Three truncated supercongruences for an Apéry-like sequence

For G_n = sum_{k=0}^n 4^k binom(2n-2k,n-k)^2 binom(2k,k), this preprint proves all six cases of a conjecture of Z.-H. Sun concerning three truncated sums with denominators (-16)^n, 8^n, and 32^n modulo p^2. An exact finite-tail transformation reduces the problem to classical truncated Legendre periods and one divided-difference correction polynomial. Split primes are handled by a diagonal Padé gap for log(1+z), and inert primes by reflection and a root–Wronskian identity, together with known CM evaluations. The archive includes the manuscript, exact verification programs, SHA-256 manifests, an OpenPGP signature, and a DigiCert RFC 3161 timestamp response. The proof presented in this article was found by OpenAI Codex.