The Cosmic Web as a Generalized Murray Network: Transport-Optimal Branching Under Gravitational–Dark Energy Coupled Mass Flow

EMPIRICAL REVISION v2.0 — Supersedes v1.0 (DOI: 10.5281/zenodo.20274511) The v1.0 formula α_gravity(z) = 2 + δα × [Ω_Λ(z) / (Ω_Λ(z) + f_c × Ω_m(z))] is formally retracted as numerological — an ad hoc parametrization lacking theoretical lineage in structure-formation physics.This version derives the branching exponent α from first principles: mass transport through self-gravitating cylindrical filaments obeys R_parent^α = Σ(R_child^α), with α = 2 + β where β governs the velocity-radius scaling of dark matter infall (v ∝ R^β). Blind empirical testing using TNG100-1 subhalo velocity dispersions and half-mass radii across four redshifts (z = 0, 0.5, 1.0, 2.0) returns β = 0.28 ± 0.01 at all redshifts, yielding α = 2.28 ± 0.02 with no statistically significant redshift evolution (d(β)/dz = −0.019, p = 0.20). The revised falsifiable prediction is R_child/R_parent = 2^(−1/2.28) = 0.737 at symmetric binary filament branching nodes. This supersedes the v1.0 prediction of 0.762. Confirmation requires direct DisPerSE filament spine measurements in TNG100-1; a data request was submitted May 19, 2026. This result is derived from a subhalo proxy, not direct filament spine data. It is a necessary step toward the correct test, not the correct test itself. We report what the data says — no more, no less.This is the twenty-third preprint published through the Presignal Research Initiative and the third in a series applying generalized Murray's Law across physical scales.