Recursive reasoning dynamics: analysis pipeline, paper drafts, toy models

Failure=more-chaotic (task-general under validity labeling) reduces to convergence/completeness
detection; mechanism (transient chaos vs multistability vs input-induced) under investigation.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

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+# Recursive Reasoning Dynamics
+
+Analysis of the inference-trajectory dynamics of recursive reasoning models (HRM, TRM) on
+Sudoku-Extreme and Maze-Hard. Central finding and its honest deflation:
+
+- Along the recurrent inference trajectory, **genuine failures are more chaotic** (higher
+  finite-time Lyapunov exponents / latent drift) than successes, in the *same* trained network —
+  task-general (Sudoku; Maze under a validity/connectivity criterion, not exact-match).
+- This signal **reduces to convergence / answer-completeness detection** (the FTLE separation is
+  recoverable from late drift + the model's own halting confidence; leading + full Ginelli CLV
+  geometry add nothing beyond it). On unique-solution tasks completeness aliases onto correctness.
+- Open: the *mechanism* of the non-convergence (multistability vs transient chaos vs input-induced) —
+  the current line of work (see `paper/readiness.md`, `extend_rollout.py`, `toy/`).
+
+This repo is the **analysis half** (diagnostics, experiments, paper drafts, toy models). The model
+code (TRM/HRM forks with trajectory-augmentation training) lives in the companion `rrm` repo;
+heavy artifacts (checkpoints, npz, wandb, figures) are not committed.
+
+## Entry points
+- `paper/` — `readiness.md` (live status + all results), `claims.md` (claim/evidence/counter table),
+  `intro.md`, `setup_results.md`, `style_contract.md`, `experiment_framework.md`.
+- `analysis_2x2/` — the 2×2 (settling × correctness) decomposition, characterization, CLV reducibility,
+  checkpoint-evolution, connectivity-labeled Maze analysis. Result `.md`/`.csv` kept; npz/png ignored.
+- `diagnose_{trm,hrm}_joint*.py` — per-example FTLE (JVP+QR), drift, CLV estimators. `_maze` variant
+  forces the math SDP backend (FlashAttention lacks the JVP double-backward); `_clv` adds Ginelli CLVs.
+- `extend_rollout.py` — long-rollout probe (transient vs multistable vs persistent non-convergence).
+- `toy/` — minimal analytically-grounded toy models reproducing "failure = more chaotic".
+- `maze_pred_dump.py` — cheap forward dump (connectivity + drift, no JVP) for Maze validity labeling.
+
+## Estimator validation
+`paper/validation/validate_le_estimator.py` — the QR/Benettin FTLE core recovers known spectra
+(diagonal/symmetric/non-normal linear maps, Hénon λ₁) to <1e-3.