teams: tile spend, refused writes said, no wake prompts on tiles, sub-cent caps, wrap-up time left, local closed reports

[AbirAbbas]

Six should-fixes from the #1429 and #1494 reviews, one commit each.

What was wrong, and what is true now

1. Wall tiles showed no spend. tui3: conversation overview #1429 promised it. Each tile's state line now ends in the figure that conversation's own status line shows: spendShown for the conversation in front, and the same rule (spendOf) for held ones. A held tile uses its books, read off the loop with the transcript, and its ledger tree, read at most every 5s. Zero draws nothing, and on a narrow tile the figure gives way before the state words do.
2. A refused team write still said Made beta · 1. Every team edit now carries a number, and the write reports which edits it took and which it refused. Made, Organized and the teams page's close and move notices wait for their own edit. When the store refuses, the notice is replaced by a warning such as beta was not saved · <reason>.
3. Tiles showed the wake prompt that the live conversation never draws. A reopened manager conversation drew it too. The wake sentences are now session constants (TeamWakeNote), and one aside classifier is shared by replay and the tiles: a team delivery draws as its lines, and an empty team wake draws nothing.
4. A $0.001 cap read $0.00 and Raise to $0, which stored a ceiling of 0. There is now one cap spelling, teams.Money ($5, $5.50, $0.001). It is used by the packet, the refusal, the teams page header, the card, the settings card and the Settings row. RaiseTo is always twice the ceiling and strictly above it. A spend under a cent is no longer rounded to 0.
5. Nothing showed a wrap-up's time left. The teams page header and the manager's side column now show wrapping up · 12m left, then under a minute left, then out of time. The figure comes from the held team's persisted wrap, never from a store read on the paint clock.
6. A plain local launch said a closed team's report is not readable over this connection. localDoors now reads History from the engine's profile on this machine. --host is unchanged: no wire door carries History.

Validation contract

• A tile's figure equals its conversation's status-line figure. Zero draws nothing, a frame never calls Usage or reads the ledger, and the state words are never cut for the figure.
• A notice for a team write is drawn only after the store has taken that edit. A refused edit shows the refusal instead, and a sibling edit's refusal is not blamed on it.
• No tile and no reopened conversation shows started this turn. A task landing still draws its line.
• For every positive cap c, RaiseTo > c, and the label names exactly RaiseTo. $5 still reads Raise to $10, and every place spells one cap the same way.
• A team with a wrap-up shows its time left, which changes as the clock moves. Nothing is shown for a team without one or for a closed team.
• On a local launch a closed team shows its closing report. Over --host, History stays nil.

How it was checked

• Each contract item has a test that fails on origin/dev and passes here.
• make pr-ready passed.
• Hand check: real binary, every seat on deepseek-v4-flash, $0.001 total. Two conversations answered one message each. On the wall their tiles read $0.0008 and $0.0003, the same as their own status lines, at both 200 and 100 columns.

Follows #1429 / #1485 / #1494 / #1436 review

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