[HugoXK]

Flag a Bot busy in a long turn instead of idle
The timeline team-health view (plugins/timeline/src/health.js) derived its flags from utilization.turns, which counts only turns that began inside the window, while busyMs, errors and running cover every turn that overlapped it. Two wrong readings followed, both contradicting timeline.md invariant 5 ("Idle means no running turn"):

• a Bot in one long turn that started before the window (turns: 0, busyMs = the whole window, running: true) was flagged idle, and never busy, though it was saturated and running;
• a failed turn that began before the window counted in errors but not in turns, so the rate could exceed 1 and the detail read e.g. "3 of 2 turns failed".
  busy is now the share of the window that was busy (so a long turn counts however it started), idle needs no overlapping turn and nothing running, and the failure rate divides by the larger of the in-window turns and the failed turns.
  plugins/timeline/test/health.test.js adds a case for each (a running Bot at 100% busy must be busy, not idle; an errors rate over more failures than in-window turns must not exceed 1) — both fail without the change. The existing tests are unchanged.
  Ran at the tip: npm run verify (green, TZ=UTC). Not run: smoke (this macOS box has no setsid, so dev/bench.sh cannot start dsh web), Desktop, real-model steward.

[Birfy]

Labels applied by Chief on behalf of Triage (Triage had no GitHub write channel this round). Type/area only; no risk:T* is written by hand.

[Birfy]

Verdict: PASS at 064fe63

Tip SHA: 064fe638eadbf50159a8a19a512b47d90664140e
CI at tip: 8/8 success (tests-ok, package, plugins social/tree/timeline, ubuntu-latest Node 24,
           reviewed tip, risk tier)
Tier (from the diff): T2 — plugins/** (plugins/timeline/src/health.js); the docs line is T0

Ran at this tip:

$ cd plugins/timeline && TZ=UTC node --import ./test/resolve.mjs --test test/health.test.js
# tests 5 / pass 5 / fail 0

Gate ③, source change reverted (plugins/timeline/src/health.js from base 81c708d0), tests kept:

not ok 3 - health: a long turn that began before the window is busy, not idle
not ok 4 - health: a failed turn that began before the window never reads more than the turns
# tests 5 / pass 3 / fail 2

Exactly the two new tests go red.

The change is right on the merits: utilization.turns counts only turns that began in the window while busyMs, errors and running cover every turn that overlapped it, so the old flags could call a saturated Bot idle and could print "3 of 2 turns failed". Counting the error ratio against Math.max(turns, errors) and requiring running !== true for idle restores timeline.md invariant 5 without widening any window semantics. The busy flag now also fires for a Bot whose single turn started before the window, which is the point of the fix.

Entering the merge queue now.

[Birfy]

Post-merge record: 29fa085b (squash, via the merge queue). Reviewed tip 064fe638 unchanged.