CARTOGRAPHY OF THE SENTIENT MANIFOLD

We present the Möbius-Dilaton Torus, a non-orientable warped product manifold M = S¹_τ ×_w T²_Möbius from which geometry, time, probability, quantum mechanics, and every fundamental constant emerge as consequences of a single rendering cascade. Building on four prior papers establishing the dilaton-consciousness identification, scrambling suppression at finite cutoff, and the torus as a new mathematical object, we prove ER=EPR as a topological theorem on this manifold: the non-orientable identification produces the Einstein-Rosen bridge necessarily, while the boundary perspective produces Einstein-Podolsky-Rosen entanglement necessarily, with a distinguishing parity-odd witness μ = −1. We derive the fine-structure constant α⁻¹ = 4π³ + π² + π = 137.0363 from the torus geometry (agreement: 2.2 × 10⁻⁶ with CODATA 2022), the dark-to-visible matter ratio Ω_DM/Ω_b = φ³ × 4/π (1.3%), the CMB first acoustic peak ℓ₁ = α⁻¹ × φ (0.8%), the baryon asymmetry η_B = α⁴κ² (1.8%), and the neutrino mass hierarchy Δm²₃₁/Δm²₂₁ = (1 + √2)⁴ = 17 + 12√2 (4.3%). Seven predictions with zero free parameters, all under 5% agreement with observation. Predictions organize by metallic mean: topological invariants carry the golden ratio φ, boundary quantities carry the silver ratio 1 + √2, with the recursion depth of each derivation determining which constant appears. Dark matter is identified as unrendered gravitational contribution, dark energy as rendering in progress, and neutron stars as the observable face of white holes. The Born rule emerges as thermodynamic accounting of cascade displacement costs. The framework resolves the hierarchy problem, addresses the cosmological constant, and recovers string theory as interior cascade harmonics on the torus fiber. No adjustable parameters are introduced.