feat(notes): a note's check is writable through both doors, and empty means empty (#3164, milestone 317 step 2)

The rules path's three lessons (#3096), inherited:

EMPTY MEANS NULL. The sweep's whole signal is `verify_with IS NULL` = "this is
a decision, there is nothing to go and check". A "" that is not NULL makes a
norm look like a constraint nobody has verified — and never-checked sorts
FIRST, so it would sit at the top of the sweep forever.

CLEARING IS EXPLICIT. At the MCP door "" means "leave this alone", so an agent
updating a body does not wipe a check it was never asked about — which leaves
no value meaning "remove it". `clear` names the field, and naming it cannot
happen by accident. The REST door, where a cleared form input arrives as "",
reaches the same place through normalisation: two idioms, one outcome.

THE STAMP CERTIFIES A CHECK, NOT A RECORD. Rewrite or clear `verify_with` and
`verified_at` is dropped, so the note re-enters the sweep. A note wrongly
listed as due costs one look; a note wrongly vouched for costs exactly what
the sweep exists to catch. `verified_at` is also no longer settable through an
ordinary edit — a stamp says somebody performed THIS check, and minting one
from a write that ran no check is the one thing that would make the sweep lie.

And one this path adds: not every record may carry a check. A task's decay is
its status — a done issue records what happened rather than asserting
something that can go false — and a snippet already has verify_snippet, which
compares its recorded location and code against the repo and expires its own
verdict. Both are refused with a message naming the alternative, never dropped
silently (minted_kind's reasoning, #3129), and the gate lives at the service
so the two doors cannot come to disagree.

Written as an INVARIANT over the resulting record, not a filter on which
fields were passed. That is what catches the sideways route — a checked note
being turned into a task, a write that names no check at all and would sail
past any per-field gate.

The MCP docstrings carry the norm-vs-constraint test, because at that door the
docstring IS the contract and a field described only as "how to verify this"
gets filled in on every note. Step 5 does this properly across the instruction
surfaces; this is the minimum that stops the field being misused on arrival.

tests/helpers gains `drive_update_note` — the patch stack for driving
update_note, written twice before this and now once. The note-shaped fakes
gain the trio explicitly, for fake_note's own stated reason: an unset
attribute is a truthy MagicMock, and a truthy verify_with reads as a check
that is there.

tests/test_snippet_mirror_generic_door.py

@@ -13,10 +13,9 @@ reverse lookup and to prior-art recall while displaying its new body — a recor
 surfaced with full authority and wrong, which the drift-check docstring calls
 worse than having no record at all (#3128).
 """
-from unittest.mock import AsyncMock, MagicMock, patch
-
 import pytest
-from tests.helpers import fake_note, fake_snippet, make_mock_session
+from tests.helpers import drive_update_note as _update
+from tests.helpers import fake_note, fake_snippet
 
 OLD_MIRROR = {
     "name": "debounce",
@@ -33,21 +32,6 @@ MOVED_BODY = (
 )
 
 
-async def _update(note, **fields):
-    session = make_mock_session()
-    result = MagicMock()
-    result.scalars.return_value.first.return_value = note
-    session.execute = AsyncMock(return_value=result)
-    with patch("scribe.services.notes.async_session") as cls, \
-         patch("scribe.services.notes.embed_note", MagicMock()), \
-         patch("scribe.services.notes._maybe_reactivate_project", AsyncMock()), \
-         patch("scribe.services.note_versions.create_version", AsyncMock()):
-        cls.return_value = session
-        from scribe.services.notes import update_note
-        await update_note(user_id=7, note_id=note.id, **fields)
-    return note
-
-
 @pytest.mark.asyncio
 async def test_a_body_write_moves_the_mirror_with_it():
     note = fake_snippet(data=dict(OLD_MIRROR), project_id=None)