Topological Vacuum Protection and Parameter-Free Finite QFT from B = −1 in Array Cosmology
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2026
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| _version_ | 1866901083360591872 |
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| author | Lim, Han-Jun |
| author_facet | Lim, Han-Jun |
| contents | <p>Abstract</p> <p><br>The rendering algebra R12 ∼= M12(C) of Array Cosmology satisfies the closure relation B ≡ e1e2 · · · e12 = −1. We prove that this single algebraic fact forces antiperiodic boundary conditions (APBC) on the internal cyclic structure, with four<br>consequences of increasing scope.</p> <p>(I) Vacuum Protection. All zero-modes are topologically forbidden, generating a mass gap mgap = sin(π/12), and the vacuum polarisation vanishes identically: Π(q) = 0 for q ̸= 0 (mod 6).</p> <p>(II) Complete n-Point Protection. All odd-n-point lattice loop factors vanish unconditionally. All even-n-point factors vanish at generic external momenta. Non-vanishing contributions occur only at self-energy momenta q ∈ {0, 6}, removed by wave-function normalisation. The 3-point vertex correction vanishes for all 122 = 144 momentum assignments (numerically verified to < 10−13).</p> <p>(III) Convergent Perturbation Series. UV finiteness (Nmax = 2241 < ∞), IR protection (mgap > 0), and APBC loop suppression combine to yield a geometrically convergent perturbation series with ratio α · Nint = 12/137 < 1—in contrast to the asymptotic (divergent) series of continuum QFT.</p> <p>(IV) Parameter-Free Finite QFT. We define a QFT on R12 with zero free parameters (all 19 SM parameters derived), zero divergences (all loops are finite sums), and no renormalisation. The “running” of coupling constants is identified as a residual artefact of the continuum approximation in which the APBC protection is lost</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19219854 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Topological Vacuum Protection and Parameter-Free Finite QFT from B = −1 in Array Cosmology Lim, Han-Jun Array Cosmology 배열우주론 R12 Rendering Algebra Rendering Defect Zero-Parameter Derivation Z_noise Topo-Thermodynamic Framework Hanjun Lim 5 Axioms Array Cosmology 임한준 <p>Abstract</p> <p><br>The rendering algebra R12 ∼= M12(C) of Array Cosmology satisfies the closure relation B ≡ e1e2 · · · e12 = −1. We prove that this single algebraic fact forces antiperiodic boundary conditions (APBC) on the internal cyclic structure, with four<br>consequences of increasing scope.</p> <p>(I) Vacuum Protection. All zero-modes are topologically forbidden, generating a mass gap mgap = sin(π/12), and the vacuum polarisation vanishes identically: Π(q) = 0 for q ̸= 0 (mod 6).</p> <p>(II) Complete n-Point Protection. All odd-n-point lattice loop factors vanish unconditionally. All even-n-point factors vanish at generic external momenta. Non-vanishing contributions occur only at self-energy momenta q ∈ {0, 6}, removed by wave-function normalisation. The 3-point vertex correction vanishes for all 122 = 144 momentum assignments (numerically verified to < 10−13).</p> <p>(III) Convergent Perturbation Series. UV finiteness (Nmax = 2241 < ∞), IR protection (mgap > 0), and APBC loop suppression combine to yield a geometrically convergent perturbation series with ratio α · Nint = 12/137 < 1—in contrast to the asymptotic (divergent) series of continuum QFT.</p> <p>(IV) Parameter-Free Finite QFT. We define a QFT on R12 with zero free parameters (all 19 SM parameters derived), zero divergences (all loops are finite sums), and no renormalisation. The “running” of coupling constants is identified as a residual artefact of the continuum approximation in which the APBC protection is lost</p> <p> </p> |
| title | Topological Vacuum Protection and Parameter-Free Finite QFT from B = −1 in Array Cosmology |
| topic | Array Cosmology 배열우주론 R12 Rendering Algebra Rendering Defect Zero-Parameter Derivation Z_noise Topo-Thermodynamic Framework Hanjun Lim 5 Axioms Array Cosmology 임한준 |
| url | https://doi.org/10.5281/zenodo.19219854 |