Program architecture
One program. Explicit bridges.
CGG, CFC, UCFT, CGBC and ART share a research direction. Each mathematical connection still needs its own stated premises and calculation.
Branches and connections
| Branch | Mathematical object | Connection status |
|---|---|---|
| CGG geometry | Ricci eigenplanes, spectral-area form Ω, curvature r, shear S | Static transport and conditional local classification are recorded. |
| Magnetic matter | F = Ω; L(I) proportional to √I | Exact local realization of the selected static families; does not derive the full selection condition. |
| CGBC scalar sector | Chosen DBI action P(X) | Scalar field equation follows after choosing the action. A unified scalar–gauge–gravity action remains open. |
| CFC discrete proposal | Weighted graph Laplacian; algebraic connectivity λ₂ | New operational extension dated 29 September 2026. Graph connectivity is not automatically quantum coherence. |
| ART / biology | Aromatic networks, molecular structures, measured optical response | Candidate applications. No calibrated map from biological measurements to r or Ω is established. |
| UCFT | Proposed synthesis of coherence, collapse and gravity | Program-level goal; the branches do not yet constitute a completed unified physical theory. |
Discrete CFC proposal
L(w) = Σₑ wₑ bₑ bₑᵀ = D − A
λ₂ = min{xᵀLx : x ⟂ 1, ‖x‖ = 1}
∂λ₂/∂wₑ = (vᵢ − vⱼ)² [simple λ₂, normalized v]
κ_rate = λ₂ / γ [declared measured reference rate γ > 0]The Laplacian’s kernel proves the connectivity criterion. A threshold, physical edge weights and disruption rates are additional model choices. A controlled continuum action selecting DBI has not been derived.
Source: Spectral resilience as a discrete CFC starting point, Thomas Lee Allen Jr., 29 September 2026. This proposal is distinct from the Ricci spectral gap.