The cosmic web's graph runs over-connected at the top: massive nodes carry more filaments and more multi-filament junctions than hierarchical growth from Gaussian initial conditions supplies, with connectivity-mass relations deviating from the halo-model baseline (Codis 2018; Darragh-Ford 2019). A node should not out-connect its growth history, yet the measured ones do.
In the standard picture connectivity is accumulated: shear funnels matter along preferred axes toward deepening wells, so the number of filaments per node is an output of growth, rising gently with mass. An over-connected population forces non-Gaussian initial conditions or missing assembly dynamics, because the model has no way to hand a node its connections up front.
SCT reads the graph the other way around: the most massive clusters form at collision nodes where filaments of different orientations intersect (P34), so connectivity is not accumulated by growth but inherited from the number of cascade events whose geometry crossed there. Each cascade stage threading an intersection contributes its own deposited filament to the node, and the cascade's multi-stage structure (P36, P37) makes multiply-crossed locations both the most massive and the most connected, simultaneously and for the same reason. High connectivity at high mass stops being a coincidence the growth model must engineer and becomes the defining geometry of what a massive node is.
The secondary signature is rotational: angular momentum inheritance (P31, P32) gives each contributed filament its own J imprint, so high-connectivity nodes should carry multi-axis spin structure correlated with their filament directions, a registered cross-check on the same geometry. The web-as-deposited-graph picture is laid out in Paper 1, From Chaos to Convergent Foundations, with the cascade seeding mechanics in Paper 4, From Chaos To Collisothermal Cosmogenesis. The same single inversion, deposited rather than grown, carries the filament length function (recid 72) and the width-mass flatness (recid 73); connectivity is the third axis of one geometric statement.
Keystone economy: P34 alone supplies the intersection nodes; P36 and P37 supply their multiplicity. Nothing non-Gaussian is added, because the graph was never drawn by Gaussian growth in the first place.
DESI and Euclid connectivity functions carry the kill: if node connectivity tracks halo mass exactly as hierarchical growth predicts across the full mass range, with no excess at the massive end and no correlation between connectivity and multi-axis spin structure, the intersection picture is refuted. SCT requires the over-connected massive population and its rotational fingerprint; a clean growth-only graph ends the M4 reading of the web sector.