Identify runtime path that fired June 1 #11428 duplicate post-push nudges + wire dedupe gate into that path

Sub-agent execution. Doc-layer dedupe fix shipped via PR #11517 / BOLT-1129 (AGENTS.md / HEARTBEAT.md / post-push docs). However the actual runtime that fired the Slack messages at ts 1780297818.391849 (07:10 UTC June 1) and 1780336542.039489 (17:55 UTC June 1) has not been identified — so the doc fix protects future heartbeats that consult AGENTS.md but not the specific automation that produced the regression. DoD: (0) eval "$(~/bin/gh-fleet-token.sh)" on its own line + export LINEAR_API_KEY=$(cat /home/agent/agents/carson-engineer/.linear-token). (a) Identify the runtime path: grep ~/agents/carson-engineer/.agents/, ~/bin/, HEARTBEAT.md, IDLE-PROTOCOL.md, AGENTS.md and any heartbeat scripts for post-push automation hooks; look for code/templates that send Slack DMs to Carson with PR-status content; cross-reference with Slack ts pattern (07:10 + 17:55 UTC = morning + afternoon heartbeat cadence). (b) For each identified runtime path, decide whether to (i) wire the AGENTS.md dedupe-gate logic inline into the script/template (preferred if path is a small script/template), or (ii) make the path consult AGENTS.md at startup and run the gate before any auto-send (preferred if path is a larger system). (c) Ship the code/template fix as a separate PR under BOLT prefix (stacked on #11517 or independent depending on what files it touches). (d) If no runtime path can be identified — e.g., the nudges were sent by a one-off heartbeat with no persistent home — explicitly document that finding and propose either a dedicated runtime artifact for post-push automation OR codifying the universal rule that ALL contact heartbeats must consult AGENTS.md before any auto-send to Carson. (e) PATCH this task completed with result.runtime_path_identified (string or 'not_identified'), result.fix_pr_url, result.fix_strategy, result.linear_issue_id, result.summary. No Slack DM. Lineage: LEARNINGS 2026-06-02 identified the duplicate-nudge as the regression; PR #11517 / BOLT-1129 added the doc rule. LEARNINGS 2026-06-03 04:10 UTC names this follow-up as the runtime-path triangulation step.