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Cohesion Dynamics (CD)

Cohesion Dynamics — Paper B v0.9 - Continuum Physics in Cohesive Phases

Paper B develops the continuum limit of Cohesion Dynamics (CD) in cohesive phases—regions where the substrate exhibits finite height on all finite regions, locally bounded mismatch propagation, and stable refinement of mismatch-minimizing configurations.

Key Results:

  • CD admits a continuum description consisting of: (1) a limit field ϕ(x)\phi(x), (2) a hyperbolic partial differential equation governing its evolution in closure time, and (3) an effective Lorentzian causal structure derived from the PDE’s principal symbol
  • In any cohesive phase satisfying assumptions (B1) and (M2), CD necessarily yields second-order hyperbolic dynamics with a Lorentzian cone structure
  • Derives universal mismatch Lagrangian from assumption M2, second-order closure recurrence, continuum limit, and metric structure
  • Introduces operational time field; analyzes divergence surfaces and horizon formation

Scope: Makes no claims regarding gravity, Einstein equations, quantum structure, or cosmology. Goal is strictly structural: to show that cohesive phases necessarily yield hyperbolic dynamics with Lorentzian cone structure.

Paper ID: CD-B | Series: B-series (Continuum Physics) | Status: Draft v0.9 | Dependencies: Paper A (Substrate Mechanics)