Population candidate attractor · coexistence or exclusion?

Competition

Two producers, one resource. Do they partition the world and coexist — or does one drive the other out entirely?

Kernel role Population · ecological — a candidate attractor (ADM-A5 §3.6). An authored design claim, not a measurement.

Stack No. A single panel, not a vertical layering of dependent layers.

Substrate Synchronous (α = 1). Temporal order is partly supplied by the clock rather than produced by the system.

The four sovereignty conditions (SOV §7.2) — what this panel supplies, not how it scored

out of scope 1 · Recursion lock. There is no self-closing recursive loop here. Two producers compete for empty cells; the dynamic is selection/exclusion under ADM-A5, not a loop that catalyzes its own re-closure.
exercised 2 · Internal recurcline persistence. The two populations are the basin and the growth sliders are bounded perturbations of it; you can watch the run settle to coexistence or tip to competitive exclusion. Caveat: The update runs synchronously at α=1, so part of the temporal order is supplied by the clock.
out of scope 3 · Boundary retention. No boundary is modeled. Cell states are producers/empty, not a membrane, and the lattice wraps.
supplied 4 · Maintenance-bearing continuation. Both producers grow into empty cells at authored rates with no modeled inflow — the shared resource (empty space) is replenished for free by baseline mortality, so nothing pays to persist.

No sovereignty verdict is claimed here or anywhere in this gallery. The Sovereign column is empty, and that emptiness is the honest reading: no panel here has been shown to produce its own order.

The simplest ecological contest: two species, X and Y, both grow into the same resource — the empty space of the lattice, which is finite. Neither eats the other; they simply race for the same ground. When their growth rates are balanced they coexist, partitioning the board into shifting territories. Tip the balance and one species out-races the other into every open cell — competitive exclusion, the classic outcome when two demands press on one shared resource.

What you can read, and what you cannot

The two populations are the basin; the growth sliders are bounded perturbations of it. What you can trust is the run's own answer: do both species persist (coexistence), or does one go to zero and stay there (exclusion)?

What you should not read in is a sovereignty verdict — whether either species “pays its own way” is the harder measurement the series keeps gated. This panel shows coexistence-or-exclusion, nothing more.

Two Competitors, One Resource

X ↔ empty ↔ Y · both racing for the same ground

species X—

species Y—

free resource (empty)—

neighborhood anisotropy 𝒜—

both persisting — coexistence

Synchronous substrate (α = 1). Every cell updates in lockstep, so part of the temporal order is supplied by the clock, not produced by the structures. The basin and its coexistence/exclusion are honest run observables — but this is not a sovereignty verdict. Space is kept honest: the lattice runs on Duncan(√5), whose anisotropy 𝒜 is shown above (admissible ≤ 0.02).

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