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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2026
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| Accesso online: | https://doi.org/10.5281/zenodo.20257066 |
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- <p>=== v9 (May 2026) — update over v1728 ===</p> <p>This is v9, an editorial and audit revision of v1728. The paper PDF is<br>121 pages (vs 73 in v1728). The architecture and all headline numerics<br>are preserved exactly:</p> <p> alpha^{-1} = 137.035999202<br> mu = 6 pi^5 = 1836.15267343 (NLO residual 0.009 ppm)<br> R = Delta m^2_31 / Delta m^2_21 = 33.48<br> sin^2 theta_W = 3/13<br> sin^2 theta_12 = 4/13 (JUNO 2025: +0.17 sigma)<br> sin^2 theta_13 = 2/91<br> sin^2 theta_23 in orbit pair {81/145, 64/145}<br> (structural representative 81/145; lower branch 64/145 active<br> under current NuFIT 6.1 IC23 NO comparison)<br> gamma_CKM = arctan(9/4) = 66.04 degrees<br> delta_CP = 270 degrees (sin delta = -1)<br> m_e = 0.51099895 MeV (sole dimensionful input)</p> <p>What changed vs v1728:</p> <p> - LHCb 2025 direct gamma_CKM measurement integrated<br> (LHCb-CONF-2025-003, DOI 10.17181/CERN.GFHE.LM6W, CDS:2948394).<br> - NuFIT 6.1 IC23 NO benchmark adopted consistently across all<br> PMNS comparisons.<br> - JUNO 2025 first result integrated (arXiv:2511.14593).<br> - DESI DR2 cosmological context for Sigma m_nu (arXiv:2503.14744);<br> Lambda CDM exclusion at 2.9 sigma but DESI itself excludes<br> Lambda CDM at 2.8-4.2 sigma; in w_0 w_a CDM the LD prediction<br> Sigma m_nu = 69.8 meV lies inside the allowed region.<br> - Form A triply determined post S541: anchor Fricke-pair (X.423),<br> Grothendieck whole-eigensummand (X.247c.cond), Fricke-pair<br> log-residue (G.10C).<br> - Prior art section expanded (Sections 3.8 and 17):<br> Tatitscheff-He-McKay, Bao-He-Zahabi, Bao-Foda-He et al.,<br> Ashok-Cachazo-Dell'Aquila, He-McKay.<br> - Gap 9 (X.247c) preserved as [CONJ HEADLINE].<br> - Gap 10 (I.1) [DER, ratchet-conditional via T.10 Universality<br> candidate].<br> - Three-way audit (Logos + Cloud Code + GPT-5.5): 9 Tier-2 findings<br> closed via 8 atomic paper commits + 1 DB commit + PDF rebuild.<br> Zero architecture-lock baselines mutated. Companion drift = 0.</p> <p>LD is not proposed as a classical field theory with a fundamental<br>action. Its primitive object is the dessin d'enfant of X_0(6). Two<br>structural questions remain open: the identification of the PMNS<br>operator in the monodromy algebra (Gap 9) and the formulation of an<br>action principle (Gap 10).</p> <p>Companion document and verification suite:<br>https://github.com/zinchenko-denis/LD-supplementary<br>Interactive 3D explorer:<br>https://zinchenko-denis.github.io/LD-explorer</p> <p>Previous versions:<br> - v1728 (Apr 2026): DOI 10.5281/zenodo.19520240<br> - v8 (Apr 2026): DOI 10.5281/zenodo.19393365<br> - v6 (Mar 2026): DOI 10.5281/zenodo.19150365<br> - v5.5 (Dec 2025): DOI 10.5281/zenodo.19046582</p> <p>================================================================<br>=== Below: v1728 (April 2026) original description, preserved ===<br>================================================================</p> <p>The finite noncommutative-geometry algebra A_F = C + H + M_3(C) that<br>classifies the internal geometry of the Standard Model supplies two<br>integers, d_1 = 2 and d_2 = 3. Their product N = 6 defines the level<br>of a congruence subgroup Gamma_0(6) <= SL_2(Z), uniquely selected by<br>three primary filters together with corroborating structural<br>characterisations. The dessin d'enfant of the associated modular<br>curve X_0(6) -- a bipartite graph with 4 black vertices, 6 white<br>vertices, and 12 edges -- is identified with the 12 particles of the<br>Standard Model.</p> <p>From this single combinatorial structure, with zero continuous free<br>parameters:</p> <p> - 10 fermion and boson masses (RMS 1.45% LO; all 10 NLO signs<br> correct, R^2 = 0.89)<br> - Fine structure constant alpha^{-1} = 137.035999202 (pull -1.2 sigma)<br> - Proton-to-electron mass ratio mu = 6 pi^5 (1 + ...) (0.009 ppm)<br> - All 4 CKM parameters (chi^2/dof = 0.65)<br> - All 3 PMNS mixing angles: sin^2 theta_12 = 4/13,<br> sin^2 theta_23 = 81/145, sin^2 theta_13 = 2/91<br> - Maximal CP violation (sin delta = -1)<br> - Weak mixing angle sin^2 theta_W = 3/13<br> - 16+ hadronic observables (15 of 16 within 1.7 sigma)</p> <p>The sole dimensionful input is the electron mass. 18 independent<br>arithmetic outputs are supported by 15+ structural theorem families<br>and 117+ documented dead directions.</p> <p>LD is not proposed as a classical field theory with a fundamental<br>action. Its primitive object is the dessin d'enfant of X_0(6),<br>interpreted as a finite quantum kinematics. Lagrangian structures,<br>if they appear, are emergent. Two structural questions remain open:<br>the identification of the PMNS operator in the monodromy algebra<br>and the formulation of an action principle.</p> <p>Version v1728 (April 2026), superseding v8. Major additions: CKM<br>sector from uniform spanning trees, PMNS angles from Hauptmodul<br>cross-ratios and index formula, sin^2 theta_W derivation, NLO mass<br>corrections, directed operator algebra (CRT grand unification),<br>complete falsification map. Full correction log: Appendix G of the<br>paper. Supplementary material:<br>https://github.com/zinchenko-denis/LD-supplementary</p>