Exact q=5 footprint theorem: C_F=[325,65,25]_2. The proof uses the complete weight-8 dual shell: 24,375 checks, replication 600, and pair codegrees 25/5/0 in the rank-4 P-component association scheme. Even primal/check intersections give 300w ≤ 25 e1 + 5 e2 ≤ 25 C(w,2), hence w≥25.
NO_5^+(5). Exact clique enumeration gives 156 maximum cliques, precisely the 156 point footprints.Pass5207 reduced every P-heavy exotic word of apartment weight 625 to a nonzero footprint word of weight at most 24. That branch is now impossible. Together with Pass5191, every q=5 word of weight 625 is one of the 936 chamber stars.
Firewall: this closes the equality shell, not the strict minimum-distance problem. A lower-weight word has not yet been excluded.
Any q=5 word of weight below 625 has zero P-component parity. Otherwise the new footprint distance supplies at least 25 parity-odd P components and each costs at least 25 apartments. In the zero-parity sector every active P component lies in the even subcode of Cut(K6)⊗Cut(K6), whose exact minimum is 40. Therefore any strict counterexample activates at most 15 of the 325 P components.
If a dual-check orbit has coordinate replication r and maximum pair codegree λ, even intersections imply d ≥ 1+r/λ. Exact footprint anchors are now q=3: [45,15,9], q=5: [325,65,25], and q=7: [1225,175,49].
At q=7 a weight-12 dual word has a 1,920,800-word symplectic orbit with replication 18,816 and maximum pair codegree 392, so 1+18816/392=49. Fixed-coordinate MILPs exclude dual weights 9, 10 and 11.
The q=5 strict front is now: eliminate nonzero global codewords supported on at most 15 P components while satisfying the connected-L constraints. Leader 36 remains open until that block-sparse sector is closed.