partial September 11, 2026

Emergence is rare, and half of it happens after epoch 20 000

The four rates around sweep 1's transitions, re-run for 60 000 epochs — three times the budget that produced the mutation-rate window finding. It reproduces that sweep run for run and then doubles it: six of 40 runs reach a census-confirmed replicator, and half of those transitions land after epoch 20 000, where the short sweep had already stopped watching. One of its disagreements resolves the same way — the run it recorded as flagged with an empty census counts replicators at epoch 26 140. The 2^-14 arm stays silent at three times the budget, so the lower cutoff is not a censoring artefact.

Hypothesis

The mutation-rate sweep stopped every run at 20 000 epochs, and 95 of its 100 runs were still in a random soup when the clock ran out. A sweep censored that heavily measures its own budget as much as its parameter: an arm showing nothing may hold a hazard that is genuinely lower, or the same hazard watched for too short a time. The two readings separate on a longer run. If emergence at these rates is rare — a low hazard per epoch — three times the budget buys about three times the events and the arms keep their order. If the short sweep was instead watching a slow process, the extra epochs produce events out of arms that read as empty, and the window the first sweep failed to find could still be there, displaced past epoch 20 000.

Method

The four rates that bracket the short sweep's transitions — 2^-14 to 2^-11, the arm below the lowest transition through the arm above the highest of this neighbourhood — on the same 128×128 torus of 64-byte tapes, 10 seeds each, 60 000 epochs per run. Every parameter that enters the simulation is at the short sweep's value, and only the snapshot cadence is sparser — a snapshot is written output and not state — so a run here is the same run the short sweep made, byte for byte, up to epoch 20 000, and then keeps going: this is a re-run rather than a new sample, which is what makes the two sweeps directly comparable and also what stops the overlap from counting twice. The dependent variable is the transition epoch of DESIGN §1.2 — the first sampled epoch at which compress_ratio falls below 0.6 and stays below for three further samples — and beside it the replicator_count census. A run is called census-confirmed here when both fire in it.

Result

40 of the 40 runs have reached 60 000 epochs. Every run still on the clock is already past its own transition epoch and past its own census peak, so no count below is waiting on them. The table is the recorded per-arm result; the phase diagram and the per-run rows below read the same runs live.

"Peak census" is the largest replicator_count the run reached at any sample. The last column is the runs the detector flagged whose census never left zero.

The short sweep was right, and it under-counted. Within the same four arms the 20 000-epoch budget found three transitions; the 60 000-epoch budget finds eight, six of them census-confirmed — 6 of 40 runs, 15%. The six confirmed transitions land at 5 030, 7 000, 15 560, 21 540, 42 730 and 47 820 epochs, a median of 18 550, and three of them fall after epoch 20 000: half of the emergence in this region of the parameter space happens where the first sweep had already stopped watching. That is the answer to the question the sweep was queued for. Emergence here is rare — three events in the first 20 000 epochs of these runs and three more in the 40 000 that follow, which is what a roughly constant hazard per epoch looks like — rather than a process that was merely slow to start. Six events cannot tell a constant hazard from a gently falling one, but they do rule out the reading in which the short budget was missing a burst.

A disagreement that was only the clock. The 2^-12 arm's ninth seed is the run three earlier sweeps have all recorded — it flags at epoch 15 560 under the mutation-rate, world-size and radius grids alike, every one of which stops at 20 000, and in all three its census is zero at every sample. Run for 60 000 epochs, the same run counts its first replicating cell at epoch 26 140 and peaks at 57. The first sweep's flagged-with-no-census disagreement, in this run, was the budget and not the substrate: the detector saw the tape statistics turn over, and the census needed another 10 000 epochs to see the lineage that had done it.

That run's census, with its transition epoch marked: flat at zero across the whole span the short sweep watched, and only then lifting off.

Determinism, checked once more. The two earliest transitions here — the 2^-13 arm's first and fifth seeds at 5 030 and 7 000 epochs — are the short sweep's two earliest, at the same epochs, from the same (params, seed). One of them peaks at 867 replicating cells, the largest census of either sweep. Nothing about the re-run is new evidence up to epoch 20 000; that is the point, and it is the guarantee DESIGN §1.1 makes, checked rather than asserted.

The lower cutoff survives three times the budget. The 2^-14 arm has no census-confirmed run at 60 000 epochs, as it had none at 20 000. Its one flagged run collapses compress_ratio only to 0.900 by the last epoch, holds 16 370 of its 16 384 tapes distinct and never counts a replicating cell — the low-entropy attractor the other sweeps also report, not a lineage. The hint of a cutoff in the first sweep was the weakest thing it claimed, and the obvious way for it to be wrong was censoring; that way out is now closed for this arm. What the arm is not is a demonstrated zero: 10 seeds that produce nothing bound the hazard, they do not abolish it.

Two runs flagged with an empty census, and one that did not hold. The detector fires twice on runs whose replicator_count never leaves zero — the 2^-14 arm's third seed at 39 320 and the 2^-12 arm's fifth seed at 43 220, 2 of 40 runs — and the second of those ends with compress_ratio back at 0.951 and every tape distinct, which is the soup it started in. Read on the detector alone this sweep has 8 events; read on the census it has 6, and the two disagree in both directions across the programme. Separately, the 2^-12 arm's tenth seed shows that a confirmed emergence is not a terminal state: it transitions at 21 540, its census peaks at 123 cells by 28 100, and by epoch 60 000 the world has climbed back to a compress_ratio of 0.952 with all 16 384 tapes distinct. The lineage spread, saturated and dissolved, and the world it left behind is indistinguishable from one where nothing ever happened. A longer budget does not only add events; it also shows some of them ending.

The window is still not there. Confirmed emergence lands 0, 2, 3 and 1 of 10 from 2^-14 to 2^-11. That is the same shape the first sweep reported at a third of the budget — a floor with nothing below it and no peak above it that 10 seeds can resolve — and 3 of 10 against 1 of 10 is not a distinguishable pair of arms. The extra epochs sharpened the claim about when emergence happens without moving the claim about where in the parameter space it does.

This stays partial rather than published for two reasons. Runs are still on the clock, so the denominator above is read live and the arms may still gain an event. And every arm is censored again at 60 000 epochs: the latest confirmed transition of the sweep fell at 47 820, four fifths of the way through the budget, which is precisely the pattern that says the next budget would find more.

What next

The programme's cheapest events are not here. This sweep spent 2.4 million run-epochs for six confirmed transitions; the world-size sweep reads emergence as a hazard per cell-epoch, which makes a wider world the efficient way to buy events and a longer run the expensive one. The reading to test next is whether the two trade off the way that hazard predicts — 60 000 epochs at 128² and 20 000 at 256² are within a factor of three of the same cell-epoch budget and should produce comparable counts. The BFF positive control still gates reading any silent arm as a negative, the 2^-14 arm included. And the transient at 2^-12 is an argument for watching the census rather than the detector: a run that ends in a random soup can still have held a hundred replicating cells in the middle, and only the stored samples say so.

Evidence

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

Sweep: Mutation rate, long runs