LazyProxy(..., enable_cache=True) repeatedly invokes its function when the result is None. For example, two reads of .value, a boolean conversion and a string conversion invoke a None-returning function four times, despite caching being enabled.

Track whether a result has been cached separately from the result value. This lets None be cached and preserves repeated evaluation when enable_cache=False. The regression covers both cache settings and verifies that initialization stays lazy.

Validation on macOS / CPython 3.12.11, with CLDR 48.2 data imported using the repository script:

• Before the fix: the cache-enabled regression fails with 4 calls instead of 1; the cache-disabled control passes.
• After the fix: python -m pytest tests/test_support_lazy_proxy.py -q --tb=short: 8 passed, including existing copying and exception tests.
• Full suite: TZ=UTC python -X utf8 -m pytest -q --tb=short: 7833 passed, 7 skipped, 2 xfailed. One pytest deprecation warning remains in the existing TOML tests.
• Ruff 0.14.10 and the repository's configured pre-commit checks pass for both changed files; git diff --check passes.

AI assistance: Codex investigated the bug, wrote the patch and regression tests, and ran the checks. No independent human review is claimed. The supported Python/OS CI matrix was not run locally; upstream CI and maintainer review remain outstanding.