Family: pillai — Pillai equation

[roed-math]

One family: Pillai equation (pillai) — P1, effective.

• Standard form: a^x - b^y = c (a, b fixed)
• Parent: exponential-diophantine
• Examples: 3^m - 2^n = 1, 3^m - 2^n = 5

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

References cited (the claim each one supports):

• Pillai1936 — origin of the problem
• Bennett2001 — at most two solutions for fixed bases

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