docs: add clean PR-open proof note v4

docs/operations/phase4h-clean-pr-open-proof-v4.md

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+# Phase 4H — Clean PR-Open Proof v4
+
+## Purpose
+
+Prove that live Optio, after the Phase 4G runtime fix, transitions a real
+PR task to `pr_opened` with no stale `errorMessage` or `resultSummary`
+carried over from earlier states, while running host-Claude with
+reauthenticated credentials and no token env injection into the agent pod.
+
+## Proof criteria
+
+1. The task reaches `pr_opened` via `taskService.transitionTask()` on a
+   live Optio deployment (no manual state edits).
+2. At `pr_opened`, the task row has `errorMessage = null` and
+   `resultSummary` reflecting only the current run.
+3. The agent pod environment contains no injected auth token variables;
+   host-Claude auth comes from the reauthenticated host credential.
+4. Shell-sensitive text in the task prompt stayed inert end to end:
+   - Markdown backticks: `echo should-not-run` (never executed)
+   - Dollar var: $HOME (not expanded)
+   - Glob-like branch text: optio/task-* (not globbed)
+   - Literal newlines remained inside the prompt, never split into
+     separate shell commands.
+
+## Result expected from live Optio after the Phase 4G runtime fix
+
+The PR watcher detects the opened PR on its next poll cycle and the task
+transitions `running → pr_opened` cleanly. The task detail view shows no
+residual error banner, the state event log records the transition once,
+and the run's `resultSummary` describes this PR only. No
+`should-not-run` command appears in agent logs, confirming prompt
+quoting is safe under the Phase 4G runtime fix.