Exchange Life

1. Conway: all cells update synchronously. A dead cell is born with exactly 3 occupied Moore neighbors; a live cell survives with 2 or 3. Orientation colors are ignored.
2. Site percolation: each step independently samples every site with probability p using the continuing seeded generator. It is a sequence of independent spatial samples, not an interacting automaton. Connectivity uses four neighbors. A cluster spans if it touches both opposite edges, horizontally or vertically. No bond variable is modeled.
3. Lexideck Life: six agent labels share the same Moore neighborhood. A live cell retains its agent if the total occupied-neighbor count n belongs to that agent's S set. At an empty site, a birth can inherit only a type already present among the old neighbors whose B set contains n. Choose the eligible type with the most neighboring representatives; ties use a seeded hash keyed by generation, location and type. Every agent can therefore support another type's survival or birth without being the inherited type. There are no spontaneous births, immigration, enforced population floors, or guarantees against extinction. Updates are synchronous; birth and death candidates use only the previous board. The displayed six B/S assignments are invented toy choices, not measured agent traits or UIT-IEG laws.
4. Exchange Life: first compute the Conway candidate from the old board. A dead candidate clears occupancy for no assigned cost. For a live candidate, form a local inbox histogram of the occupied neighbors' + and − signs; u is the + fraction. Compress that histogram to one majority sign. A tie keeps the prior sign for a surviving cell; a birth uses a fixed seeded sign at that location.
5. The toy assigns that inbox compression H(u) = −u ln u − (1−u) ln(1−u) erased nats, with H(0)=H(1)=0. Before the update each cell refills credit, capped at B. A compression is committed only if credit ≥ T H(u); spend exactly T H(u). An unaffordable merge retains the prior cell occupancy and sign. It can suppress births or freeze a surviving sign. Deaths still proceed.
6. Neighbors remain available. This ledger describes a chosen local inbox accounting, not loss of information from the whole computer. Occupancy change itself is never counted as erasure. The downloadable event ledger records accepted and rejected conflicting inbox compressions; it does not erase its own history.

Source relationship: inspired by UIT-IEG sections 3–4 (rate per erased nat) and 7 (binary entropy). These cellular rules, credits, tie field, and dimensionless k_B=1 convention are invented. They are not physical laws, a derivation of UIT-IEG, an Ising model, or evidence of a universality class. Entropy labels characterize the specified toy operation only.

Reset gives identical initial states and runs at fixed settings. For exact replay, preserve the settings and edit history; parameter changes and manual edits are recorded in the event ledger. Runs stop at 10,000 generations to keep the complete trace and ledger bounded.