g-potential equilibrium map - #5
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…_full arm Adds a new equilibrium map, g = grad_z Phi. Phi is a scalar potential with capped spectral norms. This makes J_g = grad^2 Phi symmetric by construction. Changes: - ftnode/latent/equilibrium.py: add GradPotentialG. It bounds ||g||_2 with an l2 ball, not an l-infinity box. It applies unequal spectral caps per layer. It provides project_() to hold the caps after each optimizer step. It provides curvature_headroom() as a diagnostic. - ftnode/latent/nets.py: add the ACTIVATION_LIPSCHITZ table and lipschitz_bound(). These certify ||grad Phi||_2 through the spectral caps. - ftnode/latent/feasibility.py: add fit_potential() and FeasibilityResult. This checks if a frozen field already has a symmetric-J_g representation. The check runs in minutes. A full training arm takes much longer. - ftnode/train.py: add a project_() hook after each optimizer step. The hook finds modules with a project_() method by duck typing. It does nothing for models that do not define one. - ftnode/diagnostics.py: add jg_stats(). It reports the skew fraction and lambda_max(sym J_g) of an equilibrium map. - tests/test_grad_potential.py: add tests for the new map's structural properties. - tests/test_recovery.py: update the bound test. It now checks the bound each map declares, instead of assuming one shape for all maps. - experiments/duffing/sym_jg_full.yaml, sym_jg_quick.yaml: add the new experiment. It compares svd_clamp+grad_potential against the l-ft-k-svd-clamp control. Both arms use the same operator, budget, and data. - scripts/run_g_potential.sh, scripts/analyze_sym_jg.py, scripts/execute_notebooks.py: add scripts to run the experiment and report its diagnostics. - examples/duffing/pkg_kappa_analysis.ipynb: re-run against runs/sym_jg_full. Results: - J_g is symmetric to float32 round-off. - The ||g||_2 <= 3.0 cap never binds during training. - No saddle point forms. The model stays monostable. - Rollout RMSE is about 9 times worse than the incumbent map. The mechanism works as designed. This arm does not match the incumbent's (svd_clamp) fit quality.
dde27b9 (the _proto_*.py scratch and duffing_learned_splitting_control.ipynb) was dropped from history. Rewrite the docstrings and comments that named those files so the surviving provenance and rationale no longer points at absent paths. Meaning and behavior are unchanged; the stale citations become 'the earlier prototype' / 'the control study', and the checkpoint-freeze rationale is restated as 'frozen committed artifact' rather than 'the frozen notebook loads it'.
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