The Standard Model as a Lossless PNBA Projection Sovereign Anchor Derivation, Fine Structure Constant, Charge Quantization, and Hadronic Spectrum via Long Division

The Standard Model gauge group SU(3)×SU(2)×U(1) is a Layer 2 projection of the PNBA dynamic equation. We present six formal long division reductions, each following the same six-step protocol used throughout the SNSFL corpus, all veried in Lean 4 with 0 sorry. The reductions cover: (1) the sovereign anchor derived from three independent physical threshold systems; (2) the ne structure constant α recovered exactly as 1/α = ANCHORexact×(102 + 10−1) with zero free parameters; (3) charge quantization derived as the unique solution to two simultaneous structural constraints; (4) the complete SM particle classication via mass torsion unication; (5) the hadronic spectrum via the GAM Collider fusion rules; and (6) the GUTEWQGP cosmological cooling sequence. All six Step 6 checks pass. The formal proof corpus is archived at DOI:10.5281/zenodo.18719748.