Emergent Tetradic Gravity, Operational Interaction-Frequency Time, and Cyclic Cosmology on a Superfluid Möbius Manifold

Building strictly on the microscopic core anchor r₀ = 0.000635 fm established in Paper I, we develop the gravitational, temporal, and cosmological sector of the ESEM framework without free cosmological parameters. Proper time is formalized operationally as the internal Madelung phase-locking frequency (dτ = dN_int/ν₀) within a Painlevé–Gullstrand acoustic metric, deriving the emergent gravitational constant G_ESEM and reproducing solar gravitational redshift (636.02 m/s), Mercury's perihelion precession (42.96″/century), and the net relativistic clock drift of GPS satellites (+38.49 μs/day). Two-dimensional Fubini–Beltrami integration over the orthogonal 2-torus fixes the cosmic matter fraction at Ωₘ = 1/π ≈ 0.3183 (Ω_Λ ≈ 0.6817, Ω_b ≈ 0.0500). Three-dimensional Stefan–Boltzmann closure locks the CMB temperature to node N = 121 (T_CMB ∈ [2.722, 2.751] K), while Peebles' recombination ODE yields z_dec = 1069.8 and acoustic scale ℓ_A = 303.39. Parameter-free primordial nucleosynthesis reproduces ⁴He (Yₚ = 0.2473), Deuterium (D/H = 2.52 × 10⁻⁵), and resolves the ⁷Li problem via WKB transition-state suppression (⁷Li/H = 1.46 × 10⁻¹⁰). Finally, a 1/8 Bernoulli enthalpy jump reconciles global/CMB (67.82 km/s/Mpc) and local (72.66 km/s/Mpc) Hubble rates, accounts for SPARC galactic rotation curves (a₀ = 1.17 × 10⁻¹⁰ m/s²), and enforces proper-time extinction (dτ = 0) across a Weyl-invariant conformal bounce