skill: graph-health gate (Step 4.5) + anchor caches on the scan root

[bahcgscateringsa-design]

Two integrity improvements to the core skill runbook (edited in
tools/skillgen/fragments/core/core.md, artifacts + expected/ regenerated via
python -m tools.skillgen / --bless). These are independent — happy to split,
drop, or cherry-pick either one (see note at the bottom).

1. Anchor the caches on the scan root (consistency fix)

The skill currently passes cache_root=Path('.') to AST extraction and lets
check_semantic_cache / save_semantic_cache default to . — i.e. it keys the
cache on the cwd. The CLI extract path keys on the scan root:
ast_kwargs = {"cache_root": out_root} and check/save_semantic_cache(root=out_root),
with out_root = out_dir or target. build_from_json() / save_manifest() already
take root='INPUT_PATH' in the runbook (#1361).

This change makes the runbook match the CLI: both AST and semantic caches anchor on
INPUT_PATH. Without it, running graphify from a cwd ≠ scan root cold-misses the
cache (every file re-extracts) and can even split AST vs semantic cache locations.

2. Step 4.5 — read-only graph-health gate (proposal)

graphify/diagnostics.py (diagnose_extraction / format_diagnostic_report) is a
ready integrity checker that isn't wired into the default pipeline. This adds a
read-only Step 4.5 after build / before labeling that surfaces dangling /
missing / self-loop and same-endpoint-collapsed edges — the silent-corruption modes
of incremental updates and AST/LLM id mismatches. It never aborts; it just makes
an integrity issue visible (per the Honesty Rules) instead of letting users query a
silently-broken graph.

Tests

• Full suite: 2229 passed, 28 skipped.
• tests/test_skillgen.py: 53 passed (check / audit-coverage / monolith-roundtrip /
  lean-core invariants all hold), tests/test_cache.py: 27 passed.

Note on scope

I know the skill is mid lean-core split. #1 is a straightforward CLI-parity fix and
stands alone. #2 adds a step to the core, which may be at odds with the lean-core
direction — totally fine to take only #1, or to treat #2 as a discussion. Tell me
how you'd like it sliced and I'll adjust.

[safishamsi]

Merged into v8 as e7ba16b (cherry-picked). Verified all five skillgen guards pass on the PR (check / audit-coverage / schema-singleton / monolith-roundtrip / always-on-roundtrip) — the fragment was edited and artifacts regenerated/blessed correctly, and since the PR branched off current v8 it already carries the #1417/#1419 core.md fixes (no conflict, no stale artifacts). The cache anchoring is consumer-side only (passes root= into the already-shipped check_semantic_cache/save_semantic_cache), no conflict with the graphify.paths work. Step 4.5 calls a real diagnose_extraction API and never aborts. Thanks @bahcgscateringsa-design!