Exact continuation of the W(3,q) apartment-code program: q=5 leader wall, decoder radius, intrinsic unipotent controller, binary bicycle theorem, and three outside-box closures.
A sub-625 counterexample now requires chamber leader at least 18. At weight 625 an exotic equality word must contain at least three heavy K6 charts in one type; the minimum nonzero heavy profile is (h8,h9)=(2,1).
The S4-equivariant hard-decision decoder is certified for every weight-five error pattern within at most three sweeps. The fixed-apartment connected weight-five census contains 381,480 sets.
A reconstructed chamber carries a regular q^4-element type-C2 maximal-unipotent torsor. Its 4q^3 active charts are the positive-root right cosets. On a chamber-star support the theta graph is the associated root-direction Cayley graph.
Using the established binary incidence rank of W(3,q), every odd prime power obeys dim Bike_2(Levi)=q^3+q-1. Repo anchors q=3,5,7,11 give 29,129,349,1341.
State coordinates (b;a,c,d) and program coordinates (a;b,c+ab,d+2ac+a^2b) are related by an exact finite-field polynomial bijection, checked at q=2,3,4,5.
Boundary: q=5/all-q minimum distance is still open for leaders ≥18; weight-six decoding is not certified; finite algebraic controller results are not hardware-performance claims.