Machine-checked finite results on the W33 / GQ(4,2) carrier. Claims below deliberately distinguish binary codes, ternary homology witnesses, quotient metrics, and class-level automorphisms.
The Levi repetition-cycle code is an exact PGSp-invariant subcode of [2025,399,14]₂. In the canonical sparse-check model, the syndrome engine has exact minimum depth 3: two local layers plus one layer containing all six representative-adjusted W₆ global checks.
The weight-2 repetition shell plus the 135 local quotient relations is too symmetric: its class-level automorphism group is S₃^135:S₁₃₅. The first cross-cell sector has dimension six and is exactly W₆=[27,6,12]₂. Its 27 nonzero generator-column types recover the quotient lines; local triples recover 45 points, each repeated across three sheets.
Every binary Levi minimum cycle lies in exactly three induced K₃,₃ ternary witnesses; every induced K₃,₃ contains exactly nine binary cycles. The incidence matrix has ranks 324, 359, 360, 360 over F₂, F₃, F₅, F₇.
Its binary right kernel is [360,36,20]₂. The complete minimum shell has 36 words; each is all 20 K₃,₃ witnesses inside a K₆,₆ minus a perfect matching. Over F₃, the only right-kernel relation is the all-one sum.
On the 360 K₃,₃ witnesses, adjacency by sharing a binary Levi cycle gives a connected 18-regular graph. Its spectrum contains
with multiplicities 1, 60, 84, 81, 64, 20+20, 15+15. The graph has diameter four and uniform shells 1,18,108,227,6, but is not distance-regular.
C399/CLevi has dimension 335 and physical coset minimum distance 14. Its complete minimum shell contains exactly
distinct minimum cosets.
Pass4837 subsequently closed all four formerly gated computations: the characteristic-two Brauer semisimplification, exact PSp/PGSp Burnside counts for the 64-dimensional sign sector, all six arbitrary-ρ outage phase diagrams, and the exact rank-64 common-generator intertwiner proving the binary sign-H¹ and Levi-H¹ modules are PSp- and PGSp-isomorphic.
Evidence boundary. The complete nontrivial Loewy ordering of the 5671-dimensional flag-H¹ module remains a separate MeatAxe problem. Flow statements remain fractional-network results, and no physical hardware threshold is inferred.