The unified theory at eleven parameters: general relativity and the Standard Model on one algebra

@misc{reynaud2026unified,
  title = {{The unified theory at eleven parameters: general relativity and the Standard Model on one algebra}},
  author = {Patrick .B Reynaud},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05749759v2},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - The unified theory at eleven parameters: general relativity and the Standard Model on one algebra
AU  - Patrick .B Reynaud
PY  - 2026
DA  - 2026/09/14
PB  - HAL
UR  - https://hal.science/hal-05749759v2
AB  - Two companion papers stated special relativity for the eleven quantities of a body, time, position, energy-momentum and spin [1], and gauged their eleven-generator Weyl algebra into a theory of gravity that is Einstein's in vacuum and Einstein-Cartan's in matter [2]. This paper puts that theory together with the Standard Model. The three gauge interactions are first written in the same language: electromagnetism as a Lorentzclosed eleven (A µ , J µ , W µ EM ) with W EM = F J as its spin, filling the sixteen slots of the tetraquaternion T = H ⊗ H = M 4 (R); the electroweak sector as the hyperquaternion T ⊗ H = M 4 (H), whose scalar quaternion is the Higgs doublet with SU (2) L on the left and U (1) Y on the right; chromodynamics as T ⊗ Cl(0, 6) = Cl(9, 1), with colour the stabiliser of an octonionic unit. Connes' finite algebra A F = C⊕H⊕M 3 (C) is recalled, and the Standard-Model algebra is T⊗A F = M 4 (C)⊕M 4 (H)⊕M 12 (C) inside the container Cl(5, 7) = M 32 (H) with chirality γ 5 ×2T 3 ×e 7 . The mixing with gravity is then layered as the Coleman-Mandula theorem requires: the symmetry is the direct sum (P ⊕ M ⊕ D) ⊕ g SM , 11 + 12 = 23; the associative algebra is C ⊗ T ⊗ A F , of complex form M 4 (C) ⊕ M 8 (C) ⊕ M 12 (C) with each simple type once, the complex tetraquaternion of [1], whose u(2, 2) is the sixteen of a body, tensored with A F ; the Clifford closure is Cl(6, 8) = M 64 (H), with spinor C 128 = Dirac ×H F . The unified action is the gravitational action of [2] plus the Standard Model, Weyl invariant term by term once the one dimensionful parameter µ 2 becomes 8πζϕ 2 with the compensator ϕ that sets Newton's constant, M P = √ 8π ϕ 0 ; ζ = λ H (v/M P ) 2 = 5 × 10 -35 is the hierarchy, located rather than explained. The mixing is regular where its four-parameter counterparts are singular: normalising the fields of each interaction by a scalar of weight -2 needs, without a gauged dilatation, a scalar built from the fields-|F |, |Φ| 2 , ⟨G 2 ⟩-each of which vanishes somewhere, on radiation, in the symmetric phase, in the deconfined phase; at eleven parameters the normaliser is the compensator, pure gauge, whose zero set is empty. The comparison is between Weyl-invariant formulations of each sector, which placing the fields of a sector on one element of so(2, 4) with the weights of [1] requires, and not with electrodynamics or chromodynamics as usually written, which normalise nothing and divide by no field. The theory has three faces: its symmetry and units (the Planck units of [1]), its identities (the Hertz chain of the linearised Einstein operator, with algebraic torsion as polarisation, thirty propagating modes), and its matter (the Mathisson-Papapetrou-Dixon particle, which is the eleven of [1], whose equations of motion the unification completes: Mathisson-Papapetrou-Dixon plus Wong, every mass a pure number times the compensator so that the worldlines are the geodesics of ϕ 2 g in every gauge, and the acceleration bound of [1] reached by the Lorentz force exactly at the Schwinger field). Its predictions are exact statements-c gw = c, two polarisations, no fifth force, no echoes, κ λ = 1, the gauge group exactly U (1) × SU (2) × SU (3), no gauge-mediated proton decay, three right-handed neutrinos with M R = y M M P , Higgs inflation in its Palatini form once the Weyl vector and the trace of the torsion are eliminated together with the Higgs present, with n s = 1 -2/N and a tensor-to-scalar ratio of order 10 -12 -against six free pure numbers, ζ, ξ, y M , θ, α and the cosmological number λ, the Yukawa block, and one sign, that of the ζ term. The bound on acceleration of [1] becomes a theorem of the quantum matter sector, the compensator's Majorana term is what selects the Standard-Model algebra inside the container, and neutron stars, quark stars and magnetars are Einstein's and the Standard Model's to 10 -40 and 10 -12 .
ER  -