Complex Multiplication as a Transcendence Predicate for Degree-2 Polynomial Continued Fractions

We propose a transcendence predicate for degree-two polynomial continued fractions (PCFs) based on the sign of the balanced discriminant Delta = beta^2 - 4 alpha gamma of the denominator polynomial b_n = alpha n^2 + beta n + gamma. Working inside the Spec(K) classification framework of Papanokechi (2026), we present a v5 upgrade of the schema that fixes two cross-paper inconsistencies and adds the Stokes exponent and connection-coefficient proxy as components 6 and 7. Our central empirical finding is a sharp dichotomy across 30 degree-two families: 24 F(2,4) Trans-stratum families have Delta in {+1,+8} and admit elementary closed forms, whereas 6 candidates with Delta in {-3,-4,-7,-11,-20,-28} all return PSLQ…