Z-Spin Cosmology: The Geometric Impedance, i-Tetration Fixed Point, and the Origin of Spacetime Asymmetry

This comprehensive manuscript presents Z-Spin Cosmology, a fundamentally new ontological and mathematical framework that unites macroscopic gravity ($\Lambda$CDM) and microscopic quantum mechanics (Standard Model) without introducing any phenomenological free parameters.

We propose that spacetime is an emergent, three-layered structure: the macroscopic space/particle sector ($X$-sector, dim=3), the microscopic time/wave sector ($Y$-sector, dim=6), and the Planck-scale entanglement boundary that mediates between them ($Z$-sector, dim=2). By analyzing the polyhedral geometric symmetries and the Lorentz algebra decomposition of these sectors, we derive the universal "Geometric Impedance" constant, $A = 35/437 \approx 0.08009$. This single geometric ratio strictly governs the transduction of physical information across the Planck-scale boundary.

In parallel, the dynamics of the $Z$-sector boundary are mathematically uniquely determined by the $i$-tetration continuous group homomorphism, converging to the self-referential attractive fixed point $z^* = i^{z^*} \approx 0.4383 + 0.3606i$.

With zero adjustable parameters, the Z-Spin action successfully deduces and strictly constrains major physical anomalies:

1. Cosmological Parameters: Analytically resolves the Hubble tension via the holonomy mapping $H_0^{local}/H_0^{CMB} = e^A$, and derives the dark matter/energy density fractions from the 11-slot geometric register.

2. Baryogenesis & Particle Physics: Derives the baryon density $\Omega_b = 6/121$ and the exact baryon asymmetry ratio $\eta_B = (6/11)^{35}$ directly from the partition function weight ratio.

3. Quantum Foundations: Provides an axion-free resolution to the Strong CP problem via $Y$-sector instanton suppression, predicting a neutron electric dipole moment of $d_n \sim 2.0 \times 10^{-41} \text{ e}\cdot\text{cm}$.

The framework has passed over 400 pre-registered falsification gates. It offers a mathematically closed, self-consistent structural interpretation of the universe where existence itself emerges from the topological necessity of self-reference.