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| Main Authors: | , |
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| Formato: | Recurso digital |
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Zenodo
2026
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| Acesso em linha: | https://doi.org/10.5281/zenodo.19701263 |
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Sumário:
- Papers 13-14 derived eighty Standard Model observables from the trefoil knot T(2,3). This paper argues that (+1)-Dehn surgery on the trefoil--which produces the Poincare homology sphere S^3/2I and the icosahedral completion A_5 used for nuclear binding in companion Paper 17--also organises the integers appearing in the gravitational constant. The first 2I-invariant Laplacian eigenvalue on S^3/2I is lambda_1 = 168, which factorises two complementary ways: 168 = 8 x 21 (matching the spinor and adjoint dimensions of Spin(7) = B_3) and 168 = 7 x 24 = |Irr(2T)| x |2T| via the McKay correspondence on the binary tetrahedral group. The integer 7 appears simultaneously as the spectral quotient (n_1+2)/2, as the McKay-node count on the extended E_6 diagram, and as the vector rep dimension of Spin(7); 2T embeds explicitly into Spin(7) via the octonion Clifford algebra Cl(0,7). These integers enter the proposed hierarchy m_e/m_Pl = (8/7)(1 + alpha/7) alpha^(21/2), where the exponent arises, under PSL(2,7)-equivariance, from a Wilson-line amplitude on the 21-edge complete graph K_7 (the Heawood map on the Heegaard torus of S^3/2I; 21 = dim so(7)). The resulting gravitational constant G = (8/7)^2 (1+alpha/7)^2 alpha^21 hbar c / m_e^2 agrees numerically with CODATA at 0.013% using the NWT-derived alpha, or 0.029% using the measured alpha. Within the present accounting, no integer in the formula is introduced as an independent input beyond those already generated by the trefoil's surgery and spectrum; the cinquefoil T(2,5) and heptafoil T(2,7) appear as derived labels rather than additional free knots. The theory still contains a distinguished mass scale v_EW (equivalently m_e), treated as a reference scale setting the unit of measurement; the zero-parameter claim refers to the dimensionless content. Reproducibility: all analysis code (Laplacian eigenvalues on S^3/2I, the Cl(0,7) construction of 2T in Spin(7), the one-loop BPS pipeline, the SU(N) robustness scan, and the G-formula verification) is available at https://github.com/JimGalasyn/null-worldtube.