The conversion service must retain exact rational values across compatible units. Implement conversion so incompatible dimensions are rejected and valid results are returned in the defined reduced form.
Build the implementation in Rust 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 units mapping names to dimension string and positive rational scale [numerator,denominator] relative to that dimension base; from, to unit names; and value as rational [integer numerator, nonzero integer denominator]. Return the reduced [numerator,positive denominator] after value*from_scale/to_scale. Units are purely multiplicative, without offsets. Validate all unit scales, including unused units. Reject unknown or incompatible units, booleans/nonintegers and invalid fractions.
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.