2.401×10²³
Maximal doubly-even code extensions.
W33 Theory · exact certificate b141dd0f82e4a6b1ee62d1c57f0e92bdfc9f58d3b32515f9521a0175fdca88a1
Codes, meshes,
holonomy & flags.
Eight exact fronts from one six-bit minus-type quadratic parent.
≥4.632×10¹⁸
Exact lower bound on U4(2):2 extension orbits.
418 / 69
Exact adjacent rotations / layers.
79 / 10
Terwilliger algebra / center dimensions.
51,840
All ordered abstract standard pairs.
40 + 160
W33 points plus point-line flags.
Maximal-code census
The discriminant module is the minus-type space O−24(2), with Witt index eleven. Hence
N = ∏i=212(2i+1) = 240137905387279785868125.
An explicit [36,17,8] extension has trivial stabilizer, while the total census forces at least 4,632,289,841,575,613,440 group orbits. The result is an exact census and orbit-explosion theorem, not a fabricated representative ledger.
Exact adjacent mesh
The 36-port involution H=(2A−J)/6 compiles to 418 adjacent symbolic Givens rotations in 69 layers, with 212 exact zero skips and one final π phase.
| quantity | exact value |
|---|---|
| gate interval | 35 ≤ g ≤ 418 |
| depth interval | 6 ≤ d ≤ 69 |
| distinct c² values | 144 |
| parameter hash | 5c933c…6b6b |
Rank-five holonomy scheme
The 120 Fischer triples close under five Gram relations with valencies 1, 2, 54, 36, 27. All Krein parameters and all fusion partitions are exact.
0
Q-polynomial orderings.
4
Fusion schemes.
83
Point-stabilizer ordered-pair orbitals.
Monster target, fail-closed
For a fixed size-45 involution, exactly 1,152 order-five partners satisfy the required (2,5,9) and commutator-three relations. They form two centralizer orbits of 576, and each orbit generates U4(2). No serialized Monster words, embedding, or 196883-character restriction is present.
Three chained constructions
160 flags
The tripod orbit is exactly every incident W33 point-line pair.
4 → 1
Tripod port columns quotient onto the 40 W33 line-versus-spread columns.
rank 48
The 1|27|36|40|160 fibers form one O6−(2) orbital coherent configuration.
Evidence boundary
The packet does not claim a materialized ledger of quintillions of orbits, globally optimal photonic depth, concrete Monster elements, a Leech/rootless lattice, fabricated hardware, laboratory performance, remote CI success, or compiled PDFs.