Machine-certified finite-geometry continuation of the W(3,q) apartment-code program.
Cut gauge: the chamber-generator kernel is exactly the binary Levi cut space, so the apartment code is Levi edge cochains modulo cuts.
Intrinsic charts: the complete dual minimum shell reconstructs theta, geodesic-root blocks, and every opposite-pair Kq+1 tester chart without external point/line labels.
q=3 decoder: the S4-equivariant local-vote rule corrects every apartment error pattern of Hamming weight at most three within two sweeps.
Perfect duality: the apartment code is canonically Hom of the apartment/theta presentation over F2.
The sqrt(17) structures form the nested conductor ladder 1→2→4 with discriminants 17→68→272. The q=3 code reconstructs its own U81⋊V4 local controller, including the H27 state and F3^3 program torsors up to point/line dual swap.
The q=5 and all-q minimum-distance theorem remain open. Pass5118 later strengthens the q=5 chamber-leader barrier from ≥14 to ≥17. Pass5123 falsifies the naive extrapolation of the q=3,5 native root-coset rank drops. Decoder statements are finite hard-decision code claims, not physical noise thresholds.