Filament lengths should be set by tidal shear acting on the Gaussian initial field, yet catalogs and simulations find filaments longer and more coherent than the shear-sculpting picture predicts (Bond 1996; Pogosyan 2009; Cautun 2014), with the extreme tail reaching gigaparsec walls and arcs that no shear field should assemble in the time available.
The model assumes filaments are grown: condensations sculpted along shear-tensor axes over cosmic time, with length an output of the shear environment and smoothing scale. A population running long and coherent has nowhere to go except missing baryonic physics or a confession that the shear treatment is incomplete, and the gigaparsec extremes strain even that.
SCT inverts the causality: filaments are direct geometric products of the collision cascade, deposited at thermalization rather than sculpted afterward. Head-on, low-impact-parameter collisions convert kinetic energy into heat and compression along the collision axis while matter collapses freely in the perpendicular directions, producing elongated filaments whose length scales with the combined pocket extent along that axis (P33). The impact-parameter distribution P(b) ∝ b makes grazing collisions the geometric majority, but the head-on minority is exactly the filament population (P34).
Length then inherits the cascade hierarchy rather than the shear field. Earlier, larger cascade stages deposit longer filaments, capped at the first-stage characteristic scale Λ_max ≈ 2 × R_pocket ≈ 5 Gpc (P55), which is why the Sloan Great Wall and the Hercules-Corona Borealis Wall are predictions here and anomalies elsewhere; later stages operating on daughter fragments deposit the shorter population (P36, P37). The observed length-shear correlations are then second-order: deposited filaments evolve forward under ordinary gravity, picking up shear signatures without being created by them. The geometry is laid out in Paper 1, From Chaos to Convergent Foundations, with the cascade-seeded structure mechanics in Paper 4, From Chaos To Collisothermal Cosmogenesis.
One premise is the keystone: P33. Remove head-on deposition and the long-coherent population must be grown by shear after all; keep it and the length function becomes a fossil record of the cascade stages.
DESI, 4MOST, and Euclid filament catalogs carry the kill: if the length distribution is a smooth continuous function fully consistent with shear-driven assembly, with no characteristic scales echoing cascade stages and no coherent population beyond what shear can build in the available time, the deposition picture is refuted. SCT requires the long tail to exist and to cap near the Λ_max ≈ 5 Gpc first-stage scale; a clean shear-only length function ends the M4 reading.