Fundamental foundations and derivation of model parameters: tensioned vacuum, coherent volume and Y-junction mechanism

We define the microscopic foundation of the T3 model and derive all parameters from first principles. The zero state is a tensioned empty vacuum with a single 1D filament of zero thickness and zero energy, thickening into a tube of 1 fm. The filament carries unit norm, bare tension around 1e38 GeV squared renormalized to 0.18 GeV squared, and Berry phase coupling to fermions. The first grain is set by LQC bounce instanton around 50.38 with suppression about 1.3e-22 and spectral dimension 11 over 3, giving effective grain 0.11 micron and coherent volume as cube of that length. Physical normalization is 1 over coherent volume, yielding 0.027 critical density for harmonic 3 and 0.26 for harmonic 9. Unit norm follows from vortex topology, homogeneity from coarse-graining. We derive the origin of 10 to 102 grains via Y-junction cross-link instability. A single infinite filament unfolds when curvature exceeds threshold, splits into Y-junction and exposes new grain, giving 78 volume e-folds to 50 to 75 Gpc. The 0.11 micron scale links theory to experiment: deviation from inverse square law below micron, Casimir correction, PdHx NMR shift, gravitational wave dispersion, T3 topology with circles in the sky and low multipole suppression, and dark energy and dark matter as harmonics 3 and 9 of the same elasticity.