BZK 1.0 — The Excitable Baseline
The trunk of the Belousov-Kernel lineage. A Greenberg–Hastings-style excitable cellular automaton on a CA lattice, reproducing the Belousov–Zhabotinsky phenomenon seen in a thin Petri-dish layer: a quiescent, near-uniform medium in which nucleation at pacemaker sites is followed by autocatalytic propagation outward as target waves and rotating spirals.
What Stage A reproduces — and what it does not
Stage A faithfully reproduces the phenomenon: threshold-gated excitation, neighbour recruitment, refractory recovery, and the target/spiral patterns that follow. In kernel terms the baseline supplies:
T0-P(Asymmetric Admissibility) — the resting state is not equivalent to the excited state; excitation is a threshold-gated, directional transition.T0-σ(Adjacency) — excitation recruits bounded neighbour cells across the lattice.
It does not supply the rest of what ignition requires. There is no T0-M recursive closure, no T0-B identity-bearing boundary, and no MBC self-paid maintenance. The wave propagates and then dies; the medium goes refractory and, without continuous external feed, relaxes back to quiescence.
T0-P+T0-σ threshold-triggered waves, not kernel IST-ignitions (I-Pop). Treating a nucleation as an ignition would be the BAEP category error. Per the validation discipline (§ 14.3): a simulation is an attractlet model unless proven otherwise; visual stability alone is insufficient.The substrate is round, not square — Duncan's Neighborhood
A wave is only as honest as the grid it spreads on. On the ordinary eight-neighbour lattice, the four diagonal neighbours sit a step farther away than the four orthogonal ones, yet excitation reaches them at the same cost — so a target wave that should be a circle spreads as a square, and a spiral's shape bends toward the grid's axes. That is the lattice drawing the picture, not the chemistry.
So the Belousov-Kernel substrate uses Duncan's Neighborhood — the same isotropic neighborhood the Bio-Kernel rebuild adopted, in which one cell influences another by distance alone, never by direction. Round waves come out round; spirals keep their symmetry. This is a fidelity requirement, and worth being precise about what it is and isn't: at this stage it means the reproduced phenomenon is geometrically honest — it is not a claim that the wave produced its own order. BZK 1.0 is still attractlet-class; a round wave is a faithful picture, not a sovereign one. The isotropy control only becomes a test of self-produced-vs-supplied structure later, once a stage actually claims to hold its own form (Stage B/C).
Where the lineage goes from here
Stage A is the well-understood before-picture — a real pattern-forming system that we know is attractlet-class — so we can watch precisely what has to be added to cross the line. The planned climb:
- BZK Stage B — add the missing primitives (a self-maintained
T0-Bboundary;T0-Mclosure feeding back on the conditions of continuation) and test whether an ignited region can hold identity through the refractory period instead of relaxing. This is theAC₀→AC₄climb (closure, positive feedback, cross-feeding, basin formation) on an excitable substrate. - BZK Stage C — apply the four
SOVconditions. Does the structure pass, or is it still an attractlet? The burden of proof is on the simulation.
Per § 14.3 negative-results discipline: if Stage B/C fails to ignite, that is a valid V-class result about the mechanism, not a failure of the kernel — the kernel predicts most mechanisms will not satisfy all four SOV conditions.