Family: plane-cubic — Plane cubic curve (ternary cubic)

[roed-math]

One family: Plane cubic curve (ternary cubic) (plane-cubic) — P2, algorithmic.

• Standard form: C(x, y, z) = 0 homogeneous cubic
• Parent: genus-one-curve

Contents: the registry entry and its docs/FAMILIES.md section.

References cited (the claim each one supports):

• Nagell1928 — the classical reduction of a cubic with a rational point to Weierstrass form
• Selmer1951 — 3x^3 + 4y^3 + 5z^3 = 0: failure of the Hasse principle for plane cubics

Independent of every other family PR: it needs only the registry backbone it is based on.

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