Family: sum-of-four-squares — Sum of four squares (Lagrange)

[roed-math]

One family: Sum of four squares (Lagrange) (sum-of-four-squares) — P1, solved.

• Standard form: x^2 + y^2 + z^2 + w^2 = n
• Parent: quadratic-form-representation

Contents: the registry entry, its docs/FAMILIES.md section, its rows in the classification corpus, its solver and solver-layer tests.

References cited (the claim each one supports):

• RabinShallit1986 — randomized polynomial-time four-squares algorithm

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