Cosmic Void Formation and Coherence Consolidation Geometry: Why Voids Empty, Where Boundaries Fall, and Why Mass Concentrates in Sheets

Cosmic voids occupy 60-80% of the universe's volume yet contain only 15-20% of its mean matter density. Standard cosmology derives void properties from N-body simulations — computational outputs, not analytical predictions.

We show that both void formation and sheet-like mass consolidation arise analytically from the coherence gradient equation d(rho_c)/dr = -M(r)*rho_c + R(r) - A_xt(r) combined with the empirical Kennicutt-Schmidt star formation law (Sigma_SFR proportional to Sigma_gas^1.4).

Key results:

- Predicted void interior density of ~17% of cosmic mean matches observations (15-20%) with zero free parameters. The superlinear K-S scaling (N = 1.4) means reducing density cuts regeneration faster than it reduces coherence maintenance demand, producing a sharp threshold.

- Sheet-like consolidation predicted as the symmetric consequence: above threshold, increasing density amplifies regeneration faster than maintenance demand, concentrating organization into planar and filamentary structures.

- Independent confirmation from Wempe et al. (2026, Nature Astronomy): using 169 constrained LCDM simulations of the Local Group, they found mass distribution concentrated in a sheet aligned with the Supergalactic Plane with deep voids above and below at 26% and 31% of cosmic mean. Spherical model rejected at 5.4 sigma. The geometry matches the gradient equation prediction without constrained initial conditions.

- Four testable predictions distinguishable from LCDM: non-constant void expansion rates tracking bandwidth evolution B_c(z), organized magnetic fields in voids detectable via Faraday RM surveys, redshift-dependent void boundary density, and anisotropic velocity fields correlating with magnetic organization gradients rather than enclosed mass alone.

The mechanism differs from gravitational evacuation: voids form because cooperative processes (star formation, dynamo action) become unsustainable below a density threshold. Organization consolidates into the cosmic web where maintenance remains viable.

Part of the Coherence Institute publication sequence. Tier 1 novel proof — LCDM produces void density only as simulation output, not analytical prediction.