docs(web-ui): document the first-turn ctx stats chip
The per-agent stats page gained a "first-turn ctx" summary chip (the input tokens of the most recent fresh session's first turn — a system-prompt/CLAUDE.md sprawl proxy), but agent.md's chip-row description didn't mention it. Add it next to the reminder chips, noting the stats.rs derive and the inert-until-capture behaviour (omitted from JSON until the sessions / turn_stats.session_id capture has rows).
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@ -393,7 +393,15 @@ hit-rate** (`cache_read` over all input-side tokens) and
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**tokens/turn**. When `reminder_stats` is present (fetched via
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**tokens/turn**. When `reminder_stats` is present (fetched via
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`ReminderRollup` RPC and merged into the snapshot in
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`ReminderRollup` RPC and merged into the snapshot in
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`web_ui.rs::api_stats`) three more chips appear: **reminders
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`web_ui.rs::api_stats`) three more chips appear: **reminders
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scheduled / delivered / pending** for the window.
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scheduled / delivered / pending** for the window. When the
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per-session capture has data, a **first-turn ctx** chip shows the
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input tokens of the most recent fresh claude session's first turn —
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a proxy for system-prompt + CLAUDE.md sprawl (a fresh session's first
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turn pays the full static prefix uncached). It's derived in `stats.rs`
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(`first_turn_ctx`: the first turn, `ORDER BY started_at LIMIT 1`, of
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the latest `sessions` row in the window) and is omitted from the JSON
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until the `sessions` / `turn_stats.session_id` capture has rows — so
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the chip stays hidden on older dbs (inert-until-capture).
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`stats.rs` opens the sqlite db read-only and degrades to an
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`stats.rs` opens the sqlite db read-only and degrades to an
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empty snapshot on any error — the page is decorative, never
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empty snapshot on any error — the page is decorative, never
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authoritative.
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authoritative.
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