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| 1. autor: | |
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| Format: | Recurso digital |
| Język: | angielski |
| Wydane: |
Zenodo
2026
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| Hasła przedmiotowe: | |
| Dostęp online: | https://doi.org/10.5281/zenodo.18925475 |
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- <p>The merkabit is a balanced ternary computational unit based on dual spinors (u, v) ∈ S³ × S³ with counter-rotating phase evolution at π-lock. The Eisenstein lattice ℤ[ω], balanced ternary logic {−1, 0, +1}, and the gate set {Rₓ, Rz, P, F, C-SWAP} are derived — not assumed — from this definition. The governing algebra E₆ enters via the McKay correspondence from the binary tetrahedral group P₂₄ with zero free parameters; E₆ is uniquely isolated from its Langlands companions B₆ and C₆ by the McKay constraint and the self-duality condition h = h∨ = 12.</p> <p>Three algebraically independent routes yield α⁻¹ = 137: Route A (phase-space counting: 7 × 24 − 31), Route B (Casimir–Eisenstein: N(12 + 5ω) + dim(so(8)) = 109 + 28), and Route C (zero-point Berry phase: −ln F/10, where the return fidelity F is transcendental with two exact rational layers capturing 99.999966% of −ln F). A three-order correction from the E₆ Coxeter spectrum gives α⁻¹ = 137.035999083, matching experiment to 0.005 ppb.</p> <p>Error correction is intrinsic and geometric at three nested levels (π-lock, pentachoric complementarity, E₆ root syndromes), with composite suppression of 3,500–6,200× at ε = 10⁻³. The fault-tolerance threshold is ε ≈ 22%; the Peierls bound on the intrinsic torus gives <span>ε_th ≈ 43</span> — both far above the surface code's ~1%. The ouroboros cycle (period 12) is a discrete time quasi-crystal with Z₂ topological order and Z₃ subharmonic character. The F gate reduces long-range coupling from O(d) to O(1). Appendices A–P (46 parameter-free simulations, Python 3 + NumPy only) verify every testable claim. <br><br><br></p>