partial September 12, 2026

Emergence is a state a world can leave

DESIGN §1.2 fixes when a world enters the transitioned state, and the engine reports only that first crossing; nothing said when a world leaves one. Every terminal run now carries a persistence summary read off its own stored samples, and this reads every one of them the lab has, whichever sweep it came from: how many transitioned worlds were still in the state at their last sample, how many climbed back out, how long each held, and how high its replicator census rose. Relapse is not an edge case — the design record's two recorded relapses are only the ones that were noticed — and the outcome is split by whether the census ever saw a colony, since a world can leave a state no replicator was ever counted in. Every number is read from the database at render time and describes the runs the lab happens to have: each was censored by its own budget, so a world that persisted persisted to its last sample and no further.

Question

Every other finding in this log counts transitions: DESIGN §1.2 says when a world enters the transitioned state, the engine's tracker reports the first epoch it does, and a sweep is scored on how many of its seeds got there. None of that says anything about what happens next. The 60 000-epoch re-run already showed why that is a gap: one of its confirmed emergences ends with the world back in the soup it started in. So the question here is not how often emergence happens but whether it lasts — of the worlds that crossed, how many were still across at their last sample, how many climbed back out, and how long the ones that held held for.

Method

Every terminal run in the lab with a transition epoch, whichever sweep queued it, read through the persistence summary derived from its own stored samples (Runs::PersistenceSummaryService). "In the transitioned state" is the engine's own rule applied sample by sample — compress_ratio below 0.6 with no alphabet collapse — so Rails re-reads a stored series by the criterion the engine used to flag it and never invents a second one. Leaving the state is that rule's hold in reverse: the state ends at the first of 4 consecutive samples the rule rejects, mirroring the 3 further qualifying samples that confirm an entry, so a single sample flickering back over the threshold is no more a relapse than a single sample under it is a transition. A state that never ends persisted to the run's last sample. Beside it the summary records the largest replicator_count the run ever sampled and the epoch it first stood at.

This is a survey and not a sweep. The runs below come from different grids at different budgets, chosen by nothing but having transitioned, so what follows is a count of outcomes and never a hazard.

Result

Emergence is not a terminal state, and it is not usually left either. The lab has 472 terminal runs that crossed, finished or failed, across 15 sweeps, and a persistence summary behind 472 of them. The split is 316 still in the transitioned state at their last sample against 156 that climbed back out of it — 33% of the summarised runs relapsed within their own budget. The worlds held the state for 30 to 54,970 epochs, a median of 5,130. 239 of them counted a replicating cell at all, and those censuses peak at 2 to 4,000 cells, a median of 120.

The census splits the outcome in two. The transitioned state is the compression rule's, and a run can be in it without the census ever seeing a colony, so the two halves are worth separating. Of the 239 summarised runs that counted a replicating cell, 204 persisted and 35 relapsed. Of the 233 runs whose census never left zero — or was never taken — 112 persisted and 121 relapsed. So part of the relapse count is worlds the census never saw as a colony at all, and reading the totals alone would bury that.

One row per terminal run the detector flagged, grouped by sweep. "Epochs persisted" is the span from the transition to the last sample the transition rule still accepted; "Census peak" is the largest replicator_count the run ever sampled, with the epoch it first reached it in brackets; "—" means the run never had a value. The table stops at 50 rows and leaves 422 further transitioned runs out; every one of them is counted in the figures above.

What this does not claim

A persister persisted to its last sample, not forever. Every run here was stopped by its own budget — or, for a run that failed, by whatever ended it — rather than by the world settling anything, so "persisted" means "had not relapsed when the clock ran out". The longest span above is a lower bound on nothing but itself.

No hazard is estimated. These runs are not an arm of anything — they are whatever transitioned across sweeps with different world sizes, mutation rates, interaction budgets and horizons — so the relapse share above is a description of this set of runs and not a rate the substrate has. Whether the hazard of relapse falls with a colony's age, which is the question the design record's first rung asks, cannot be read off a set assembled this way.

Entering and leaving are decided by compression alone. Both ends of the state are the compress_ratio rule of §1.2 with its collapse guard; the census enters neither. A relapse in a run whose replicator_count never left zero is therefore a soup that briefly compressed and then stopped compressing, not a colony that died, and it is counted here because the transitioned state is defined that way — not because anything replicated. Every zero-census row above should be read as the detector's event ending, and only the rows with a census peak as a colony that was seen and then was not.

The exit rule is a Rails-side definition. §1.2 and the engine own entry; leaving the state is defined over stored samples, at the sampling cadence each sweep chose. A world that dipped out and back between two samples reads as having held throughout, and a sparser cadence makes both the persistence span and the census peak coarser. By §2 the engine has to be the one that measures persistence, and it does not yet.

This stays partial for both reasons at once: runs remain on the clock, so the denominators above move, and the set they are drawn from was assembled by accident rather than designed.

What next

The persistence sweep of the evolution programme is what turns this survey into a measurement: the parameter points that already transition, at 20 seeds and a budget several times 60 000, so the relapse hazard has enough events and enough post-transition time to be fitted against colony age rather than merely counted. The observable belongs in the engine before then. Until it is run, the honest reading of the table is that a transitioned world is not safe: some of them come back.

Evidence

Transition, flagged, census and arm are used here in the senses set out in the glossary.

This finding rests on no single sweep: its evidence is every transitioned run in the lab, tabled above with the sweep and the seed each one came from.