Assessment and Passing Standard

Score each gate 0 (missing/incorrect), 1 (partly correct or materially prompted), 2 (independent, correct and verifiable), or 3 (also defends a changed case and limitations). Every gate requires at least 2; no average compensates for a missing proof or omitted solutions.

• I1: Model and boundaries. Give canonical signed division and explain gcd(0,0), inverse modulus restrictions and exponent-zero conventions.
• I2: Euclid and certificates. Independently trace a fresh signed pair, prove preservation and termination, and verify the Bezout certificate.
• I3: Primes and inverses. Justify the square-root boundary, distinguish prime/coprime and derive the inverse criterion; refute invalid cancellation.
• I4: Efficient powers. Implement repeated squaring, defend its invariant and separate arithmetic-operation count from bit cost.
• I5: Complete solutions. Derive existence and all representatives of a fresh linear congruence, including a changed unsolvable case.
• I6: Reproduction and transfer. Pass the lab checks, supply original edge tests, defend the cycle project and explain what the printed witness check cannot prove.

Fresh defense prompts: compute gcd(-105,66) with coefficients; solve 9x ≡ 6 (mod 15) and then 9x ≡ 7 (mod 15); compute 4^9 mod 19 by repeated squaring. Attempt before viewing calibration. An instructor or self-reviewer should change values if the key was already seen.

After 7–14 days, redo the weakest gate on a changed case and preserve both attempts. Use self-assessed ready; independent review pending until someone independently reviews the evidence. Describe any AI help and reproduce at least one function and proof without a generated solution. Reading, speed and number of tests do not substitute for the six gates.