Restructure: descriptive tier and experiment names, paper/manuscript

- paper/pnas -> paper/manuscript (venue-neutral)
- configs/layer1 -> configs/inheritance, src/knowledge -> src/inheritance
  (imported as `inheritance`), make layer1 -> make inheritance; layer2 alias dropped
- inheritance and trained-network bundles named after the manuscript figure
  they feed (fig2_grounding_sweep, figS3_rebaselining, ...), or descriptively
  where they feed none; configs keep their `experiment:` value so parquet
  hashes are unchanged, only output.dir moves
- figure scripts, SI figure sources, notebooks, REPRODUCING.md, README and the
  SI Methods/tables updated; make clean no longer deletes tracked manifests;
  reproduce.sh hashes the s{seed}/ layouts too

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y64o8FKP7rCuXzC48pxpMm

results/figS8_multiparent_union/README.md

@@ -0,0 +1,33 @@
+# E4 — Recombination supplies the rare tail; only a union-preserving *merge* realises it
+
+**Claim tested:** if several specialist models each remember a different slice of the rare tail, can
+combining them reconstruct the whole tail? And does *how* you combine them matter?
+
+**Setup (Layer 1, pure math).** `K = 500` items. We build `K_T` teacher models that each retain the
+rare tail with probability `q`, and we control how **correlated** their retained tails are with a
+single knob `ρ` (rho): `ρ = 0` = fully complementary teachers, `ρ = 1` = identical teachers. Swept:
+`K_T ∈ {1,2,3,5}`, `ρ ∈ {0, 0.25, 0.5, 0.75, 1}`, grounding `g ∈ {0, 0.02, 0.05}`, 200 repeats.
+
+### Symbols
+- **`K_T`** number of teacher models; **`ρ`** how correlated their retained tails are (0 = diverse, 1 = clones).
+- **union coverage** — fraction of the tail covered by *at least one* teacher (the raw supply).
+- **surviving coverage** — fraction that actually survives in the pupil after it retrains on the combination.
+- **mean-distill** — pupil trained on the pooled/averaged teacher outputs. **max-merge** — keep, per item, the strongest teacher (a union-preserving merge, à la M2N2).
+
+### The three panels
+1. **Supply.** Union tail coverage vs `ρ`, one curve per `K_T`; solid lines are the exact closed form
+   `U(K_T, ρ, q)`. More teachers and more diversity (lower `ρ`) supply more of the tail — and the
+   simulation matches the formula exactly.
+2. **Realisation.** Surviving coverage vs `ρ`. **Solid = max-merge rises** with more/diverse teachers;
+   **dashed = mean-distill stays flat.** Averaging dilutes each teacher's rare items back below the
+   survival threshold — the gain is supplied but not realised.
+3. **The benefit needs the right operator (`ρ = 0`).** Surviving coverage vs `K_T` under both
+   operators. Max-merge climbs with teacher count; mean-distill is flat — a **conservation law**:
+   averaging's `1/K_T` dilution exactly cancels the union gain.
+
+### Takeaway — "merge, don't average"
+Complementary specialists *contain* enough to rebuild the tail, but **naive multi-teacher distillation
+(averaging) throws it away**; you must combine them with a union-preserving merge. This is load-bearing
+for the paper's recombination claim and is re-tested in real neural weights in `results/recombination/`.
+**Falsifier (not triggered):** if mean-distill had also risen with `K_T`, or max never beat mean, the
+recombination story would collapse into "just average your models."

results/figS8_multiparent_union/manifest.json

@@ -0,0 +1,14 @@
+{
+  "experiment": "E4_multiteacher_decorrelation",
+  "master_seed": 20260704,
+  "git_commit": "a6eb9b75124779375fa1a0b3a64115ecd705b218",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0"
+  },
+  "rows": 12000,
+  "results_sha256": "a200ed088070015f41c983a367a252c09d06a865b45f117769df73fa00df52a2"
+}

results/figS8_multiparent_union/resolved_config.yaml

@@ -0,0 +1,39 @@
+experiment: E4_multiteacher_decorrelation
+seed: 20260704
+n_replicates: 200
+source_config:
+  experiment: E4_multiteacher_decorrelation
+  kind: coverage
+  seed: 20260704
+  n_replicates: 200
+  truth:
+    K: 500
+    R: 1
+    tail: zipf
+    zipf_s: 1.1
+    tail_frac: 0.5
+    tail_threshold: 0.002
+  coverage:
+    n: 300
+    q: 0.5
+  sweep:
+  - param: K_T
+    values:
+    - 1
+    - 2
+    - 3
+    - 5
+  - param: rho
+    values:
+    - 0.0
+    - 0.25
+    - 0.5
+    - 0.75
+    - 1.0
+  - param: g
+    values:
+    - 0.0
+    - 0.02
+    - 0.05
+  output:
+    dir: results/figS8_multiparent_union