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| Үндсэн зохиолч: | |
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| Формат: | Recurso digital |
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Zenodo
2026
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| Нөхцлүүд: | |
| Онлайн хандалт: | https://doi.org/10.5281/zenodo.19150963 |
| Шошгууд: |
Шошго нэмэх
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Агуулга:
- <p><em>Paper 11 in the Merkabit series.</em></p> <p>The 168-element group PSL(2,7) = GL(3, ₂) — the phase space of the merkabit architecture — admits a unique S₃-invariant partition into three strata and nine layers. This partition maps exactly onto the force structure of the Standard Model with zero free parameters.</p> <p>The three strata arise from the Z₃ closure of the canonical 31-element binary subset (the dual pentachoron): binary (31 elements, deconfined matter), Z₃-boundary (62 elements, weak force interface), and purely ternary (75 elements, strongly confined sector). All three share the same stabiliser under conjugation in PSL(2,7): S₃ of order 6, the automorphism group of the trit. The force hierarchy is not imposed — it is a theorem about trit symmetry acting on a finite group.</p> <p>Key results, all computationally verified by explicit construction of GL(3, ₂):</p> <p>The Weinberg angle sin²θ_W = N_c/(h+1) = 3/13 = 0.23077 is determined by the layer structure alone, matching the measured value 0.23122 to 0.19%. The Z₃-boundary decomposes as N₃₆ (36 = n₊(E₆), neutral sector) + W₂₆ (26 = 2×(h+1), Weinberg sector), with the 13+13 W⁺/W⁻ split produced by the three S₃-stabiliser involutions with zero fixed points.</p> <p>The purely ternary stratum carries the Yang–Mills mass gap Δ = 1/24 and decomposes internally as residual heptads R₁₂ (12 = h(E₆)) plus SU(8)-adjoint residual (63 = dim(SU(8))). Of the 75 purely ternary elements, 33 = 9 + 24 carry binary-compatible orders — the "shadow binary" elements — topologically unreachable from the matter sector despite their order type. Confinement is structural, not dynamical.</p> <p>The ternary-essential count 137 = |Z| + |T| = 62 + 75 equals ⌊α⁻¹⌋, connecting the force decomposition directly to the fine structure constant.</p> <p>The nine-layer decomposition (by element order within each stratum) has zero overlaps, full coverage, and zero free parameters. Every layer boundary is a consequence of group structure and the canonical arch_31 identification — no physical input is required.</p> <p>This paper shows that the individual results of Papers 1–10 — the fine structure constant, the Yang–Mills mass gap, the Klein quartic automorphism group, the Riemann zero threshold — are different readings of the same S₃-invariant partition of a single finite group.</p> <p><em>Part of the Merkabit series. Base document: 10.5281/zenodo.18925475</em></p>