Priority-Axis Z-Algebra Dark Matter Theory: A Unified Framework of Interface Rigidity Conservation and Dynamical Tension

【Abstract】The standard ΛCDM model treats baryonic matter, cold dark matter, and dark energy as three mutually independent fundamental fields, an ontological fragmentation; decades of null results from direct detection of particle dark matter (WIMPs, etc.) compel a re-examination of whether dark matter is an independent elementary particle field. Within the priority-axis Z-algebra axiomatic system and the odd-real spectral triple (𝒜, H, D, J_M), this paper establishes a unified algebraic ontology of dark matter: the interface anticommutator {A, B} = 2J(t² − r²) · 1 is rigorously proved to be a rigid conserved element frozen in the algebra center, rendered classically invisible by a sextuple nullification mechanism and coupled to gravity only through the virtual-curvature channel; the commutator [A, B] = 4t(xi + yj)τ of the active transverse subspace Im(D_τ) is the unique intrinsic source of local shear tension, density perturbations, and velocity dispersion. It should be noted that the virtual-curvature effective energy-momentum tensor and the modified Friedmann equations are framework-level constructions, whose rigorous derivation from the spectral action remains an open problem. Dark matter is thus embedded in the Z-algebra three-phase cosmological framework, forming an exact decoupling duality of w_DM = 0 versus w_DE = −1 with dark energy, both sharing the same priority axis (l, b) ≈ (260°, 30°). All algebraic conclusions are verified by an independent exact symbolic-verification script (41 tests, 41 passed, with strictly zero residuals), with falsifiable predictions including null direct-detection signals, logarithmic rotation-curve corrections, CMB priority-axis anisotropy, and scalar gravitational-wave polarization.