BSD Certificate Ladder: C0 to C10

Core principle: each curve must not just store a boolean "BSD true/false," but must store "which layer has been closed by what certificate." From C0 (Identity, minimal Weierstrass model, conductor, CM status), C1 (local arithmetic, bad primes, reduction type, Tamagawa numbers), C2 (numerical analytic rank, evidence only, not necessarily having a rigorous zero-order certificate), C3 (rigorous analytic rank), C4/C5 (algebraic rank lower/upper bounds, given by descent/Selmer yielding r_alg=r), C6 (weak BSD certificate, r_alg=r_an), C7 (single-prime strong BSD, p-part for a specified p), C8 (Sha is finite and exact, cannot use BSD back-calculated values as proof), C9 (full strong BSD, all components closed, including convention, Manin constant, all prime parts, no unproved assumptions), to C10 (family theorem, establishing a uniform theorem for an infinite family). It also lists a certificate status dictionary — unknown, numerical, conditional, theorem_applicable, proved_component, proved_curve, proved_family, refuted_data — and five absolute prohibitions: writing analytic_sha as proved_sha; treating rank() returning an integer as a full proof; tagging full strong BSD just because a certain p-part holds; applying rank 0/1 theorems to rank 2; and treating LMFDB data completeness as BSD completeness.