Holographic Saturation II: Shared parent action, division-algebraic gauge structure, entropic symmetry breaking, and orbit-channel closure.

We develop the internal sector of $I=\sqrt{s}\,e^{i\theta}$ from saturation,the Born phase, Clifford transport and binary free energy. Under the statedmaximal-capacity completion, the Cayley--Dickson tower selects the octonionicrung; a fixed complex direction gives $G_2\to SU(3)$, while the quaternionicrung gives global $U(2)$ electroweak kinematics, the Higgs bidoublet, hyperchargeratio and custodial $SO(4)\to SU(2)_{\rm diag}$. \textbf{Methods.}\ Fisher--canonical closure gives$m_{H,\rm curv}^{(0)}=v/2=123.11\,$GeV, $\kappa_3=1$, $\kappa_4=11/3$.Reciprocal-resolution matching fixes the FRG boundary without a Higgs-mass fit;the global Litim-LPA flow gives $m_{H,\rm curv}^{\rm FRG}\simeq125.1\,$GeV,with sub-GeV LPA$'$ sensitivity. The same flow predicts$(\kappa_3,\kappa_4,\kappa_5)\simeq(1.0272,3.9348,1.52)$ and a quartic $4.16$times the same-flow mass/VEV-matched control. The additional Fisher--KL one-loop pole difference relative to an identical-UVreference remains an independent bookkeeping theorem. Completing the commonmomentum dependence with the minimal Fisher--canonical, twice-subtractedpinch-technique kernel gives$M_H^{\rm pole,1L}\simeq125.26\,$GeV without a Higgs-pole input or an additionalcontinuous coefficient. This is an explicit one-loop/minimal-completion poleprediction; common higher-order electroweak/QCD and all-order vertex-FRGprecision are not claimed. The leading scalar thermal tadpole/curvaturecoefficients are explicit. \textbf{Results.}\ The Clifford--Fock construction gives an anomaly-free sixteen-state generationand unique right-handed Majorana invariant. The Hopf lift by$H^3=\mathcal O(3)$ gives three same-chirality zero modes, total index $48$ andno vectorlike partners in the canonical completion. Kac--Birkhoff return gives$\beta=3\sqrt2/\alpha_Z=542.7610$; the parameter-free finite-channel$\Phi$-sector completion with the pre-existing $N_\Phi=13$ count fixes the$t:c:u$ overlap ratios. The resolution-faithful lift fixes $Y_U(k_F)=\sqrt2g_2(k_F)$. Joint RG--FRG matchingthen gives $M_t^{\rm match}=172.3695$ GeV and$m_{H,\rm curv}^{\rm FRG}=125.146$ GeV without a quark-mass normalisation.The physical lift and complete fermion pole matching remain conditional/open.A separate three-family type-I benchmark completion of the already allowedMajorana channel fixes a viable neutrino spectrum without modifying the gaugerunning; deriving its flavor texture geometrically, and the down/charged-leptonmixing sectors, remain open. For the projected kinetic completion,$\overline P_T=(7/8)I_8$, $\mathcal T_8=(8/7)f^4$, and the two determinantorientations give $(16/7)f^4$ for Part~III. Sector weights obey$S_i=\kappa_i\alpha_Z^{N_i}$ with $(N_i)=(3,13,16)$ and$(\kappa_\sigma,\kappa_\Phi,\kappa_\psi)=(1/4\pi,1,2)$; stationarity fixes thecorresponding chemical tilts. Thus $s_0=\alpha_Z^3/(4\pi)=3.80\times10^{-8}$,while electroweak and colour channels reproduce the stated SPARC normalisationand QCD string scale without sector-specific continuous prefactors. \textbf{Conclusions.}\ The Born phase fixes the internal complex and timelike spacetime directions;non-zero charge selects a unique stable timelike branch without altering$G_2\to SU(3)$. The constrained parent action has one physical matter/photon/tensor metric and four propagating degrees of freedom. Gauge kinematics,representations, anomaly cancellation, orbit measure and breaking are derivedor checked at the stated tier. Confinement dynamics, down/charged-lepton flavour and mixing, a geometricderivation of the conditional neutrino Majorana texture, full fermion polematching and a propagating chiral substrate remain open; Part~I independentlyyields the GR near-zone PPN coefficients.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-28
DOI
https://doi.org/10.5281/zenodo.23014532
Primary Topic
Black Holes and Theoretical Physics
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article
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article

Holographic Saturation II: Shared parent action, division-algebraic gauge structure, entropic symmetry breaking, and orbit-channel closure.

Fabio Ruggeri
Zenodo (CERN European Organization for Nuclear Research)
Black Holes and Theoretical Physics
article

Holographic Saturation II: Shared parent action, division-algebraic gauge structure, entropic symmetry breaking, and orbit-channel closure.

Fabio Ruggeri
article en

Abstract

We develop the internal sector of $I=\sqrt{s}\,e^{i\theta}$ from saturation,the Born phase, Clifford transport and binary free energy. Under the statedmaximal-capacity completion, the Cayley--Dickson tower selects the octonionicrung; a fixed complex direction gives $G_2\to SU(3)$, while the quaternionicrung gives global $U(2)$ electroweak kinematics, the Higgs bidoublet, hyperchargeratio and custodial $SO(4)\to SU(2)_{\rm diag}$. \textbf{Methods.}\ Fisher--canonical closure gives$m_{H,\rm curv}^{(0)}=v/2=123.11\,$GeV, $\kappa_3=1$, $\kappa_4=11/3$.Reciprocal-resolution matching fixes the FRG boundary without a Higgs-mass fit;the global Litim-LPA flow gives $m_{H,\rm curv}^{\rm FRG}\simeq125.1\,$GeV,with sub-GeV LPA$'$ sensitivity. The same flow predicts$(\kappa_3,\kappa_4,\kappa_5)\simeq(1.0272,3.9348,1.52)$ and a quartic $4.16$times the same-flow mass/VEV-matched control. The additional Fisher--KL one-loop pole difference relative to an identical-UVreference remains an independent bookkeeping theorem. Completing the commonmomentum dependence with the minimal Fisher--canonical, twice-subtractedpinch-technique kernel gives$M_H^{\rm pole,1L}\simeq125.26\,$GeV without a Higgs-pole input or an additionalcontinuous coefficient. This is an explicit one-loop/minimal-completion poleprediction; common higher-order electroweak/QCD and all-order vertex-FRGprecision are not claimed. The leading scalar thermal tadpole/curvaturecoefficients are explicit. \textbf{Results.}\ The Clifford--Fock construction gives an anomaly-free sixteen-state generationand unique right-handed Majorana invariant. The Hopf lift by$H^3=\mathcal O(3)$ gives three same-chirality zero modes, total index $48$ andno vectorlike partners in the canonical completion. Kac--Birkhoff return gives$\beta=3\sqrt2/\alpha_Z=542.7610$; the parameter-free finite-channel$\Phi$-sector completion with the pre-existing $N_\Phi=13$ count fixes the$t:c:u$ overlap ratios. The resolution-faithful lift fixes $Y_U(k_F)=\sqrt2g_2(k_F)$. Joint RG--FRG matchingthen gives $M_t^{\rm match}=172.3695$ GeV and$m_{H,\rm curv}^{\rm FRG}=125.146$ GeV without a quark-mass normalisation.The physical lift and complete fermion pole matching remain conditional/open.A separate three-family type-I benchmark completion of the already allowedMajorana channel fixes a viable neutrino spectrum without modifying the gaugerunning; deriving its flavor texture geometrically, and the down/charged-leptonmixing sectors, remain open. For the projected kinetic completion,$\overline P_T=(7/8)I_8$, $\mathcal T_8=(8/7)f^4$, and the two determinantorientations give $(16/7)f^4$ for Part~III. Sector weights obey$S_i=\kappa_i\alpha_Z^{N_i}$ with $(N_i)=(3,13,16)$ and$(\kappa_\sigma,\kappa_\Phi,\kappa_\psi)=(1/4\pi,1,2)$; stationarity fixes thecorresponding chemical tilts. Thus $s_0=\alpha_Z^3/(4\pi)=3.80\times10^{-8}$,while electroweak and colour channels reproduce the stated SPARC normalisationand QCD string scale without sector-specific continuous prefactors. \textbf{Conclusions.}\ The Born phase fixes the internal complex and timelike spacetime directions;non-zero charge selects a unique stable timelike branch without altering$G_2\to SU(3)$. The constrained parent action has one physical matter/photon/tensor metric and four propagating degrees of freedom. Gauge kinematics,representations, anomaly cancellation, orbit measure and breaking are derivedor checked at the stated tier. Confinement dynamics, down/charged-lepton flavour and mixing, a geometricderivation of the conditional neutrino Majorana texture, full fermion polematching and a propagating chiral substrate remain open; Part~I independentlyyields the GR near-zone PPN coefficients.

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