Cosmic-web filament transverse widths are expected in ΛCDM to scale with the linear mass density of embedded halos through standard gravitational-collapse balance (Bond 1996; Zhu 2024). Observations and detailed simulations often find systematically different widths at fixed mass, nearly scale-invariant widths over wide mass ranges, or more complex trends than the basic shear-based picture predicts (Cautun 2014; Zhu 2025).
The standard model assumes filament width follows from gravitational collapse of mass onto a linear potential well, with width determined by velocity dispersion or thermal pressure halting collapse. Recovering the observed scale-invariant or weak-scaling widths within the model demands missing environmental physics or baryonic effects.
SCT replaces the hot-dense-center with a superluminal collision and the thermalized debris field. From this single change, filament widths are set at deposition by collision geometry, not by subsequent gravitational collapse. Head-on collisions produce filaments whose width scales with the smaller pocket's self-gravity: W ∝ M_min¹⁄³ (P33). The cascade impact-parameter distribution P(b) ∝ b (P34) gives the population statistics.
The cascade-stage hierarchy (P22, P36, P37, P38) sets the length-vs-energy and length-vs-mass scaling relations. Predicted scaling W ∝ M^β with β ≈ 0.3 to 0.4, distinguishable from ΛCDM hierarchical clustering β ≈ 0.45 to 0.55. The scale-near-invariance over wide mass ranges that surveys observe reflects the cascade origin, where width is set by initial collision geometry rather than by subsequent collapse equilibration.
The same M4 framework that produces filament-length scaling (recid 72), gigaparsec ring-and-arc structures (recid 85), and supervoid abundance (recid 86) produces the filament-width signature. There is no need for missing environmental physics or baryonic effects beyond the standard treatment. The width is what cascade-deposited filaments look like.
If precision DESI + 4MOST + Euclid filament-width measurements find W ∝ M^β with β in the ΛCDM range 0.45 to 0.55 across all mass scales (no SCT-cascade-distinct β ≈ 0.3 to 0.4 signature), the M4 cascade-deposition explanation is refuted. The signature SCT prediction is a flatter mass-width scaling than the standard hierarchical-clustering prediction.