The classification pipeline

[roed-math]

The classification pipeline.

classify() parses, splits reducible equations into components, runs the
matchers, and ranks the results by depth in the family DAG, so the most
specific family wins. Classification.explain() is the human report and
as_dict() is the JSON contract for the future website backend.

API notes:

• Classification separates the problem as submitted (parsed) from the model
  the matchers saw (model, read through working), with the map between them
  in reduction. Reducing (x + y)^2 = 0 to x + y = 0 used to return the
  factor's classification as if it were the input, losing the original text,
  the requested domain, the unknown order and the side conditions; all four now
  survive, and factors of a reducible equation inherit the parent's domain,
  parameters and checkable conditions instead of falling back to classify()'s
  default argument.
• match_for(slug) / data_for(slug) look up an emitted match, and code()
  fills each family's template from its own match. Filling an ancestor's
  template with the primary match's data produced confident nonsense, because a
  DAG edge says nothing about whose data meets whose input contract.
• explain() prints one arrow line per genuine lineage path, and as_dict()
  carries lineage_paths/lineage_graph, the structured conditions, and the
  transform — composed from the very objects the solvers use.

tests/test_classify.py starts the classification corpus (famous equation to
expected family); each family PR adds its own rows.

Part of the series that splits #1 into reviewable pieces:

1. 01-bibliography — packaging, docs, annotated bibliography
2. 02-parsing — equation strings to a term model
3. 03-registry — the YAML family registry (3 seed families)
4. 04-matchers — shape recognizers
5. 05-classify — the classification pipeline
6. 06-solvers — solver framework, two seed solvers, and the CLI
7. 07..09-backbone — the 23 parent families of the DAG, by depth
8. one PR per remaining family (38 of them, mutually independent)
9. 99-polish — restore the full doctests and tighten the invariants