Cosmic-web filament lengths are expected in ΛCDM to follow from the Gaussian initial density field and tidal shear, with simulations predicting specific length-shear correlations (Bond 1996; Pogosyan 2009). Surveys and simulations find filaments longer, more coherent, or differently distributed with respect to the ambient tidal shear than ΛCDM plus halo-model expectations (Bond 2010; Cautun 2014).
The standard model assumes filaments form as condensations along principal axes of the tidal-shear tensor, with length determined by the smoothing scale and shear amplitude. Persistent over-coherence and length-shear scaling deviations have nowhere to go in the model except as missing baryonic physics or limitations in the halo-model treatment of filament assembly.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, cosmic-web filaments are not condensations sculpted by tidal shear over cosmic time; they are direct geometric products of head-on (low impact-parameter) collisions deposited during the cascade (P22, P33). The collision impact-parameter distribution P(b) ∝ b favors grazing collisions geometrically, but head-on collisions still occur at non-zero rate and produce the observed filament population (P34).
Filament length scales with the combined pocket extent along the collision axis, which traces back to the cascade-stage hierarchy: longer filaments come from more energetic earlier collision stages with larger v_rel and parent-pocket separations (P22, P36). The largest first-stage filaments cap at the parent-pocket scale Λ_max ≈ 5 Gpc (P55), reproducing the observed ultra-long coherent structures like the Sloan Great Wall and the Hercules-Corona Borealis Wall. Shorter filaments come from later cascade stages operating on smaller daughter-fragment scales (P37, P38).
The length-shear scaling deviates from ΛCDM expectations because tidal shear is not the originating mechanism. Once filaments are deposited by the cascade, they propagate forward under standard gravitational evolution, and the resulting length-shear correlations reflect collision-deposited geometry plus subsequent-evolution shear effects. The same M4 framework that produces gigaparsec ring-and-arc structures (recid 85), supervoid abundance (recid 86), and the cosmic-web morphology in general accounts for the filament length distribution.
If precision DESI + 4MOST + Euclid filament-shear catalogs find length-shear scaling fully consistent with the ΛCDM tidal-shear formation prediction at the 1% level (no cascade-stage hierarchy signature in length-vs-energy correlations), the M4 cascade-stream explanation is refuted. The signature SCT prediction is a discrete length distribution reflecting cascade stages rather than a continuous shear-driven distribution.