recombination: reproduce the E4 "merge, don't average" finding in real weights

src/neural/recombine.py mirrors Layer-1 run_coverage but trains K_T specialist RNNs on
assignments from the exact shared-switch retention construction (K_T/rho/q clean; union
matches the closed form), then recombines the measured teacher distributions two ways:
mean (naive pooling) vs oracle-guided max-merge (per-mode strongest teacher, M2N2-style),
each followed by size-n resampling.

Result (8 reps): at rho=0, union rises 0.49->0.96 (supply matches closed form); analytic
surviving_max rises 0.043->0.087 while surviving_mean stays flat ~0.045 — the conservation
law (averaging cancels the union gain, max-merge realises it). At rho=1 (identical
teachers) union and max are flat. The lesson holds in the neural setting; trained-weight
columns show the same signs but noisier (smoothing inflates baseline; deep tail barely
clears n=200 resampling). torch-gated test added. 93 tests green.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

configs/neural/recombination.yaml

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+experiment: recombination
+kind: recombination
+seed: 20260704
+n_replicates: 8
+
+# (load-bearing; maps to Layer-1 E4 / blueprint C2+C4): does the recombination finding hold
+# in REAL weights? K_T specialist RNNs are each TRAINED on samples from their assigned mode
+# subset (assignments from the exact shared-switch retention construction, so K_T/rho/q are
+# clean knobs and union_coverage matches the closed form U(K_T,rho,q)). The pupil then
+# recombines the trained teacher distributions two ways: mean (pool outputs — naive multi-
+# teacher distillation) vs max (oracle-guided union, M2N2-style), each followed by size-n
+# resampling. Expect (per Layer-1 E4): union rises with K_T and (1-rho); surviving_max rises
+# with K_T while surviving_mean stays FLAT (the conservation law); at rho=1 (identical
+# teachers) more teachers buy nothing. Falsifier: surviving_mean also rises with K_T, or max
+# does not beat mean -> the "merge, don't average" lesson dies in real weights.
+
+synthetic:
+  K: 256
+  R: 1
+  tail: zipf
+  zipf_s: 1.3
+  tail_frac: 0.5
+  tail_threshold: 1.0e-3
+  style_len: 3
+  style_vocab: 5
+  id_base: 2
+
+model:
+  kind: rnn
+  hidden: 128
+  embed: 24
+  epochs: 22
+  lr: 2.0e-3
+  batch_size: 256
+  n_eval: 12000
+
+coverage:
+  n: 200                 # pupil resample size (drift); tail survives iff mixture mass > ~1/n
+  q: 0.5                 # marginal tail retention per teacher
+  retain_thresh: 1.0e-3
+  region_specialisation: false
+
+sweep:
+  - param: K_T
+    values: [1, 2, 3, 5]
+  - param: rho
+    values: [0.0, 1.0]   # decorrelated vs identical teachers (the control)
+
+output:
+  dir: results/recombination