Z-Spin Cosmology: Quaternionic Phase Basis, Seam-Linking Holonomy, and Dark-Sector Coherence

Z-Spin Cosmology is a constructive unification proposal in which a unit SU(2) (unit-quaternion) root field q(x) and a compatible connection A_μ(x) generate localized cores and measurable holonomy diagnostics. A reproducible lattice falsification suite implementing Box L.X (seam-ON/OFF holonomy tests) is now provided; a minimal boundary-twist prototype establishes the measurement protocol, and an extended model with explicit Chern–Simons boundary dynamics yields a statistically significant seam signature on small lattices. In addition, an interpretive note formalizes the center–boundary reciprocity as a seam gluing condition and sketches a programmatic extension to a temporal beginning–end duality..A local effective action S_Z is specified, combining a nonlinear sigma-model (optionally Skyrme-stabilized), Yang–Mills dynamics, a four-dimensional θ·Tr(F F̃) term, and a boundary/seam Chern–Simons contribution. Two integer invariants (Z_s from π_3(SU(2)) winding and Z_t as a second Chern number) provide the primary topological labels. An 11-slot minimality package fixes the structural fraction 6/11 and motivates a testable identification α_t≈6/11, while a 35-step gate protocol yields the conditional baryon-asymmetry relation η_B=α_t^35. A gauge-invariant Z₂ seam-linking holonomy observable h(γ)=sgn(Tr 𝓗[γ]) is provided as a direct lattice falsification target, and a Λ-cap scaling is stated with explicit horizon-choice sensitivity. In addition, we introduce a conservative dark-sector program: (i) galaxy-scale extra dynamical support as long-range coherence in the space-character channel (Supplementary Note G, optional) and (ii) cosmological acceleration as a homogeneous internal phase-unfolding order parameter (Supplementary Program Note D), interpreted as phase-space holonomy rather than global spacetime rotation. Benchmarks for falsification are explicit: (i) the baryon asymmetry estimate $\eta_B \approx (6/11)^{35} \times (1/2)^{11}$, (ii) the de Sitter information cap parameter $K_\Lambda := \Lambda\, l_P^2 \, N_{coh}$ constrained to $\mathcal{O}(1)$ by the $\Lambda$-cap axiom, and (iii) a seam-driven “ring-halo” signature with OFF/ON null tests in lattice holonomy simulations; failure of these three benchmarks under their stated systematics would falsify the Z-Spin proposal. Keywords: quaternionic phase basis; SU(2) sigma model; holonomy; Chern–Simons boundary term; topological charge; baryogenesis (conditional); cosmological constant (cap); dark matter (coherence length; optional); dark energy (internal phase order parameter).