feat(lanes): prime and nudge codex lanes into declaring their own stage

A codex lane's declared stage has always depended entirely on the session
reading AGENTS.md and calling `ccam stage` on its own — no hook, no wrapper,
no enforcement. Two additions make that more reliable without touching the
declared-wins / inferred-never-done invariants:

- LaneConsolePane pre-fills a codex pane's opening prompt with a plain-text
  stage-declaration checklist built from the lane's own pipeline_nodes —
  the same up-front priming a Claude lane gets from its pre-filled
  /ccam:ship-feature-lane skill command, just as prose since Codex has no
  slash commands.
- server/lib/codex-nudge.js sweeps every 60s and types a one-line reminder
  into a lane's live tmux pane (tmux.sendText, a new literal-text primitive
  alongside sendCommand) when its fresh detected_stage has sat undeclared
  for over two minutes. It never writes stage/detected_stage itself — any
  resulting declaration is still the codex session's own real ccam stage
  call, just server-prompted instead of relying on memory alone.

server 1354/1354, client 449/449, tsc clean.

ARCHITECTURE.md

@@ -1569,6 +1569,30 @@ at a live rollout file, so reading the JSONL avoids coupling to a schema the
 next Codex release renames. `rolloutFiles()` is the single function to re-point
 if that changes.
 
+### Codex declared-stage reliability (`server/lib/codex-nudge.js`)
+
+Detection alone only paints the amber badge; a codex lane's *declared* stage
+depends on the session calling `ccam stage` itself, so two mechanisms make
+that more likely without weakening declared-wins/inferred-never-`done`:
+
+- **Opening-prompt priming** (`LaneConsolePane.tsx`'s `promptPrefill`): a codex
+  pane's first prompt is pre-filled with a plain-text checklist of
+  `ccam stage <stage> --tool codex` calls, one per node of `Lane.pipeline_nodes`
+  — the same up-front nudge a Claude lane gets from its pre-filled
+  `/ccam:ship-feature-lane` skill command, in plain text since Codex has no
+  slash commands.
+- **Stale-detection nudge** (`sweepCodexNudges`, an unref'd 60 s interval from
+  `server/index.js`, tunable via `DASHBOARD_CODEX_NUDGE_MS`, `0` disables):
+  when a codex lane's fresh (non-stale) `detected_stage` has sat ahead of its
+  declared `stage` for at least two minutes and hasn't already been nudged for
+  that exact detected stage, it types a one-line `[ccam] ... run: ccam stage
+  ...` reminder into the lane's live tmux pane via `tmux.sendText` (skipped if
+  the pane isn't running an interactive program — `pty-run.js`'s
+  `SHELL_COMMANDS` — since Enter there would execute the reminder as a shell
+  command instead of submitting it as a chat turn). It never writes `stage` or
+  `detected_stage` — any resulting declaration is still one the codex session
+  made itself, through the real `ccam stage` call.
+
 ---
 
 ## Agent Extension Layer