Two lattices run side by side on one seed and one fault set. Only the aggregation rule changes. Inject a single ⊥ and watch a k-of-n majority stay green while the S₄ meet collapses the whole envelope.
QSCD — Quaternary Spatial Control Dynamics — is the lattice semantics underneath the AI2 authorization architecture, developed at Asymmetric Intelligence & Innovation.
This is a software simulation of a lattice semantics. It shows that the algebra behaves as specified. It asserts nothing about silicon, timing, or any physical device. Both panels run one identical noise realization and one identical fault set; only the aggregation rule differs.
How to read the two panels
conventional redundancy
Each node polls its closed neighborhood and takes whichever state the majority reports. A single faulted neighbor is outvoted by the healthy ones and never reaches the output.
This is how redundancy is normally built, and it is why redundancy normally reports clean.
One ⊥ injected → 0 reported → panel stays green.
The fault is present. The aggregator does not carry it.
fail-closed lattice
Each node takes the greatest lower bound over the same neighborhood, against neighbors' barrier values rather than their committed states. ⊥ is the bottom of the order and its barrier is latched, so ⊥ is absorbing while HOLD stays recoverable.
Propagation is a property of the algebra, not a detection heuristic. There is no threshold to tune and nothing to outvote.
One ⊥ injected → absorption spreads across N[v] → envelope collapses.
The fault is present. The aggregator cannot hide it.
Both panels share the seed, the noise realization, and the fault set. In an 8×8×8 FCC sublattice of 256 nodes, it takes 52 faults — 20.3% — before majority voting reports anything at all. Copy the run link to hand someone the exact state you saw; download the log to check it line by line.
What it costs
A lattice that collapses on one fault is brittle by design. The question is what that brittleness costs you in availability.
That is what the enforcement-cost readout and the intervene control measure. Clicking a ⊥ node under intervene clears the fault and drives its barrier to 1.0 — trivially recoverable in the vote panel, unwinnable in the meet panel. That asymmetry is the trade, stated in the open.
Run it at σ = 0.05 and again at σ = 0.20. The detection argument is settled in the first four seconds; the trade you are actually buying is in those two numbers.
The algebra