feat(doi): Repository DoI automated gate and dashboard integration (CUST-WP-0024)

Implements the 14-criterion DoI checklist as a runnable gate with API,
MCP tools, CLI script, and dashboard integration.

Core components:
- api/doi_engine.py — async engine evaluating all 14 criteria (asyncio.to_thread
  for non-blocking HTTP self-calls), shared by API and CLI
- api/schemas/doi.py — DoICriterion, DoIReport, DoISummaryEntry schemas
- api/routers/repos.py — GET /repos/{slug}/doi + GET /repos/doi/summary
- scripts/check_doi.py — CLI: make check-doi REPO=<slug> / check-doi-all
- mcp_server/server.py — check_repo_doi(), get_doi_summary() tools

Dashboard (repos.md):
- DoI tier badge per repo (None/Core/Standard/Full) colour-coded red→green
- Domain block shows lowest DoI tier across its repos
- DoI KPI card in summary row
- DoI filter in All Repos Table
- Link to Repository DoI policy page

Also fixes: TPSC snapshots 500 error (missing nested selectinload for
catalog_entry relationship in list_snapshots endpoint).

Co-Authored-By: Claude Sonnet 4.6 (1M context) <noreply@anthropic.com>

mcp_server/server.py

@@ -2045,6 +2045,40 @@ def get_gdpr_report() -> str:
     return json.dumps(_get("/tpsc/report/gdpr"), indent=2)
 
 
+# ---------------------------------------------------------------------------
+# Repository Definition of Integrated (DoI)
+# ---------------------------------------------------------------------------
+
+@mcp.tool()
+def check_repo_doi(repo_slug: str) -> str:
+    """Evaluate the 14 DoI criteria for a repo and return a full report.
+
+    Criteria are grouped into three tiers:
+      Core     (C1–C4):  registered, domain, path, remote URL
+      Standard (C5–C9):  SCOPE.md, CLAUDE.md, workplan, SBOM, TPSC
+      Full     (C10–C14): repo goal, capabilities, agents, clean consistency, host paths
+
+    Status values: pass | fail | warn | skip
+
+    The 'tier' field shows the highest tier where ALL criteria pass or warn:
+      none | core | standard | full
+
+    Args:
+        repo_slug: Registered repo slug (e.g. 'llm-connect', 'the-custodian')
+    """
+    return json.dumps(_get(f"/repos/{repo_slug}/doi"), indent=2)
+
+
+@mcp.tool()
+def get_doi_summary() -> str:
+    """Return DoI tier for all active repos, sorted worst-first.
+
+    Useful at session start to spot repos that need integration work.
+    Tiers: none (red) → core → standard → full (green).
+    """
+    return json.dumps(_get("/repos/doi/summary"), indent=2)
+
+
 # ---------------------------------------------------------------------------
 # Entry point
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