Exterior-square continued fractions of hypergeometric Calabi-Yau operators: a closed formula for every CY-symmetric parameter set

Theorem. For every real parameter set a = (a1, a2, 1-a2, 1-a1) with 0 < a_i < 1, the exterior square L5 = theta^5 - T m1(theta) + T^2 m2(theta) of the hypergeometric Calabi-Yau operator theta^4 - T prod(theta + a_i) gives a polynomial continued fraction a(n) = kappa m1(n), b(n) = -kappa^2 n^5 m2(n-1) whose convergents decrease strictly to K = 2 kappa / (T2 - rho T1). Here T1 and T2 are explicit Hurwitz-zeta values (sums of derivatives of f(x) = (2x+1)/prod(x + a_i)) and rho = (st_2 - g2 st_0)/st_1 is a ratio of conifold values of the Frobenius solutions, with g2 = (pi^2/2)(2/3 - csc^2(pi a1) - csc^2(pi a2)). The case (1/2,1/2,1/2,1/2) is row 5 of Table 1 in Elimelech et al. (PNAS 2024), proved earlier in 10.5281/zenodo.23709285. The proof builds the vanishing cycle at the conifold as a Meijer G-function, identifies the solutions analytic there through a constant alternating form of the self-adjoint operator, evaluates the Wronskian moments by Parseval as Hurwitz-type sums, and uses a telescoping identity and an order-2 zero to obtain the minimal solution of the recurrence. Every finite identity is checked by exact computer algebra with the parameters as symbols (85 negative controls), the proof was reviewed by three separate adversarial AI sessions, and no human has checked it yet. Version 2 adds a second theorem: for the levels N = 8, 9, 16 and 36 the conifold ratio rho is expressed through L-values of the conifold newform, which proves the closed forms 1/K = (93/4) zeta(5) - (pi^4/8) L(f8,2)/L(f8,1), K = 15/(45 zeta(3) - sqrt3 pi^3), 1/K = (21/2) zeta(3) - pi^2 L(f16,2)/L(f16,1) and 1/K = 6 zeta(3) - pi^2 L(f36,2)/L(f36,1). The proof writes the conifold values as Mellin transforms of explicit eta-theta products through Ramanujan's theories of signature 2, 3 and 4; for N = 8 it gives a proof of the PNAS row 5 identity that does not use the Rogers-Wan-Zucker evaluations. It was reviewed by two adversarial AI sessions. For the 14 arithmetic members (conifold newforms of weight 4 and levels 8 to 864) the archive gives the continued fractions, their limits to 1080 digits and closed forms of the limits in zeta values, Dirichlet L-values and L-values of the conifold newforms and their twists, for example K = 15/(45 zeta(3) - sqrt3 pi^3) for (1/4,1/3,2/3,3/4). Apart from the four proved levels, these closed forms are numerical identities checked to at least 656 digits. We found no earlier statement of these continued fractions, their limits or the formula (search of 2026-10-28, listed in the README). Searches and verification were carried out with Claude (Anthropic) under the direction of Kerem Özdemir. The proofs were also written with Claude.