Molecular candidate attractor · the shortest loop that makes more of itself

Two-Species Loop (A ⇄ B)

The shortest possible mutual catalysis — two species, each helping make the other. The barest closed loop there is, and the cleanest place to watch a loop live or die on its feed.

Kernel role Molecular · autocatalytic — a candidate attractor. 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

exercised 1 · Recursion lock. A catalyzes B and B catalyzes A — a mutual loop of length two that makes more of itself; cut the feed and neither can be made, so you can watch the loop fail to close and go dark.
exercised 2 · Internal recurcline persistence. The pair's population either sustains itself against decay or collapses. 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 chemical species, not a membrane, and the lattice wraps.
supplied 4 · Maintenance-bearing continuation. A and B form only where there is feed — supplied raw substrate. Cutting the feed starves the loop (T0-Φ throughput-conditionality made visible), so persistence is bought with an authored feed, not paid by the structure.

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.

Strip the three-species loop down to its irreducible core. Here there are only two reacting species: A catalyzes the formation of B, and B catalyzes the formation of A. Each needs the other to be made, so the pair catalyzes its own formation around a loop of length two — the smallest autocatalytic set that can exist. The same central caution rides on top of it: a loop that runs is not the same as a loop that pays its own way.

The feed is supplied — and that is the point

Real molecules run on a feed: a supplied flow of raw substrate and energy. A bare lattice has none, so this panel authors one, visibly — the feed slider below. That authored gate is shown up front, never buried, so an imported gate is never mistaken for an emergent one.

Which is exactly what makes the honest test possible: cut the feed and watch. With only two species there is nowhere to hide — a mutual loop that keeps closing without feed would be self-holding; one that goes dark the moment the feed stops was living on what was handed to it. That collapse is T0-Φ (throughput-conditionality) made visible — not a sovereignty verdict, which stays gated.

The Reaction Loop

A → B → A · each catalyzed by the other

species A—

species B—

feed (supplied)—

loop closed — the pair self-sustaining on the feed

Synchronous substrate (α = 1); the feed is authored. The loop's motion runs partly on a supplied clock, and its raw material on a supplied feed — both shown, neither hidden. What you can trust is the run: does the loop stay lit, or go dark when the feed is cut? Space is kept honest on Duncan(√5). No sovereignty verdict is claimed — that is gated.

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