knowledge: learning kernel — model the estimator bias, not just sampling

Revisiting Layer 1 against Layer 1.5 (and Riis 2026, arXiv:2604.08554):
neutral Wright-Fisher is a null that BOTH neural architectures deviate
from, in opposite directions. Add a learning kernel to the refit step,
p_{t+1} = T_theta(counts/n), with two population-genetics knobs -- reset u
(mutation toward a prior = smoothing) and temperature tau (sharpening =
mode-competition) -- both identity by default, so the histogram bridge and
all 68 scientific-validation/correctness tests are unchanged.

Result: neutral drift fails both neural models, oppositely.
- VAE regime (n=6000, K=30): neutral drift is inert (no collapse), yet the
  real VAE collapsed to one mode. Sharpening tau=0.8 reproduces it -- the
  estimator ADDS collapse pressure.
- RNN regime (n=200, K=256): neutral drives H->0, but the real RNN only
  partially collapses. Mutation u=0.006 reproduces the H-floor -- the
  estimator REMOVES collapse pressure. Honest caveat: uniform-mutation
  overshoots the RNN's forward-KL, evidence its smoothing prior is
  truth-like, not uniform (future refinement).

This mechanistically explains the architecture-generality result and the
softened neural g*, and develops the estimator axis Riis names as future
work. New: knowledge/kernel.py, configs/layer1/kernel_{sharpen,smooth}.yaml,
figures/plot_kernel.py (overlays analytic arms vs committed neural
endpoints), READMEs, tests/test_kernel.py (+6, 105 total green). Strategic
Riis positioning recorded in CLAUDE.md: concede "collapse=drift" as prior
art; lead with recombination, the kernel axis, and the Lamarckian society.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

results/kernel_sharpen/README.md

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+# kernel — the learning kernel: why real learners deviate from neutral drift
+
+*(This legend covers both `results/kernel_sharpen/` and `results/kernel_smooth/`; the figure
+`kernel.png` is written into both.)*
+
+**Claim tested.** Neutral Wright–Fisher drift (the histogram bridge, and the baseline of Riis
+2026) is the *null* model of collapse. But Layer 1.5 showed real trained models deviate from it —
+and in **opposite directions**. Can a single extension of Layer 1 — a parameterized *learning
+kernel* on the refit step, `p_{t+1} = T_θ(counts/n)` — reproduce both deviations, and does neutral
+drift genuinely fail without it?
+
+**Setup.** The kernel (`knowledge/kernel.py`) has two population-genetics knobs, both reducing to
+neutral drift at their defaults (so the histogram and every scientific-validation test are
+unchanged): **reset `u`** — mutation toward a prior (`p ← (1−u)p + u·π`), i.e. smoothing; and
+**temperature `τ`** — sharpening (`p ∝ p^{1/τ}`, `τ<1` concentrates), i.e. mode-competition. Two
+matched-to-neural regimes, 24 replicates each.
+
+### The four panels (`kernel.png`; blue = neutral, red = kernel-on, green dashed = the real neural model)
+**Top row — VAE regime (`n=6000`, `K=30`), pro-collapse:**
+1. **Heterozygosity.** Neutral drift is **inert** — at `n=6000` it barely moves (`H` stays at
+   `H*`). Yet the real VAE (green) collapsed to `H≈0`. **Sharpening (`τ=0.8`) reproduces the
+   collapse.** Neutral drift is *falsified*; the estimator's mode-competition is required.
+2. **Support.** Neutral holds ~all 30 modes; sharpening → 1 mode, matching the VAE.
+
+**Bottom row — RNN regime (`n=200`, `K=256`), anti-collapse:**
+3. **Heterozygosity.** Neutral drift drives `H → 0`, but the real RNN (green) only *partially*
+   collapses (`H` floors at ~0.68). **Mutation `u=0.006` reproduces the floor.** The estimator here
+   *removes* collapse pressure.
+4. **Forward-KL.** Neutral diverges; smoothing plateaus. Honest caveat: uniform-mutation plateaus
+   *above* the RNN's KL (~5 vs ~2) — evidence the RNN's smoothing target is **truth-like, not
+   uniform** (a refinement for future work). The *sign* is unambiguous.
+
+### Takeaway
+Model collapse in real learners = **neutral drift ⊕ an architecture-specific estimator-bias
+operator that can point either way.** The histogram sits at the neutral null (`u=0, τ=1`); the VAE
+**sharpens** (adds collapse); the RNN/MLP **smooth** (add a diversity floor). This mechanistically
+explains the Layer-1.5 architecture-generality result and the softened neural `g*`, and develops
+the exact axis Riis (2026) names as future work ("different smoothing schemes… each induce their
+own fixed-point geometry… a natural direction for further work"). `u`/`τ` are calibrated from a
+single neural diagnostic and pinned in the configs. **Falsifier (not triggered):** if neutral drift
+had already reproduced the neural curves, the estimator axis would be superfluous — instead it fails
+in *both* regimes, oppositely.

results/kernel_sharpen/manifest.json

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+{
+  "experiment": "kernel_sharpen",
+  "master_seed": 20260705,
+  "git_commit": "79bbc45f41822757e60d7f1994a82c5171a9e554",
+  "python": "3.14.5",
+  "libraries": {
+    "numpy": "2.5.0",
+    "scipy": "1.18.0",
+    "pandas": "3.0.3",
+    "pyarrow": "24.0.0"
+  },
+  "rows": 768,
+  "results_sha256": "d5651a841d58f12abed1339476b1839fb03fe02329e38d675d0602ccb5691e52"
+}

results/kernel_sharpen/resolved_config.yaml

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+experiment: kernel_sharpen
+seed: 20260705
+n_replicates: 24
+source_config:
+  experiment: kernel_sharpen
+  kind: lineage
+  seed: 20260705
+  n_replicates: 24
+  truth:
+    K: 30
+    R: 1
+    tail: zipf
+    zipf_s: 1.5
+    tail_threshold: 0.01
+    init: truth
+  dynamics:
+    n: 6000
+    grounding:
+      m: 0
+      policy: proportional
+    kernel:
+      reset: 0.0
+      temperature: 1.0
+      floor: 0.0
+  generations: 15
+  metrics:
+    kl_floor: 1.0e-09
+    support_eps: 1.0e-09
+  sweep:
+  - param: dynamics.kernel.temperature
+    values:
+    - 1.0
+    - 0.8
+  output:
+    dir: results/kernel_sharpen
+grid:
+- label:
+    temperature: 1.0
+  lineage_cfg:
+    truth:
+      K: 30
+      R: 1
+      tail: zipf
+      zipf_s: 1.5
+      tail_threshold: 0.01
+      init: truth
+    dynamics:
+      n: 6000
+      grounding:
+        m: 0
+        policy: proportional
+      kernel:
+        reset: 0.0
+        temperature: 1.0
+        floor: 0.0
+    generations: 15
+    metrics:
+      kl_floor: 1.0e-09
+      support_eps: 1.0e-09
+- label:
+    temperature: 0.8
+  lineage_cfg:
+    truth:
+      K: 30
+      R: 1
+      tail: zipf
+      zipf_s: 1.5
+      tail_threshold: 0.01
+      init: truth
+    dynamics:
+      n: 6000
+      grounding:
+        m: 0
+        policy: proportional
+      kernel:
+        reset: 0.0
+        temperature: 0.8
+        floor: 0.0
+    generations: 15
+    metrics:
+      kl_floor: 1.0e-09
+      support_eps: 1.0e-09