negative September 27, 2026

After emergence, one lineage takes the world at every reach

DESIGN §1.3 sweep 12 asked rung 2's question: once a world has made replicators, does it stay polyphyletic, and do more lineages survive as a cell's reach shrinks? All 360 runs finished and 32 emerged. Read by the pre-registered rule, on lineage tags that follow descent through reverse copies, none of them stayed polyphyletic: 27 read monophyletic, 5 between one lineage and two, and the median effective number of lineages is 1 in every arm, well-mixed to radius 1. The trend toward more lineages at shorter reach is neither shown nor refuted, at a permutation p of 0.079. Emergence itself differed by reach — 3, 16, 9 and 4 runs of 90, well-mixed then radius 4, 2 and 1 — which the sweep was not designed to test and is reported descriptively only.

Question

Rung 2 of the programme asks what a world does after it has made replicators. The radius sweep asked it first and left it open: locality was supposed to keep a world diverse once a lineage exists, by stopping one winner from reaching every cell, and that sweep read only whether locality bought emergence. DESIGN §1.3 sweep 12 asks the diversity half on its own: after a transition, does a world stay polyphyletic, and do more lineages survive as a cell's reach shrinks?

Method

The radius sweep's four arms — radius 1, 2, 4 and 0, the well-mixed world — on a 128×128 torus of tapes held at 64 bytes, at the emergent mutation rate 2^-13, with lineage_rule = oriented, 90 seeds per arm and 20 000 epochs per run. oriented is the point of the sweep: the replicators of every emerged world copy themselves in reverse, and under the aligned rule a reverse copy passes no tag on, so the tags would count the survivors of a takeover rather than descent from it.

The reading is pre-registered, and was clarified in five places before any run was read: docs/design_record.md, 2026-09-25, "Lineage diversity after a transition" and "The lineage-diversity reading: five clarifications". A run is emerged where it has a confirmed emergence epoch and reads replicator_share of at least one half at some sample after it. Each emerged run is read on the median lineage_effective_count — the effective number of lineages, 1 for a world one lineage holds — over the last tenth of its samples since emergence: polyphyletic at 2 or more, monophyletic below 1.5, between otherwise. The trend across the arms is a one-sided Jonckheere–Terpstra test with a permutation p, and the hypothesis is shown only where that trend holds at p < 0.05 and the arm of shortest reach is itself polyphyletic.

Result

neither shown nor refuted No emerged world stayed polyphyletic: of the 32 measured, 27 read monophyletic and 5 between, and the median effective number of lineages is 1 in every read arm.

The trend toward more lineages at shorter reach reads permutation p = 0.0793: the locked hypothesis is neither shown nor refuted. After emergence one lineage takes the world whatever the reach, and the half of the hypothesis that says a transitioned world stays polyphyletic is not supported.

The worlds that read between one lineage and two: radius 4 seed 23 (1.88), radius 4 seed 66 (1.61), radius 2 seed 39 (1.73), radius 2 seed 65 (1.99), radius 1 seed 51 (1.88). None reaches 2.

Every count on this page is read from the sweep's stored runs at render time, through the same reading the sweep page draws.

The pre-registered reading final

Every run of the sweep has finished. A run emerged where it has a confirmed emergence epoch and reads replicator_share of at least 50% at some sample from it on. It is polyphyletic where the median lineage_effective_count of the last decile of its samples since emergence is at least 2.0, monophyletic below 1.5, between otherwise, and unmeasured where fewer than 10 of that decile's samples carry it. An arm with fewer than 2 measured emerged runs is unread.

Arm	Runs	Finished	Emerged	Measured	Polyphyletic	Between	Monophyletic	Unmeasured	lineage_effective_count	Reading	lineages_over_one_percent	lineage_variation_oriented	conserved_core_bytes_oriented	conserved_core_ops_oriented	copy_latency, first → last decile	Radius sweep emerged
well-mixed	90	90	3	3	0	0	3	0	1	read	1	34.7	0	0	1090 → 908	2 of 10
radius 4	90	90	16	16	0	2	14	0	1	read	1	40.1	0	0	955 → 1010	1 of 10
radius 2	90	90	9	9	0	2	7	0	1	read	1	51.1	0	0	712 → 736	1 of 10
radius 1	90	90	4	4	0	1	3	0	1	read	1	45.2	0	0	469 → 663	1 of 10

Hypothesis

After a transition a world stays polyphyletic, and more lineages survive as a cell's reach shrinks: neither shown nor refuted

One-sided Jonckheere–Terpstra trend over well-mixed < radius 4 < radius 2 < radius 1: statistic 194, permutation p = 0.0793 over 100,000 dealings, read at p < 0.05. The read arm of shortest reach, radius 1, has a median effective count of 1.

Emergence by reach, descriptively

The sweep was built to read lineages, not emergence, and this is not a pre-registered test. 32 of its 360 finished runs emerged, and not evenly across the arms. The radius sweep beside it ran ten seeds an arm at another rate and saw one or two emergences in each, so it can neither confirm nor contradict the spread.

A run with a confirmed crossing that never read replicator_share of one half after it is not emerged here: the census that confirms a crossing is blind to reverse copiers, and the share clause asks that the world was, at some point, mostly replicators. The radius sweep sampled no share, so its count carries no such clause. Descriptively, a Freeman–Halton exact test (Fisher's, extended to 4 arms) of emerged against not emerged reads p = 0.00308. It is a candidate for a sweep that pre-registers emergence against reach, not a result.

What is not claimed

• Lineage tags approximate descent. A cell takes its partner's tag when its final tape is closer to what the partner brought than to what it brought itself. They are not a phylogeny: two lineages that converge on one tape stay two, and a copy overwritten by a stranger's partial write may keep or lose its tag on a byte count.
• The tags are oriented ones. They follow descent through reverse copies, which the aligned rule every earlier sweep ran under does not, so these counts are not comparable with the distinct_lineages of earlier sweeps.
• 20 000 epochs. A world read monophyletic at its last tenth may split again later; what is read is the end of the budget, not an equilibrium.
• One world size. Every run is 128×128. A larger torus gives a reach of 1 more room to hold colonies that never meet, and that is untested.

Evidence

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

Sweep: Lineage diversity