Two-Energy Theory (TDE) v14.11 Gravitational Closure with a Geometric Topological Barrier (Octant Unification)

This deposition contains the main preprint of Two-Energy Theory (TDE) v14.11 and a structured set of supplementary verification packages. TDE is formulated as a resonant effective field theory with a “Shadow” response sector and a topological barrier governing branching between stable (baryonic) and shadow (dark) channels. In v14.11 the previously empirical barrier value is fixed geometrically by the Octant Unification: the 4D anchor k = 4π + 1 projected onto the 8 octants of 3D space, giving ΔS = (4π + 1)/8. This removes the last arbitrary numerical input and turns the barrier into a geometry-fixed quantity. The main PDF presents the covariant action, the gravity-closure mechanism (screening/gates), and the minimal consistency conditions. Supplementary packages provide: (i) a detailed geometry note and microscopic anomaly-map factors, (ii) engineering verification pipelines for galaxy rotation curves (SPARC) and Solar-System weak-field constraints (PPN/Solar Gate), and (iii) cosmology-focused renormalization tests on public DESI DR1 posteriors. This work is released as a falsifiable research program. Readers are explicitly encouraged to reproduce the calculations, challenge assumptions, and test the framework against independent datasets.