Bootstrap Cosmic Web: Coherence Waveguides, Symmetry-Breaking, and Pattern Formation at Cluster Scale

We extend the Bootstrap Dark Matter framework from galaxy scale to cluster and cosmic-web scales. At galaxy scale, dark matter signatures arise from Kuramoto synchronisation of lattice vibrational modes, with coherent disk rotation providing injection locking at K/Kc = c/v (Keeble 2026). At cluster scale, the coupling mechanism changes: three hierarchical processes replace the single galaxy-disk driver. (1) Filaments as coherence waveguides: cosmic-web filaments are self-organising coherence conduits whose observed three-zone radial structure — outer thermal, intermediate vortex, inner cold stream (Lu & Mandelker et al. 2024) — maps directly onto the Kuramoto sub-critical → transition → super-critical progression. (2) AGN jet symmetry-breaking: at cluster scale, N ~ 1,000 galaxies orbit on random axes, causing gravitomagnetic cancellation by 1/√N (standard statistical mechanics). Relativistic jets from brightest cluster galaxies define a preferred axis, partially aligning galaxy orbits and converting incoherent (√N) summation to coherent (N) summation within the jet cone. Direct electromagnetic coupling is ruled out: the jet's helical field rotates at ~10⁻¹³ Hz, 36 orders of magnitude below the proton frequency. (3) Galaxy–galaxy pattern formation: mutual coupling between internally coherent galaxies (each at Q ~ 1) creates interference patterns whose geometry naturally produces the void-filament-node topology of the cosmic web. Filament one-dimensionality is explained through the tidal tensor: coherence propagates fastest along axes of maximum lattice compression, reproducing the Zel'dovich collapse sequence without requiring dark matter scaffolding. The Bullet Cluster observation — gravitational lensing offset from X-ray gas — is reinterpreted: lensing traces coherence (compact galaxies retain internal Q through collision) while hot ICM plasma loses external coupling; the observed mass ratio of 6–8:1 matches the Bootstrap prediction of 1 + 27/5 = 6.4:1 with no free parameters. The cluster-scale coupling deficit — where the effective coupling quality Qcluster < Qgalaxy — explains both the known failure of single-parameter acceleration-scale models at cluster scale (resolved in detail in the companion Bootstrap MOND paper) and the Planck cosmic average Qcosmic = 0.9935. Six observational tests are proposed, including a new prediction for the Sunyaev-Zel'dovich hydrostatic mass bias.