neural: real-MNIST external-validity tier (collapse + grounding)

Confirms model collapse and its arrest by grounding on REAL images, not
just the synthetic sandbox. A conv VAE (the canonical generative-collapse
model) is retrained each generation on its own generated digits, with a
fraction g of fresh real MNIST mixed in. Modes = digit class x stroke-
thickness bin (K=30, Zipf, ~18 tail modes); the oracle is a frozen CNN +
deterministic thickness at 98.5% mode accuracy (30x30 confusion matrix
recorded in the manifest as the measurement-noise floor).

Result (4 reps): dry (g=0) collapses to a single mode -- forward-KL
0.5->18, support 30->1, tail 1.0->0.06, H->0 -- while 10% grounding holds
all 30 modes (KL~0.6, full tail, H~0.9). Signs, not magnitudes (blueprint
3.5); the exact synthetic oracle stays the quantitative anchor. The VAE
needs ~10% grounding vs the synthetic histogram's ~5%, consistent with the
grounding finding that trained nets need more than the exact operator.

Plugs into the existing data-agnostic contract (metrics/grounding/output
reused verbatim): mnist_data (thickness bins, class x thickness bijection,
MnistSampler), mnist_oracle (ClassifierOracle + confusion matrix),
mnist_vae (ConvVAEGenerator), mnist_loop (run_mnist_lineage), kind=
mnist_lineage dispatch, MnistCfg/OracleCfg. Figures: plot_mnist (parquet-
only) + mnist_montage (eyeball diagnostic showing digits degenerate to one
blurry mode). make mnist / make env-mnist, kept out of the make neural
loop. 99 tests green (+5 torchvision-gated).

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

CLAUDE.md

@@ -16,9 +16,11 @@ This file provides guidance to Claude Code (claude.ai/code) when working with co
   **Done:** scaffold, the histogram bridge gate (reproduces Layer 1 exactly), `bridge` (neural
   g*=0.047 ≈ Layer 1), `collapse` (in RNN weights), `grounding` (refined; sign confirmed, threshold
   softened by neural smoothing — see finding below), `architectures` (architecture-generality),
-  `recombination` (the E4 "merge, don't average" finding reproduced in real weights), and all five
-  neural figures (`figures/plot_{bridge,collapse,grounding,architectures,recombination}.py`, wired
-  into `make figures`). **Remaining:** `region_matched`, `remint`, the MNIST tier, VAE fidelity. The LLM/LoRA rung and the C3 vertical claim are deferred. Experiments are
+  `recombination` (the E4 "merge, don't average" finding reproduced in real weights), all six
+  neural figures, and the **real-MNIST external-validity tier** (`mnist_collapse`: a conv-VAE
+  collapses to a single mode under dry self-training, ~10% grounding holds all 30 modes; frozen-CNN
+  oracle, confusion matrix recorded). **Remaining:** `region_matched`, `remint`, the synthetic-VAE
+  fidelity fix — all optional. The LLM/LoRA rung and C3 vertical claim stay deferred. The LLM/LoRA rung and the C3 vertical claim are deferred. Experiments are
   named descriptively (`configs/neural/<name>.yaml`), not by code.
 
 The two design documents are the source of truth for intent:
@@ -72,6 +74,8 @@ E4's whole purpose is to isolate the effect of teacher **decorrelation ρ**, so
 
 **Finding (2026-07-05, neural `grounding`) — grounding's SIGN transfers to trained RNN weights, but the sharp `g*` does not; and tail-survival is the *wrong* neural collapse metric.** Re-ran the phase-boundary sweep at 18 replicates. Two results: (1) **forward-KL is the operative neural collapse metric, not H or tail-survival.** The RNN's smoothing inductive bias keeps *spurious* tail modes alive (it generalises to unseen codewords), so `tail_truth_mass_alive` is flat/**non-monotone** in g (dry 0.54 > most grounded points) and H stays ~0.77–0.85 of H\* throughout — neither shows a threshold. Stationary **forward-KL** falls monotonically (dry 2.08 → g=0.2: 0.75), significant at g≥0.05 (paired t up to 3.3; 89% of lineages improve at g=0.2). This *refines* the earlier "forward-KL AND tail survival" note: for a smoothing model, support-counting decouples from closeness-to-truth. (2) **The sharp `g*≪1` is an exact-operator feature, softened by neural inductive bias.** Half the achievable KL reduction closes by a *median-recovery* grounding g≈0.04 (bootstrap CI [0.004, 0.116]) — a striking echo of Layer-1's 0.048 — but full (95%) recovery needs g≈0.19, far more than the histogram bridge, because smoothing both caps dry collapse (KL~2, not ∞) and slows full recovery. So the quantitative `g*≪1` claim rests on the **histogram bridge** (g\*=0.047, exact reduction to Layer 1), which the trained RNN confirms in *sign* and softens in sharpness. Honest note: the pre-registered 95%-of-H\*/tail-survival falsifier is not met, but that is because those are the wrong metrics for a smoothing model, not because grounding fails — the blueprint §3.5 directional claim (grounding arrests collapse) holds robustly. Robustness fix landed alongside: a fully-degenerate RNN can emit only invalid codewords, so `measure_distribution` returns a terminal-collapse sentinel (fixation on the dominant mode) instead of crashing a long sweep.
 
+**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.
+
 ## Build order (blueprint §7) — respect the gate
 
 1. Scaffold: repo layout (§5), container, pytest skeleton, config system, seeding utils. `make test` green.