A Spectral Bridge Programme for Deficit-Fractal Governance: Trace Formulae and Zeta Structures

This technical note states a conjectural spectral bridge programme for Deficit-Fractal Governance. It explores structural analogies between DFG path-zeta functions, FDCL complex dimensions, log-periodic corrections, trace-formula ideas, and Riemann-type spectral analogies. The document explicitly does not prove a trace formula, a Riemann-zero correspondence, or a completed zeta theory. Instead, it isolates the mathematical conditions that would be required for such a programme, including a canonical self-adjoint FDCL Laplacian, a rigorously defined path zeta function, a trace formula linking primitive FDCL paths to spectral data, and an independent justification for any Riemann-type comparison. The log-periodic frequency ωF=2π/log⁡2\omega_F = 2\pi / \log 2ωF=2π/log2 is treated as a dyadic FDCL substrate diagnostic, not as a substrate-independent prediction of the full DFG framework. This is Paper 6 of the six-part DFG Unified Interaction Field Theory Series.