jpascher/T0-Time-Mass-Duality: Release v1.4.2

Abstract

Release Notes — v1.4.2 (28 September 2026) DOI: assigned upon Zenodo release — supersedes v1.4.1 Running corrections: 2/pdf/190_T0_Korrekturen_De.pdf Change log: 001_FFGFT_Changelog_De.md FFGFT — Fundamental Fractal-Geometric Field Theory shows: all Standard Model constants follow from a single dimensionless parameter ξ = 4/30000 on a compact 4D torus T⁴/ℤ₃. The foundational relation is T̃ · m = 1 — intrinsic time and mass are inversely coupled. Author: Johann Pascher · ORCID 0009-0000-6518-4064 Overview v1.4.2 supersedes v1.4.1 without new documents; the English translations of several documents have been corrected. The notes below are those of v1.4.1. This release collects the work from 18 to 28 September 2026: thirteen new documents (Docs. 366–378), three new popular-science books, and seven register entries (R121–R127). The main themes are the lepton masses via the icosahedron (Koide phase θ = 2/9 as a matrix element), the electroweak boson spectrum from v (Weinberg angle 2/9, trace rule for the Higgs mass), and the bridges to other frameworks, in particular Observer Patch Holography (OPH). The foundational relation and ξ are unchanged; corrections to older documents are recorded in Doc. 190 (see "Corrections"). New books The Number That Nobody Explained / Die Zahl, die niemand erklärte (Icosahedron book, EN/DE, 73/75 pp., 6×9 in, prologue, 8 chapters, appendix) Sources: https://github.com/jpascher/T0-Time-Mass-Duality/tree/main/2/kdp/IKO_Ikosaeder_Leptonmassen/ A popular-science account of the findings in Docs. 285, 293, 338, 352, 364 and 367–370: why the Koide formula with θ = 2/9 works, how three (ℤ₃) and five (φ) meet in the icosahedron, and where the open edge lies. No new FFGFT result. Fields in FFGFT / Felder in der FFGFT (Book edition of Doc. 366, EN/DE, 38 pp. each, 6×9 in) Sources: https://github.com/jpascher/T0-Time-Mass-Duality/tree/main/2/kdp/366_Feldstruktur_FFGFT/ Energy, flux and geometry, using the Goubau line as the example; the Poynting and Ohm views as reciprocal projections, analogous to time-mass duality. Dark Matter — an Illusion / Dunkle Materie — eine Illusion (EN/DE, 18/20 pp., 6×9 in, 10 chapters) Sources: 2/Sources/wr_narrativ/FFGFT_Dunkle_Materie_De/En.tex, PDFs in 2/Sources/wr_narrativ/pdf/ Rotation curves from T̃·m = 1 in the inertial regime (a ≪ a₀) without dark matter as a substance; the Bullet Cluster and gravitational lensing are assessed critically, explicitly without claiming a conclusive proof. New documents (Docs. 366–378) | Doc. | Title | Pages DE/EN | Verification script | |------|-------|-------------|---------------------| | 366 | Fields in FFGFT: Energy, Flux and Geometry | 26/25 | 14/14 | | 367 | Why θ = p₀ = 2/9 — probability and phase as two readings of one quotient | 9/9 | 18/18 | | 368 | From p₀, p₁, p₂ to lepton masses — φ skeleton and Galois correction factors | 8/8 | 18/18 | | 369 | Four routes to the lepton masses — an inventory | 9/9 | 25/25 | | 370 | Why the icosahedron — three, five and non-commutation | 10/9 | — (explanatory document) | | 371 | The factor 4/3 — sphere volume, Casimir operators, electromagnetic mass, (3,4,5) | 12/12 | 28/28 | | 372 | The matrix-element principle and its reach | 12/12 | 45/45 | | 373 | The Yukawa mechanism as a consequence of T̃·m = 1 | 11/11 | 35/35 | | 374 | Common anchor — bridge equations to OPH | 9/8 | 30/30 | | 375 | The hierarchy v/E_P — FFGFT and OPH compared | 6/6 | 11/11 | | 376 | The coefficient 8π and the status of Issue 740 | 6/6 | 9/9 | | 377 | Interfaces of FFGFT with other frameworks | 6/6 | 20/20 | | 378 | Peer review under present-day conditions | 12/12 | 25/25 | Verification scripts in 2/python/DokNNN_Skripte/. Key new results Koide phase as a ℤ₃ quotient [B]/[K] (Docs. 367, 370) The Koide angle θ and the icosahedral transition probability p₀ = |⟨v₀|R₅ vₑ⟩|² are the same quotient 2/3² = (non-trivial ℤ₃ modes)/(ℤ₃ order)². The relation θ = |A|² has the structure of the Born rule. The full matrix |⟨v_j|R₅|v_k⟩|² is doubly stochastic; the row of the symmetric mode is (5, 2, 2)/9, trace R₅ = φ. The icosahedron acts on the unrolled ℝ³, not on the compact T⁴ (5 ∤ 1152); the five enters as a phase ζ₅ ∈ GF(81). φ skeleton of the lepton masses [B] (Doc. 368) New exact identities: p₁/p₂ = φ⁸, p₀/p₂ = 2φ⁴, p₁/p₀ = φ⁴/2. Approximations m_τ/m_e ≈ 74·φ⁸ (0.03%) and m_μ/m_e ≈ 30·φ⁴ (0.56%) [K] — the first link between Doc. 293 and Doc. 338. Four routes to the lepton masses (Doc. 369) T0 ladder, Koide with θ = 2/9, Galois GF(3ⁿ) and the φ skeleton compared directly against PDG 2024. Two accuracy classes: percent and 10⁻³ %. FFGFT predicts the shape of the spectrum without parameters (dimensionless ratios); absolute values in MeV need one declared anchor. A second reading of the fractal correction without QED (R121). Matrix-element principle [B]/[K] (Doc. 372) In the ℤ₃ mode basis, A₅ generates exactly eight squared matrix elements, all with denominator 9. Consequences: on-shell Weinberg angle 1 − M_W²/M_Z² = 2/9, prediction M_W = M_Z·√(7/9) = 80.420 GeV [K]; atmospheric mixing sin²θ₂₃ ∈ {4/9, 5/9}, maximal mixing excluded [K]. Negative results stated: θ₁₂, θ₁₃ and α_s are not in the set of eight [X]. Yukawa mechanism and trace rule [B]/[K] (Doc. 373) y_i = m_i/v follows from T̃·m = 1 under the fluctuation v → v + h(x), for all fermions at once [B]. The Higgs particle is the vibration quantum of the lattice scale. Trace rule M_W² + M_Z² + m_h² = v²/2 to 0.45% [K]; together with 2/9 and 11/8 this gives M_Z²/v² = 288/2113 and hence the electroweak boson spectrum from v alone at tree level (0.17–0.31%). Galois chain M_Z : m_h : m_t = 1 : 11/8 : (11/8)² [K]. Inventory of the particle zoo (as of 21 September 2026). The factor 4/3 [B]/[E] (Doc. 371) The factor 4/3 in the electromagnetic electron mass (Abraham/Lorentz) is an effect of three-dimensionality, 4/3 = 2·(1 − 1/3). C₂(SU(2)) = 3/4 and C₂(SU(3)) = 4/3 are reciprocals; N = 2 is the only case with C₂(N)·C₂(N+1) = 1 [B]. Bridge to Observer Patch Holography [B]/[K] (Docs. 374–376) Bridge equations B1–B4: cell energy = bit energy E_bit = ħc/L, collapse threshold at the cell edge, cell clock T̃ = √P·t_P, L_cell/L₀ = √P/ξ ≈ 9578. FFGFT's own chain ξ → G → ℓ_P → E_P: v/E_P = 2.0389·10⁻¹⁷ (+1.10%, fully attributed to the bare residual of the lepton ladder). The coefficient 8π is derived on the OPH side; the statement that Issue 740 was closed has been withdrawn (R124). Interface overview (Doc. 377) Eleven frameworks with comparison and bridge documents, seven overlapping quantities with their derivation routes. Only α⁻¹ and v/E_P are quantified by more than one framework; the hadron sector appears in no comparison. Peer review under present-day conditions (Doc. 378) A methodological inventory: what the FFGFT bookkeeping (status markers, Doc. 190, verification scripts, negative results), IPI audit practice and Dot Theory governance already provide for a review framework; ten building blocks and graded review depth. No physical claims. Corrections (Doc. 190, R121–R127) | Entry | Concerns | Content | |-------|----------|---------| | R121 | Doc. 352 §10, 369 | Origin of ε_i: second reading without a QED bridge; R113 bridge needed only in reading A | | R122 | Docs. 041, 005; 372, 373 | Higgs mass and Λ_QCD in Docs. 041/005 not tenable [X]; candidates via Galois chain and trace rule (Doc. 373) | | R123 | Doc. 160 | K_frak naming conflict: in Doc. 160 to be read as the hadronic factor K_had | | R124 | Doc. 374 | Withdrawal of the Issue 740 statement; Doc. 374 corrected directly | | R125 | Docs. 085, 176, 179, 186 | Literature references and one standard statement in the photonics documents | | R126 | Doc. 230 | Cylinder representation of the qubit: placement in the literature, justification of Born statistics | | R127 | Docs. 043, 044, 261 | α = 1 is not a choice of units [X]; α is derived dimensionlessly from ξ | Open bridges (as of R127) | Bridge | Status | |--------|--------| | τ_μ directly from FFGFT (without G_F and v) | [S] (R112, Doc. 351) | | Why the rational approximation carries the GF(3ⁿ) winding numbers | [S] (Doc. 369 §4, R121) | | Koide amplitude d/c = √2 from the geometry | [S] (Doc. 352 §8) | | Hadronic factor K_had | [S] (R123) | | Λ_QCD from ξ | [X] (R122, Doc. 372) | | Higgs potential V(h) | [S] (Doc. 373) | | m_Pl and α_em(M_Z) from ξ | [S] | | Quark/hadron sector | open (Doc. 318, R76) | | CMB peaks {1,6,14,26}; |n|²=30 | open (P29/P31) | | Icosahedral phases (GF(81)) and Galois orders (GF(3ⁿ)): common root | [S] (Doc. 370) | Entry point for new readers Doc. 205 "FFGFT in Simple Language" (DE+EN, 13–14 pp.) remains the recommended entry point for the physics. Quantum Mechanics is Deterministic remains the recommended entry point for the quantum mechanics and quantum computing perspective. The icosahedron book The Number That Nobody Explained is the recommended entry point for the lepton masses. What has not changed ξ and T̃·m = 1 are unchanged. All results from v1.4.0 remain valid unless refined or corrected by R121–R127. All derivation chains from v1.3.6 are unchanged.