Correction first. Pass 4503 withdraws the old Pass-4493 claim that an order-648 point or line stabilizer splits the apartment extension. The full-group nonsplitting theorem remains valid.
The canonical incident point-line flag stabilizer has order 162 and instead gives 384/384, an affine section family of dimension 6: exactly 64 sections.
All 64 flag-equivariant sections were exhausted. In the canonical quotient coordinates the best score is (42,9,13): total minimal ambient weight 42, maximum column weight 9, union support 13 lines.
Those 13 lines are exactly the closed neighborhood of the fixed line. The induced line-intersection graph is K1 ∨ 4K3: the center line plus four pencils of three neighboring lines.
All three nonzero classes generate the same 23D support W/J=(K∩row(N))/J, the Pass-4492 route-hull/sentinel module 8|(1|14). The separate 6D radical factor does not appear in any nonzero class closure.
The order-162 coincidence was checked internally rather than assumed. The flag stabilizer has a unique Sylow-3 subgroup of order 81; its normalizer inside the full 25920-element PSp action is exactly the flag stabilizer. Thus the corrected splitting threshold is the W33 chamber/Borel gauge.
The exact Borel double-coset sizes are:
For one representative from each double coset, <H,g> is always only one of four groups: the Borel H, the order-648 point parabolic, the order-648 line parabolic, or all of PSp(4,3). Their section ranks are 384/384, 387/388, 386/387, and 389/390 respectively. So the Borel is the unique splitting member of its complete overgroup interval.
Choose the radical cohomology basis eP=fixed_line and eL=sum. The third nonzero class is eP+eL=second. The point parabolic kills exactly eP; the line parabolic kills exactly eL; their incident chamber/Borel kills the full F₂². This is the exact rank-two-building coordinate reading of the computed restriction barcode.
For Q(5,q)=GQ(q,q²) and every q ≡ 3 (mod 4), the general apartment formula gives HHᵀ=NᵀN over F₂. The family counts are:
If h(q)=rank₂(H) and ρ(q)=rank₂(NᵀN), the protected quotient is exactly ρ(q) and the apartment radical is h(q)-ρ(q). At q=3 this is h=279, ρ=70, radical 209. No polynomial rank formula is extrapolated from that anchor.
The ten quotient columns have degrees 1,1,1,1,5,5,5,5,9,9. Treat each source-line→accumulator use as a bipartite edge and forbid reuse of a source or accumulator within one clock. Maximum degree is 9, giving a 9-clock lower bound, and an explicit 9-round coloring attains it. This is therefore optimal in that single-port Boolean model.
The 24 internal edges are exactly 12 center spokes plus 12 triangle edges of K1 ∨ 4K3.
Borel vertex orbits have sizes 1,3,9,27; protected edge orbits are two copies of 3,9,27,81; corresponding edge stabilizers are 54,18,6,2. This is an exact finite orbit filtration aligned with the order-81 Sylow core, not a physical scale assignment.
All 240 protected edge vectors A*(eᵢ+eⱼ) span dimension 9, not 10. Because H10 has the exact invariant-submodule lattice 0<1<9<10, this carrier is exactly the unique 9D submodule. Yet the 24 internal cell edges also have rank 9—and even the 12 center spokes have rank 9. Nine certified spokes already form a basis. The tenth protected direction is absent from the entire edge family, not merely nonlocal.
The line graph of the 240 protected edges is 22-regular. The eight Borel edge orbits form an equitable quotient
Its characteristic polynomial is (x−22)(x−12)²(x−6)(x+2)⁴. The full 240-state line graph has the same set of distinct eigenvalues {22,12,6,−2}, so this 8-state quotient is spectrally complete at the level of eigenvalue locations.
Boundary. These are finite binary incidence, module, cohomology, building, graph and scheduling theorems. The 13-line graph cell is not automatically spacetime locality; the 9-clock result is model-specific rather than hardware PPA; the 8×8 quotient is not automatically a Hamiltonian or decoder; and no E8 or physical-scale identification follows from the orbit counts.