feat: stamp the Memory inbox on quiet days, not just paper days

[Jammy2211]

Summary

The Mind leg of PyAutoMemory#58. Depends on PyAutoLabs/PyAutoMemory#60 — merge that one first: this workflow calls inbox_actions.py stamp, which does not exist until it lands.

The board half reads a last digest: <date> line to tell a quiet arXiv inbox from a broken one. That line is only worth anything if the digest writes it on days with nothing to file — otherwise it goes stale on exactly the days it exists to prove were quiet, and says "broken" about a working run.

So the inbox step loses its count != 0 guard and runs every weekday. To keep its preconditions honest, the empty-day heartbeat step now also writes arxiv_survivors.json as {"papers": []} — the same file the Claude step already writes on its own no-papers day. Every path produces one, so a missing survivors file in the inbox step stays what it has always been: a real failure, not an empty day.

The step's other invariants are untouched. It still runs after the Slack POST, so a cross-repo auth or push failure cannot cost the morning's post; the missing-survivors and unset-PAT preconditions still warn and exit 0; a denied push still reddens the run (#317).

Two consequences worth naming:

• A quiet day is now a one-line commit to PyAutoMemory rather than silence, which also re-renders the knowledge board daily. That is the point — it is the board's version of the #papers empty-day heartbeat.
• The sweep now runs every weekday too, so a lapsed line no longer lingers through a quiet stretch waiting for the next paper day to evict it.

Re-running the same day is still a no-op: the stamp is unchanged, the porcelain check sees nothing, and the step exits without a commit.

Also carries the Mind lifecycle for the task — the prompt advanced draft/ → active/, active.md registered, dashboard regenerated.

API Changes

None — a workflow change plus Mind registry state. No Python surface touched.

Test Plan

• 197 tests passing
• lifecycle.py check OK; intake dashboard --check current
• YAML parses; every run: block passes bash -n
• All four digest paths rehearsed against a real PyAutoMemory checkout, with both shell blocks extracted verbatim from this file rather than retyped: quiet day/same date (no commit), quiet day/new date (the heartbeat commit), paper day (paper lands below the stamp), and a quiet day sweeping lapsed papers

Not fired live, and cannot be. claude-code-action refuses to run when this file differs from the default branch's copy — and then exits success, so a branch dispatch silently writes no slack_payload.json and skips every later step including this one. That trap is recorded in complete/2026/08/arxiv-inbox-pat-scope.md and already cost one wasted dispatch. The scheduled 02:00 UTC run on main is the first genuine end-to-end exercise; the steps are plain bash with no dependency on claude-code-action.

Generated by the PyAutoLabs agent workflow.

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