不変条件分析付きディープリファクタリング

Analyze the supplied module for a safe refactor.

Steps (show work):
1. List public entrypoints and side effects (DB, HTTP, filesystem).
2. For each non-trivial loop/recursion: state invariant, variant function, and termination argument.
3. Identify hidden coupling (shared mutable state, implicit ordering).
4. Propose refactor as small steps; each step must preserve observational equivalence for listed entrypoints.
5. Flag race conditions under concurrent calls.
6. Output test cases that would fail if invariants break (table: input, expected, property checked).

Do NOT rewrite code until step 6 is approved. Use markdown headings.