303,810
All two-edge insert/delete mixtures have distinct complete residuals.
Topology that diagnoses,
dissipates, and rebuilds itself.
Passes 3913–3920 extend the W33 control plane from single-defect checks to bounded multi-defect decoding, explicit symmetry dissipation, partially observed control, correlated fusion, and dual-geometry all-to-all scheduling.
2,275,280
Every three-edge deletion is separated in the exhaustive ledger.
0.0632907
Unit-rate gap of the eight-jump random-unitary symmetry Lindbladian.
0.915899
Physical fusion threshold for a 99% complete twelve-round epoch in the frozen correlated model.
39 rounds
Optimal W33-plus-complement all-to-all one-port schedule.
192 entries
Sparse sensor distinguishing every two-edge syndrome.
Bounded topology immune system
The matrix checksum R(B)=B²+2B−8I−4J is used as a content-addressed syndrome. General ambiguity is impossible below weight three, and deletion-only ambiguity is impossible below weight four. Mixed three-edge insertion cases remain open.
Symmetry Lindbladian
Four transvections and their inverses define L(X)=Σg(Ug X Ug†−X)/8. Its fixed algebra is exactly span{I,A,J−I−A}. Each transvection compiles into nine disjoint three-mode cycles, giving 72 directed cycle macros for the eight jumps.
Closed-loop process benchmark
| controller | six-step discounted cost |
|---|---|
| fully observed lower bound | 16.514150 |
| partially observed optimum | 23.115384 |
| best static mode | 30.176037 |
The controller is exact for the declared hidden-Markov model; it is not learned from hardware.
Correlated virtual-edge factory
With twenty links per matching, twelve matchings, five attempts, 5% common outages, and 0.995 stored-edge survival, the 99% full-epoch threshold is p = 0.9158993399430635. The independent no-decay threshold is 0.8668344006872047.
Topology DNA and dual geometry
Four four-trit generators plus one ordered edge reconstruct the complete 480-element oriented-edge orbit. Twelve W33 matchings plus twenty-seven complement matchings partition all 780 edges of K40, reaching the information-theoretic minimum of thirty-nine one-port rounds.
Phase diagram
| implementation | wins on 500-point frozen grid |
|---|---|
| bus W33 | 310 |
| virtual W33 | 84 |
| native W33 | 54 |
| local ring | 37 |
| mesh W33 | 15 |
Every implementation wins somewhere: there is no coefficient-independent machine.
Evidence boundary. Not established: general mixed weight-three decoding, sparse local Lindbladian synthesis, measured process-tensor operation, microscopic fusion correlations, measured platform coefficients, minimum topology memory, simultaneous all-to-all coupling, minimum sensor size, remote CI/PDF completion, or laboratory performance.
Semantic certificate: 019183d46768ff68a5f57676540d8aefd853010614545fd834656b69c4c7eb15