Family: thue-mahler — Thue-Mahler equation

[roed-math]

One family: Thue-Mahler equation (thue-mahler) — P1, algorithmic.

• Standard form: F(x, y) = m * p_1^N_1 * ... * p_s^N_s
• Parent: thue
• Examples: x^3 + 2*y^3 = 5^a * 11^b

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

References cited (the claim each one supports):

• Mahler1933 — origin of the problem: finiteness with prime-power right-hand sides (p-adic method)
• TzanakisDeWeger1992 — the classical practical algorithm
• GhergaSiksek2022 — the modern efficient implementation (Magma code)

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