Hexagonal Toroidal Lattice Cosmology: Observational Pipeline, CMB Falsification, and Branch A Statistical Design

We test the hypothesis that the universe has a hexagonal T³ fundamental domain at scale L ~ 13–28 Gpc. A three-gate observational pipeline is constructed covering CMB angular power, galaxy large-scale structure, and SZ cluster statistics. The SDOP coupling chain (topological identification → reciprocal lattice → discrete Fourier modes → predicted Cℓ → Planck comparison) is derived and executed via a transfer-function-independent ratio test. The hexagonal T³ geometry predicts 10–15× too much CMB TT power at ℓ = 4–30 relative to Planck 2018, yielding χ²_CV = 36,524 versus 341 for ΛCDM. The geometry is falsified at >>100σ (TRIDENT Case Card HEX-T3-001). The falsification is geometry-specific and does not exclude other compact topologies or emergent hexagonal structure in large-scale structure data. Branch A — a pre-registered test for hexagonal angular periodicity in DESI DR1 galaxy correlations — remains open. The statistical design, DESI ingestion pipeline, and pre-registered failure modes for Branch A are included. Keywords: cosmic topology, CMB power spectrum, Planck 2018, toroidal universe, hexagonal lattice, large-scale structure, DESI, Landy-Szalay, angular correlation function, Sachs-Wolfe approximation, falsification, pre-registration, compact manifolds, low multipole anomalies, reciprocal lattice