The FDCL Substrate in Deficit-Fractal Governance: Spectral Gap, Bifurcation, and Fractal Propagation

This bridge paper connects the Deficit-Fractal Governance framework to the Fractal Diagonal Cut Lattice mathematical substrate programme. It summarizes the FDCL results relevant to DFG and states their implications for the governance instability operator. Key imported results include the FDCL attractor construction, self-similar measure, skeleton dimension, spectral gap scaling, backbone/bulk spectral-gap bifurcation, and retained-backbone spectral laws. The paper carefully separates distinct FDCL spectral objects, including retained S2S_2S2 / CR1-projected backbone objects, full geometric FDCL face-adjacency objects, and proxy spectral channels. It also emphasizes that the actual containment gap in bulk regimes scales as cn6−nc_n 6^{-n}cn6−n, not as cnc_ncn alone. The paper is a bridge document, not an independent proof paper, and preserves object-level distinctions between proved FDCL results, conditional continuum-limit claims, and open substrate questions. This is Paper 3 of the six-part DFG Unified Interaction Field Theory Series.