[nofuturekid]

Refs #294

What changed

• nova-pr.js: after the builder returns, a light read-only agent runs gh pr list --head <branch> --state open and the script uses that number as the source of truth. A builder that omits pr_number no longer drops the task (it happened with ci: release only pull-request-green commits, changelog section required, publish draft-first #309 and feat: offer updates as a browser download instead of installing them inside the app #312). A differing builder number, several open PRs, a failed lookup or no open PR is refused with a reason. pr_number is now required in the builder schema.
• nova-pr.js: new optional task field closes (boolean, default true), validated and documented in the header and whenToUse. With closes: false the builder prompt asks for Refs #<n> and forbids closing keywords; a PR body that closes the issue anyway makes the task not ready. There was no body gate before, so a small one was added (the facts agent also returns the body).
• nova-pr.js: the title error names the task slug and the rejected character.
• nova-merge-train.js cleanup: a remote branch already deleted by GitHub is the expected outcome (handled structurally by the cleanup plan, no text matching) and no longer produces a problem or partial. The rule for a branch that still exists is unchanged (tip is the pushed head or already on origin/main).
• .claude/agents/nova-builder.md: rule 6 writes Refs #<n> instead of Closes #<n> when the task says the issue stays open.
• Both headers state that scratch output goes under ~/.cache or the scratch argument, not /tmp.

Left out

• nova-research.js, .github/, app code, .claude/settings.json, and the other open items of Follow-ups after the switch to fast-forward pushes #294.
• CLAUDE.md does not describe the changed behaviour, so it is untouched.

Checked

• node --check on wrapped copies of both scripts; prettier check.
• Mock harness (20 cases): builder without pr_number proceeds to review, number mismatch refused, no open PR refused, closes: false prompt has Refs and no closing keyword, already deleted remote branch gives done without problems, differing remote tip kept and reported.
• No Gradle, docker or local-ci (docs-only change).

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