Family: brocard — Brocard-Ramanujan equation

[roed-math]

One family: Brocard-Ramanujan equation (brocard) — P3, open.

• Standard form: n! + 1 = m^2
• Parents: —

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

References cited (the claim each one supports):

• Overholt1993 — finiteness under the abc conjecture
• BerndtGalway2000 — computational verification

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