# llm_curriculum_v5_cull — differential reproduction in the six-generation population

**Claim tested (manuscript revision 2026-09-12).** In the six-generation population recombination
bought speed but not level: the declinable-merge arm led early and finished level with never merging.
The population had no differential reproduction (lineages were never culled), and the Discussion
predicted that with it a merged lineage's early lead would be inherited by more descendants and turn
into a level advantage. This run adds truncation selection: after every generation's measurement the
lowest-scoring lineage (all-families accuracy) is re-founded from the highest-scoring one, keeping
its own curriculum slot (`cull: true`; `cull_step`/`inherit_slot` in `src/llm/curriculum.py`;
ties leave the population alone). Arms: `isolated` + culling and declinable `society` + culling,
read against the existing `isolated` and `veto` arms. Latin square, Qwen2.5-1.5B, 3 training seeds
(`hpc/llm_cull.pbs`, ~35 min per seed on one L40S). Figure `curriculum_cull.png`; numbers from
`figures/stats_llm_curriculum.py` and the per-generation tables printed in the revision log.

### Result — parity again; the prediction is not supported
- **Final best-lineage accuracy (all six families), mean of 3 seeds:** never merge 0.796; declinable
  merge 0.792; never merge + culling **0.804**; declinable merge + culling **0.793**.
- **Contrasts (per seed; mean ± 95% CI):** culled declinable − culled never-merge −0.011, −0.014,
  −0.008 (**−0.011 ± 0.003**, below in 3/3); culled declinable − declinable +0.001 ± 0.007;
  culled never-merge − never-merge +0.007 ± 0.030 (−0.022, +0.028, +0.017).
- **The early lead survives, the level does not.** Best lineage at generation 1: declinable 0.680
  and culled declinable 0.679 against never-merge 0.601 and culled never-merge 0.638; by generation
  5 all four sit at 0.78–0.80. Population mean: culling lifts the *mean* early (generation 1: 0.577
  vs 0.477 for the never-merge arms) because the best genome is copied into the worst slot, but the
  final means converge too (0.775–0.786).
- **Selection was active throughout:** exactly one cull per generation in every arm and seed (no
  ties); the culled slot rotated among all three lineages. Declines in the culled declinable arm
  rose with generation as before (0.33 → 1.00).
- Retention of taught families at generation 6: 0.78–0.79 in all four arms.

**Reading.** Under a curriculum that delivers every skill to every lineage, the ceiling is set by
what one adapter can carry, and both sex and selection can only move a lineage toward that ceiling
faster. Selection spreads the best genome; recombination assembles it earlier; neither raises it.
The Fisher–Muller advantage in this population is a speed advantage, now shown with and without
differential reproduction. Falsifier for the null (not triggered): culled declinable above culled
never-merge in a majority of seeds by more than the seed-to-seed spread (~0.02). What would change
the prediction is a curriculum in which skills are *not* guaranteed to every lineage (a lineage that
never learns a family can only obtain it by merging), which is a different experiment.