ASCM Topological Journal

This manuscript presents Part II (ASCM Topological) of the Axiomatic Sector Cosmological Model, establishing the rigorous geometric and representation-theoretic completion of the boundary-coupled dual-manifold effective field theory. By replacing the phenomenological calibrations and algebraic inversions of Part I, this document derives the framework's macroscopic observables through six unconstrained topological proofs without residual parameter fitting.Core Theoretical AdvancementsOrbifold Chiral Bifurcation: Formulates the 5D warped bulk on an $S^1/\mathbb{Z}_2$ orbifold, utilizing discrete parity transformations to enforce chiral boundary bifurcation and strictly decouple the Kaluza-Klein sterile neutrino tower from the thermal bath $(\Delta N_{eff}^{KK} = 0)$.Dynamical Mass Hierarchy: Generates the right-handed Majorana mass hierarchy $(10^{14}, 10^{15}, 10^{16} \text{ GeV})$ organically via a 5D bulk scalar vacuum expectation value coupled to the fundamental 5D spin-connection invariant.Casimir Phase Isolation: Utilizes native $SL(2,\mathbb{C})_q$ Casimir invariants under the linear simplicity constraint to bifurcate the complex spin-foam saddle action, insulating the $42 \times 42$ Hermitian metric constraint matrix while projecting the topological anomaly onto the Pontryagin density.Rigorous Vertex Mixing: Derives the 4-simplex dihedral vertex-mixing factor directly from Gaussian integration of the internal dihedral boost angles for a free Barbero-Immirzi parameter $\gamma$.Dynamical E-Fold Emergence: Formulates the renormalization-group scale map strictly from the 5D-to-4D warped mass ratio, allowing the 60.0421 e-fold inflationary duration to emerge dynamically from implicit Radau integration.Combinatorial UV Capacity: Defines the horizon capacity and the exact $1.0 \times 10^{-122}$ vacuum residual directly through the combinatorial discrete area of the initial UV spin-network graph and the Turaev-Viro invariant, completely eliminating infrared circularity.