FDCL Part II: Spectral Reduction and Renormalization on FDCL Graphs

We study spectral reduction on specified graphs associated with the six-digit FDCL construction. The coordinate-merged skeleton has an exact template spectrum and explicit all-level gap upper bounds for counting and degree-weighted mass. For the auxiliary eight-edge metric carrier, a pole-free matching equation gives the complete spectrum and a rational enclosure of the simple first positive eigenvalue. Static reduction is distinguished from spectral reduction by harmonic mass and an explicit parameter-dependent remainder. An internal-cell comparison gives the sharp uniform pinned spectral lower bound for the voxel graph. A five-type barrier bounds one-step harmonic mass, while an optimal affine coordinate trial yields an explicit summable variance deficit. An exact harmonic certificate separates a fixed transfer's full, energy, and quotient spaces. A comparison form proves energy-space contraction; rational counterexamples disprove two proposed refinement recursions, and the constant-correction scheme eventually loses positivity. Constraint-kernel coercivity gives an unregularized minimizer and a regularization-bias bound. Finite numerical evidence and unresolved identifications retain their stated scope. Series and status. FDCL Part II of twelve, Version 1.0 (manuscript dated 7 October 2026, 38 pages); unsubmitted working paper. The FDCL series studies the Fractal Diagonal Cut Lattice, the three-dimensional self-similar set generated by six dyadic corner maps, and the graph, operator and gauge models associated with it. This part cites Parts I, III, V, VIII and IX as companion manuscripts. Files: the manuscript as PDF and a source archive (49 files) with the LaTeX source, a figure, explicit exact witnesses, verification scripts and the finite records behind its numerical tables. The other parts are archived separately. AI use disclosure. Generative AI (GPT-6.0, OpenAI; Claude Opus 5.5, Anthropic) was used substantively in preparing this work, including literature comparison, the development and checking of proofs and counterexamples, exact computations and the writing and running of verification code, and drafting and editing. The research questions, framework and final claims were directed and reviewed by the author, who takes full responsibility for the content, including the accuracy of all references and reported numbers. Repository metadata were prepared with assistance from Claude (Anthropic).