sw-explain

Explain a Session Watcher metric

When the user asks about a metric:

1. Call watcher_status. Read br, u (the arm it puts the session on), the lamp and the wallet clock's phase from the reply's reading; a false reading.reliable means the session is still measuring, so say that instead of quoting values. mf, pp, wall and sweet / valley are not in reading: point the user at where the host shows them, in Claude Code the dashboard at the URL the reply carries, in DSH the Session Watcher tab. mf is the hero chart's movable reading; the others are landmarks with no numeric readout.
2. Explain the requested metric in plain language.
3. Contextualize against the flat-valley / AM-GM bound where relevant.

Metric glossary

• br (bill premium) — how far the bill sits above its cost at the sweet spot, as a fraction. BR_AMBER and BR_RED are the zone boundaries. br = mf × pp.
• mf (movable fraction) — the share of cost that timing can affect. AM-GM caps it at √2−1, which is also why the reminder interval has a natural floor. Whatever sits above that share is cost no restart timing can reach.
• pp — the timing-penalty shape term (u−1)²/(2u); minimized at u=1 (the sweet spot).
• u — normalized position, accumulated causally: each API call adds the fraction of a restart interval that the conditions in force for it imply, so u only moves forward and loading more files never walks it back. Short of a whole interval = left arm (cost still falling, so the lamp stays white or green); one whole interval = sweet; beyond it = past sweet. The lamp's colour is arm-gated this way; the carry-rent reminder is not, because it reads accumulated rent instead of the position. uInst, the (x−1)/dhat ratio, is reported beside the causal u as a diagnostic that nothing acts on.
• wall — where continuing costs more per turn than a full restart.
• sweet / valley — the cost-curve minimum, reported as xSweet and read off the reference skeleton fitted across the session's own path; the valley around it is flat (small timing penalty).