1600 settings
The three ordered-pair orbit averages require and admit exactly 40+480+1080 unweighted settings. Shortest representatives cost 8,934 symmetry macros.
Twirl, Floquet, clock, and control
Passes 3787–3794 convert five architecture proposals and three outside-box mechanisms into exact finite certificates.
40-cycle
One relative incidence-round cycle averages every diagonal Hamiltonian to its common mode and cancels all traceless static diagonal disorder.
7 ticks
Frame broadcast reaches all forty points and forty checks with census 1,2,4,8,16,30,54,80, saturating the logarithmic lower bound.
Z(W33)=29
A complete reverse-forcing orbit census ends at 34,890 terminal depth-eleven orbits and proves the exact minimum control-port certificate.
352 couplers
A W33/local-ring phase pair shares 128 couplers, reducing the two-topology inventory from 480 to 352 while retaining a global two-step transport floor.
14 ticks
The optimal broadcast tree reverses into a seven-tick gather and fourteen-tick collision-free qutrit all-reduce.
Three additional mechanisms
29 + 11
Twenty-nine addressed phase ports structurally identify eleven additional modes along the exact force chain.
39 modes
Forty cyclic characters recover all traceless diagonal Fourier components while the zero character performs common-mode twirling.
79 edges
The same distributed tree carries frame broadcast, global qutrit sums, and consensus without a central eighty-link frame bus.
Evidence boundary
The packet certifies orbit-estimation cost, static diagonal Floquet cancellation, broadcast depth, the exact zero-forcing number, and explicit dynamic-topology and communication constructions. It does not certify an optimal active channel twirl, a general Floquet quantum code, noisy calibration accuracy, globally minimum layout, or laboratory performance.
Semantic certificate: aa3daf462320badd607a1720479f083df159044f24242e7f46810de30bc2e0d8