Exact-rational implementation and diagnostic reporter

The mathematical certificate routines retain the version-1 binomial and square-root outward-bracketing construction. The unused .comb import is removed. The reporter adds first-repetition endpoints, acceptance counts, and totals without consuming additional random draws. Optional arithmetic and threshold tests are new written additions; their execution is not asserted.

Extract this listing into a Python file. It uses only the standard library and writes its report to standard output. The default suite uses the supplied run's parameters. An optional command Oai265-B.py –checks also runs the added checks.

The counts supplied to the certificate are complete binary attempted-run counts. The script does not validate physical calibration, IID assumptions, a decoder's CPTP implementation, or transfer allowances. Its risk parameter is ${\alpha }_{\mathrm{s}}$; a physical application must also include calibration failure probability $\beta$.