A multivariate Gauss supercongruence for a Legendrian Apéry-like sequence

Let G_n = sum_{k=0}^n 4^k binom(2n-2k,n-k)^2 binom(2k,k). Z.-H. Sun conjectured that G_{mp^r} is congruent to G_{mp^{r-1}} modulo p^{2r} for every odd prime p and all positive integers m,r. This preprint proves a multivariate strengthening for simultaneously dilated coefficients of a four-factor Laurent polynomial. The proof separates divisible and primitive multinomial arrays; exponent-balance conditions force two base-p carries in the primitive sector, while the divisible sector is handled by the Jacobsthal–Kazandzidis congruence. 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.