The monitoring history contains overlapping heartbeat coverage. Produce the uncovered intervals so duplicated coverage does not hide an outage or create extra uptime.
Build the implementation in Go under /app, with /app/run.sh as its entry point. Read one JSON request from standard input and write one JSON result to standard output. Input has integer start < end, positive integer ttl, and integer heartbeat times in any order. Each heartbeat covers [time,time+ttl). Clip coverage to [start,end), merge overlapping/touching coverage, and return outage intervals in order plus total downtime. Duplicate heartbeats have no effect. Reject invalid window or ttl.
Reject inputs that violate an explicit validation rule with exit status 2, no standard output, and {"error":"invalid_input"} on standard error. For valid input, exit with status 0. Keep the implementation reusable for new inputs; it must work offline and must not depend on the example data being the only data it receives.
Repair or replace the unfinished /app/run.sh and add source files under /app. Malformed JSON must use the same invalid-input response. Do not read /tests or /oracle from the application.