new-pde-operator

name	new-pde-operator
description	Add a new PDE operator to AlphaGalerkin end-to-end. Use when introducing a PDE family (e.g. a new elliptic/parabolic/vector operator) so it registers in the operator registry, the PDEType enum, the canonical PDE_TYPE_MAP, and every dependent Literal enum — following the documented checklist so scenarios auto-pick it up.

new-pde-operator — register a PDE operator across the stack

Adding a PDE operator touches several coupled registration points. Missing one leaves the operator invisible to scenarios or breaks a Literal validator. Follow this checklist (it mirrors the CLAUDE.md guidance for Helmholtz/Biharmonic).

Checklist

1. Implement the operator in src/pde/operators.py (or operators_picogk.py for SDF/helical geometries), subclassing PDEOperator. Provide source_term, boundary_value, exact_solution (manufactured solution), and the residual. No hardcoded coefficients — surface them as Pydantic fields on PDEConfig/subclass, with a named module constant default (e.g. DEFAULT_HELMHOLTZ_WAVENUMBER).
2. Register it with @register_pde_operator("<name>") so PDEOperatorRegistry can find it.
3. Add to PDEType enum in src/pde/config.py.
4. Add to PDE_TYPE_MAP in src/poc/scenarios/_centaur_common.py (the canonical name→PDEType map shared by every centaur scenario).
5. Extend dependent Literal enums as needed: ood_pde (llm_prior_config.py), ScalingLawConfig.pde (scaling_law_config.py), ResearchPDEName (agents research loop).
6. Tests: tests/pde/test_ood_operators.py-style — properties/order, manufactured-solution analytics, residual-vanishes-on-exact (≤1e-3, incl. a Hypothesis parameter sweep), registry round-trip, and BasisSelectionGame construction with finite initial error.
7. Regression surface: add/extend the CLAUDE.md row for the operator family.

Guardrails

• Additive only — never change an existing PDEType value or registry key.
• ruff + mypy --strict clean; residual property test must pass on CPU.