from the fitted exponents sinθ_u = ε^{26/18} and sinθ_d = ε^{17/18} (difference 1/2) together with the approximation tanβ ≃ s_u/s_d at maximal phase, so the resulting β = 23.0° inherits the fitted inputs. The paper is transparent about this logic in Sec. VIII, but the abstract and Sec. XI list tanβ ≃ √ε and β = 23.0° among the results without noting that they are restatements of the lattice hypothesis rather than independent outputs. I recommend placing all such derived consequences in an explicitly labeled 'consequences of the lattice hypothesis' category, distinct from the genuinely predictive statements such as δ_CP ≈ 296° and the mass-ratio relations.","section":"Sec. VIII and Sec. XI"}],"minor_comments":[{"comment":"The determination of φ_FX from |V_us| uses an inverse cosine; the paper does not state how the correct branch is selected or how the ± sign ambiguity of cos φ_FX is resolved in the Monte Carlo propagation. A sentence on the branch choice would improve reproducibility.","section":"Sec. II, Eq. (4)"},{"comment":"The source column lists '[7]' for all CKM inputs, but the adopted |V_ub| is explicitly exclusive-leaning and |V_td/V_ts| is not the PDG central value. Please state the inclusive values alongside the adopted ones and clarify that these are choices meant to be tested, not PDG averages.","section":"Table I"},{"comment":"The text says the π/24 assignment is consistent with data at 1σ, but Sec. II cites the BESIII–LHCb value γ = (71.3 ± 5.0)°, which sits about 0.8σ above 67.5°; a brief comment on this newer determination would prevent readers from infering a stronger current constraint than the global fits provide.","section":"Sec. VI, Eq. (18)"},{"comment":"The phrase 'consistent with data at 1σ through α ≃ φ_FX and the theorem tanβ ≃ √ε' is difficult to parse. It should state explicitly which angles are within 1σ and which are decisive tests, especially since γ is the quantity that will discriminate between the lattice value 67.5° and the current central values.","section":"Abstract and Sec. XI"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague—read this one if you handle flavor papers. It is better than the usual numbers game: the FX inversion algebra is correct, the paper tells you explicitly what is fit and what is predicted, and it reports p=0.10 and p=0.04 with the look-elsewhere effects stated rather than buried.\n\nWhat is actually new: three Fritzsch–Xing angles as integer eighteenth powers of one parameter ε=|Vub|^(3/10), maximal phase, a π/24 quantization of the unitarity triangle, and—the genuinely interesting part—a PMNS version of the same triangle that yields a specific δ_CP near 296° in the upper octant (or 244° in the lower), with quark and lepton triangles sharing β=22.5°. The cross-sector tie m2/m3=ε^(19/18) is a clean, compact relation. The table of eleven ε-estimators is useful and the Monte Carlo error propagation is honest.\n\nThe soft spots are real and the paper mostly admits them. The load-bearing assumption is the exclusive-leaning |Vub|=0.00373. Since ε is defined from that value, an inclusive |Vub| near 0.0041 moves the sinθ_d exponent from 17.05 to about 17.4 and breaks the cleanest integer placement. The paper says this in Sec. III, but it is more than a caveat: it means the central quark-side claim is currently unresolved by the data themselves. The statistical weight is thin by the paper's own numbers, and the denominator 18, the integer exponents, and the 7.5° grid were all chosen after inspecting the same data. The theorem tanβ=√ε is a restatement of fitted exponents, and J=ε^(111/18) is arithmetic built from the same inputs. These are not independent successes.\n\nWhere the paper does earn credit: the lepton prediction is not used to set the quark constants, so it is a genuine forecast within the proposed template. The citation pattern is normal—NuFit, FLAG, inclusive and exclusive Vcb determinations, the Wolfenstein and Gatto–Sartori–Tonin lineage, and one companion paper by the author, flagged as such.\n\nWho is this for? Flavor phenomenologists in the pattern-hunting tradition, and anyone tracking δ_CP ahead of DUNE and Hyper-Kamiokande. I would cite it in a δ_CP context only after the octant starts to resolve; right now it is an interesting target, not a result. It deserves a serious referee, mostly because it is testable and honest. I would send it out rather than desk-reject, and I would ask the referee to put the inclusive/exclusive |Vub| dependence explicitly into the abstract.","headline":"A self-aware flavor numerology paper with a clean, testable leptonic prediction; the quark-side lattice is post-hoc and hostage to the exclusive |Vub|, but it deserves serious referee time.","tokens_in":23937,"tokens_out":1777,"would_cite":false,"duration_ms":19969,"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":"The measured quark and lepton mixing matrices are claimed to be organized by a single small parameter, $\\varepsilon=|V_{ub}|^{3/10}=0.1869$, through a lattice of integer eighteenth powers and a 7.5-degree angular clock.","keywords":["CKM matrix","PMNS matrix","unitarity triangle","Fritzsch-Xing parameterization","neutrino mass ordering","CP violation","flavor structure","discrete quantization"],"falsifier":"Measure $|V_{ub}|$ through inclusive decays at sub-percent precision: if it lands near $4.1\\times10^{-3}$ rather than $3.7\\times10^{-3}$, $\\varepsilon$ shifts outside the estimator band and the exponent lattice fails. Independently, a degree-level measurement of the CKM angle $\\gamma$ that stays near $65.4^\\circ$ rather than moving toward $67.5^\\circ$-$68^\\circ$ would exclude the $\\pi/24$ triangle; a resolution of the atmospheric octant to $\\theta_{23}<45^\\circ$ would falsify the quark–lepton transfer relation $\\delta_{\\rm CP}\\simeq296^\\circ$; and a DUNE or Hyper-Kamiokande measurement of $\\delta_{\\rm CP}$ far from both $296^\\circ$ and $244^\\circ$ would exclude the leptonic lattice.","tokens_in":22750,"feed_emoji":"🕐","tokens_out":10877,"duration_ms":92304,"temperature":0.7,"pith_summary":"This paper claims that the measured quark and lepton mixing parameters share two commensurate structures. Multiplicatively, the three angles of the FX parameterization of the CKM matrix are, to within a few percent, integer eighteenth powers of a single hierarchy parameter $\\varepsilon=|V_{ub}|^{3/10}=0.1869$, with the CP phase maximal. Additively, the rephasing-invariant unitarity-triangle angles sit on a $\\pi/24$ grid, $(\\alpha,\\beta,\\gamma)=(90^\\circ,22.5^\\circ,67.5^\\circ)$, and the same grid predicts the leptonic CP phase near $296^\\circ$ in the upper atmospheric octant or $244^\\circ$ in the lower octant. The same $\\varepsilon$ is claimed to set the neutrino mass ratio $m_2/m_3=\\varepsilon^{19/18}$, tying the quark and lepton sectors to one number. The paper reports the retroactive chance probabilities as modest and explicitly rests its case on prospective measurements at LHCb, Belle II, DUNE, Hyper-Kamiokande, and JUNO.","feed_headline":"One small number organizes quark and lepton mixing","feed_subtitle":"The same epsilon that fixes CKM angles sets the neutrino mass ratio and a leptonic CP phase near 296 degrees.","key_machinery":"The load-bearing machinery is the FX parameterization of the CKM matrix, a three-angle-plus-phase decomposition in which every angle is separately measurable from exact inversion of moduli ratios, making lattice hypotheses directly testable. On that representation the paper builds two lattices: the multiplicative lattice of integer eighteenth powers of the internal parameter $\\varepsilon$, and the angular $\\pi/24$ lattice for unitarity-triangle angles. The bridge between them is the theorem $\\tan\\beta\\simeq\\sqrt{\\varepsilon}$, which follows from the exponent difference $26/18-17/18=1/2$ and turns the triangular quantization into the angular approximation of the multiplicative lattice at maximal phase. The same $\\varepsilon$ then carries the neutrino mass ratio $m_2/m_3=\\varepsilon^{19/18}$, exporting the lattice from the quark to the lepton sector, and the quark mass ratios at $M_Z$ close the structure through relations such as $m_d/m_s=\\lambda^2$, $m_s/m_b=\\sin\\theta_d\\sin\\theta_u$, and $m_c/m_t=|V_{ub}|$.","core_discovery":"The central claim is that flavor data, read through the FX parameterization for quarks and the $(1,3)$-column unitarity triangle for leptons, are commensurate with two exact-looking structures whose relation is the identity $\\tan\\beta\\simeq\\sqrt{\\varepsilon}$. With $\\varepsilon=|V_{ub}|^{3/10}=0.1869$, the three measured quark angles satisfy $\\sin\\theta_u=\\varepsilon^{26/18}$, $\\sin\\theta_d=\\varepsilon^{17/18}$, and $\\sin\\theta=\\varepsilon^{34/18}$ with coefficients within 2.5% of unity, and the FX phase is maximal, $\\phi_{\\rm FX}=92.3^\\circ\\pm2.7^\\circ$ against $\\pi/2$. Unit coefficients and maximal phase reproduce the remaining CKM moduli at the percent level and fix the Jarlskog invariant as $J=\\varepsilon^{111/18}\\sin\\phi_{\\rm FX}$. The rephasing-invariant image is a unitarity triangle quantized on the $\\pi/24$ lattice, $(\\alpha,\\beta,\\gamma)=(12,3,9)\\times7.5^\\circ=(90^\\circ,22.5^\\circ,67.5^\\circ)$; for leptons, where mixing is large and only the angular structure can act, the same lattice requires $\\delta_{\\rm CP}\\simeq296^\\circ$ in the upper octant or $244^\\circ$ in the lower octant. The same $\\varepsilon$ also gives the neutrino mass ratio $m_2/m_3=\\varepsilon^{19/18}$ and the PMNS first row as powers of that ratio, $(|U_{e1}|,|U_{e2}|,|U_{e3}|)\\simeq(r^{1/9},r^{1/3},\\tfrac{\\sqrt{3}}{2}r)$. The paper is explicit that the analysis is at the parameterization level and assumes no dynamics.","pith_inferences":["If the pattern survives the coming measurements, the integer exponents point toward a charge-counting mechanism with integer charges, and the maximal phase points toward a discrete folding symmetry that quantizes phases to $\\pm\\pi/2$; the paper states this as an open requirement rather than a claim.","The framework's commitment to the exclusive-leaning $|V_{ub}|$ means the inclusive/exclusive tension is itself a decisive test: an inclusive value near $4.1\\times10^{-3}$ would move $\\varepsilon$ to about 0.193 and shift the $\\sin\\theta_d$ placement from 17.05 to about 17.4, breaking the lattice before oscillation experiments weigh in.","A testable extension of the same logic is to scan the other five PMNS unitarity triangles for $\\pi/24$ placements; the paper deliberately restricts to the $(1,3)$-column triangle and claims no selection credit, so checking the remaining triangles would quantify the look-elsewhere effect.","The same $\\varepsilon$-based mass relation predicts normal ordering and the geometric completion $m_1=m_2^2/m_3\\simeq1.5$ meV, giving a summed neutrino mass near 60 meV and an effective Majorana mass below the reach of ton-scale neutrinoless double-beta decay; this is a concrete target for cosmological mass-sum measurements."],"forward_implications":["If the unit-coefficient lattice is exact, the remaining CKM moduli are reproduced at the percent level and the Jarlskog invariant is fixed at $J=\\varepsilon^{111/18}\\sin\\phi_{\\rm FX}$, matching the measured value.","The quark unitarity triangle is predicted to have angles $(90^\\circ,22.5^\\circ,67.5^\\circ)$, so $\\gamma$ should land near $67.5^\\circ$-$68^\\circ$, one to two degrees above the current central values, testable at LHCb and Belle II.","The leptonic $(1,3)$-column PMNS triangle on the same grid predicts $\\delta_{\\rm CP}\\simeq296^\\circ$ in the upper octant (or $244^\\circ$ in the lower octant), with the upper branch also fixing $\\sin^2\\theta_{23}\\simeq0.549$; DUNE and Hyper-Kamiokande can test both predictions.","The neutrino mass ratio is predicted to satisfy $m_2/m_3=\\varepsilon^{19/18}$, equivalently $|V_{ub}|=(m_2/m_3)^{60/19}$, and the PMNS first row is given by powers of $r=m_2/m_3$; JUNO can test these at the per-mille level.","The mass-ratio relations $m_d/m_s=\\lambda^2$, $m_s/m_b=\\sin\\theta_d\\sin\\theta_u$, and $m_c/m_t=|V_{ub}|$ are parameter-free and already agree with data at 0.7%, 0.02$\\sigma$, and 1.2% respectively."],"supporting_citations":[{"why":"Supplies the three-angle-plus-phase CKM representation with exact inversion relations, the basis for testing the integer-exponent lattice.","marker":"[6]"},{"why":"Provides the adopted CKM moduli, phase, and global-fit quantities that the lattice claims to reproduce.","marker":"[7]"},{"why":"Supplies the neutrino oscillation parameters, mass splittings, and octant and CP-phase benchmarks against which the leptonic predictions are placed.","marker":"[12]"},{"why":"Provides the running quark and charged-lepton masses at $M_Z$ used for the mass-ratio lattice and for excluding the charged-lepton ratios.","marker":"[13]"},{"why":"The inclusive $|V_{cb}|$ determination that would verify the $34/18$ assignment essentially exactly if adopted.","marker":"[10]"},{"why":"The exclusive $|V_{cb}|$ average that would push the fitted exponent to 34.69, showing the lattice's dependence on the $|V_{cb}|$ tension.","marker":"[11]"},{"why":"Supplies the classical light-quark mass–Cabibbo relation that the lattice recovers as $m_d/m_s=\\lambda^2$.","marker":"[2]"},{"why":"Supplies the standard CKM power expansion that the lattice re-expresses in the $\\lambda$ base.","marker":"[1]"}],"fun_headline_variants":["One parameter sets quark and lepton mixing, predicts CP ~296°","Epsilon powers encode CKM angles and PMNS matrix","Digital-clock unitarity triangles unify flavor mixing","Same epsilon fixes CKM angles, neutrino mass ratio","Leptonic CP predicted near 296° by same epsilon"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The lattice is anchored to the adopted exclusive-leaning value $|V_{ub}|=0.00373\\pm0.00012$; if the inclusive determination near $4.1\\times10^{-3}$ is correct, $\\varepsilon$ rises to about 0.193, outside the estimator band, and the $\\sin\\theta_d$ exponent moves from 17.05 to about 17.4, breaking the eighteenths pattern.","fun_headline_variants_meta":{"raw":{"variants":["One parameter sets quark and lepton mixing, predicts CP ~296°","Epsilon powers encode CKM angles and PMNS matrix","Digital-clock unitarity triangles unify flavor mixing","Same epsilon fixes CKM angles, neutrino mass ratio","Leptonic CP predicted near 296° by same epsilon"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001144,"raw_usage":{"total_tokens":5000,"prompt_tokens":1453,"completion_tokens":3547,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":1069,"completion_tokens_details":{"reasoning_tokens":3465}},"tokens_in":1069,"tokens_out":3547,"duration_ms":25750,"temperature":1.0,"reasoning_tokens":3465,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T04:11:56.289354+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $|V_{ub}|$ through inclusive decays at sub-percent precision: if it lands near $4.1\\times10^{-3}$ rather than $3.7\\times10^{-3}$, $\\varepsilon$ shifts outside the estimator band and the exponent lattice fails. Independently, a degree-level measurement of the CKM angle $\\gamma$ that stays near $65.4^\\circ$ rather than moving toward $67.5^\\circ$-$68^\\circ$ would exclude the $\\pi/24$ triangle; a resolution of the atmospheric octant to $\\theta_{23}<45^\\circ$ would falsify the quark–lepton transfer relation $\\delta_{\\rm CP}\\simeq296^\\circ$; and a DUNE or Hyper-Kamiokande measurement of $\\delta_{\\rm CP}$ far from both $296^\\circ$ and $244^\\circ$ would exclude the leptonic lattice.","supporting_citations":[{"cited_title":"Flavor symmetries and the description of flavor mixing,","cited_arxiv_id":null,"evidence_quote":"Supplies the three-angle-plus-phase CKM representation with exact inversion relations, the basis for testing the integer-exponent lattice."},{"cited_title":"on-lattice with an order-one coefficient","cited_arxiv_id":null,"evidence_quote":"Provides the adopted CKM moduli, phase, and global-fit quantities that the lattice claims to reproduce."},{"cited_title":"Three loop calculations and inclusiveV cb,","cited_arxiv_id":null,"evidence_quote":"Supplies the neutrino oscillation parameters, mass splittings, and octant and CP-phase benchmarks against which the leptonic predictions are placed."},{"cited_title":"Simultaneous de- termination of CKM angleγand charm mixing parame- ters,","cited_arxiv_id":null,"evidence_quote":"The inclusive $|V_{cb}|$ determination that would verify the $34/18$ assignment essentially exactly if adopted."},{"cited_title":"Weak self-masses, Cabibbo angle, and brokenSU(2)×SU(2),","cited_arxiv_id":null,"evidence_quote":"Supplies the classical light-quark mass–Cabibbo relation that the lattice recovers as $m_d/m_s=\\lambda^2$."},{"cited_title":"Parametrization of the Kobayashi- Maskawa Matrix,","cited_arxiv_id":null,"evidence_quote":"Supplies the standard CKM power expansion that the lattice re-expresses in the $\\lambda$ base."}],"review_version":1}