CAT'S Theory: The Curved-Manifold Correction to the Proton Mass and the Dual-Branch Resolution of the Hubble Tension

Two results are derived within the CAT'S Theory plenum architecture. First, the proton-to-electron mass ratio is completed to eight significant figures: mₚ/mₑ = 1836 + 1/(2π) - 7/1080 = 1836.15267346, matching the CODATA 2022/PDG 2024 value $1836.152,673,426(32)$ at 3.6 × 10⁻⁸ accuracy. The integer skeleton 1836 = d³ · dP · dI / 2 was established in Paper 199; the present work identifies the residual as the curved-manifold correction to the flat-lattice confinement triangle. Second, the Hubble tension is structurally explained as a dual-branch admissibility effect on the canonical lattice Λ = 312. Both correction factors are exact corpus fractions forced by the knot topology.