Path-enhanced q=5 leader barrier, all-q four-chamber law, decoder hub pruning, dependency second shell, and odd-characteristic root metric.
Pass5148 left leader 21 in one sharp adjacency sector. Selected four-edge Levi paths force additional (1,2,3) chamber triples, closing that sector at apartment weight at least 641. A local degree-type path relaxation then closes leaders 22 and 23. At leader 24, the final two path-count equality profiles are incompatible with Levi girth eight, giving a last-sector lower bound 629. Therefore every q=5 apartment-code word of weight below 625 has minimum chamber leader at least 25.
Four distinct chamber stars have a nonzero common-apartment intersection in exactly seven six-distance patterns. The consecutive-four-edge signature (1,1,1,2,2,3) has intersection q; six other C8 signatures have intersection 1; every other signature has intersection 0. Rooted q=2,3,4,5 censuses show no signature splitting.
The original local ROM is retained. When several apartments tie for global maximum vote, only tied candidates of minimum induced degree in the chart-sharing graph are corrected. All 395,260 connected radius-five representatives through a base apartment still clear monotonically within three sweeps. All 32 centered 2+2+2 weight-six false-center motifs also clear. This repairs the complete minimal centered obstruction family, but does not yet prove global radius six.
For every finite q≥2, the chamber dependency/cut code has second nonzero weight 2q. Those words are exactly cuts of adjacent point-line Levi vertex pairs, one for each chamber, so the second-shell multiplicity is (q+1)²(q²+1).
For q=3^f the exact distance shells are 1, 4(q−1), 8(q−1)², 10(q−2)(q−1)², (q−1)²(q−3)(q−5). Together with the characteristic>3 theorem of Pass5143, symbolic formulas now cover every odd characteristic. Characteristic two remains exceptional.
The minimal q=5 exotic weight-625 profile (h8,h9)=(2,1) remains open. Its local four-clique moment is Q4_type=1250−6h8−9h9=1229, a defect of 21 from the chamber-star value, supplementing the previously found triangle defect 28. No global invariant forcing the star moment is currently proved.
Boundary. This is not the q=5/all-q distance theorem: leaders ≥25 and the weight-625 equality classification remain open. The hub-pruned decoder has certified radius five and repairs the centered minimal weight-six family, but global radius six remains open. The all-q nonlinear theta-gap target remains open in this packet.