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>

CLAUDE.md

@@ -76,6 +76,10 @@ E4's whole purpose is to isolate the effect of teacher **decorrelation ρ**, so
 
 **Finding (2026-07-05, real-MNIST `mnist_collapse`) — collapse and grounding-rescue reproduce on real images.** External-validity tier: a small **convolutional VAE** (the canonical generative-collapse model) is retrained each generation on its own generated digits. Modes = digit class × stroke-thickness bin (K=30, Zipf, ~18 tail modes); the oracle is a **frozen CNN + deterministic thickness** at **98.5% mode accuracy** (its 30×30 confusion matrix is recorded in the manifest as the measurement floor). Result (4 reps): the **dry (g=0) lineage collapses to a single mode** — forward-KL 0.5→18, support 30→1, tail truth-mass 1.0→0.06, H→0 — while **10% grounding holds all 30 modes** (KL≈0.6, full tail, H≈0.9). The VAE needs ~10% grounding here vs the synthetic histogram's ~5%, consistent with the `grounding` finding that trained neural models need more grounding than the exact operator. **Confirmation-only (signs, not magnitudes; blueprint §3.5)** — the exact synthetic oracle stays the quantitative anchor. `figures/mnist_montage.py` is an eyeball diagnostic (re-runs a short dry lineage; NOT a parquet figure). Build gates passed: CNN mode accuracy 98.5%; VAE gen-0 recovers full 30/30 support (over-smooths frequencies, KL≈0.5, no prior hole — unlike the *synthetic*-codeword VAE, which is why the MNIST VAE works where that one didn't). The MNIST tier is heavy (torchvision `--extra mnist`, downloads MNIST, ~5 min): `make mnist`, kept out of the `make neural` loop.
 
+**Finding (2026-07-05, learning kernel) — neutral drift is a null both real models fail, oppositely; the estimator bias is a signed operator.** Layer-1 extension (`knowledge/kernel.py`, `LearningKernelCfg`): the refit becomes `p_{t+1} = T_θ(counts/n)` with two pop-gen knobs — **reset `u`** (mutation toward a prior = smoothing) and **temperature `τ`** (sharpening = mode-competition) — both identity at their defaults, so the histogram bridge and every scientific-validation test are unchanged (68 core tests still green). Result: **neutral Wright–Fisher fails both neural architectures, in opposite directions.** VAE regime (`n=6000, K=30`): neutral drift is *inert* (no collapse), yet the real VAE collapsed to one mode — **sharpening `τ=0.8` reproduces it** (the estimator ADDS collapse). 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). Honest caveat: uniform-mutation matches the RNN `H`-floor but overshoots its forward-KL (~5 vs ~2), evidence the RNN's smoothing prior is *truth-like, not uniform* (future refinement). Configs `configs/layer1/kernel_{sharpen,smooth}.yaml`, figure `plot_kernel.py`. This mechanistically explains the architecture-generality result and the softened neural `g*`.
+
+**Strategic positioning vs Riis 2026 (arXiv:2604.08554, "Drift and selection in LLM text ecosystems").** Riis independently formalizes **collapse = Wright–Fisher drift** (his Thm 1) with n-gram agents: minority-mass martingale, rare-first extinction, single-token dropout ≈ αe^{−α}, de Bruijn-polytope fixed points, plus descriptive-vs-normative *selection* (Thm 2). **Concede as prior art:** "collapse is literally Wright–Fisher", the martingale, rare-first loss, the WF/effective-population formalism — cite him; do **not** frame these as our contribution. **Crucial distinction that protects us:** his "mixed environment" *retains the lineage's own old synthetic tokens* — there is **no injection of fresh real data from a fixed `p*`**, so his headline is *pessimistic* (Thm 1c: extinction is independent of α — retention only changes speed). Our **grounding is immigration from a non-drifting external truth**, giving a stationary `H_eq>0` and a critical `g*≪1` that *prevents* collapse — the mechanism his closed loop lacks. **Our defensible novelty, ranked:** (1) **recombination + "merge, don't average" conservation law** (E4) — he has no model-merging operator; flagship; (2) **the learning-kernel / estimator-bias axis** — he *explicitly names it as future work*; we now build+measure it; (3) grounding threshold (solid anchor, but immigration–drift balance is classic — not a flagship); (4) architecture-generality in real weights + MNIST; (5) **the Lamarckian society + the vertical/cumulative C3 claim — wholly ours, not yet run.** Reposition the paper from *"collapse is drift"* (now contested) to **a population-genetic *control theory* for sustaining open-ended knowledge**: drift is the diagnosed disease (cite Riis), our contribution is the engineered remedies and their integration.
+
 ## Build order (blueprint §7) — respect the gate
 
 1. Scaffold: repo layout (§5), container, pytest skeleton, config system, seeding utils. `make test` green.