The probability conversion becomes unstable for large logits. Implement temperature scaling and normalization so supported inputs produce finite probabilities that follow the stated distribution.
Build the implementation in C++ 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 a nonempty logits list of finite numbers and a positive finite temperature. Compute softmax(logit/temperature) using maximum subtraction for numerical stability; return probabilities rounded to six decimals. Reject booleans, nonnumeric/nonfinite values and invalid temperature. Inputs are limited so dividing by temperature remains finite.
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.