We provide a formal analytic proof for a class of non-canonical polynomial continued fractions representing π/4, originally conjectured by the Ramanujan Machine using algorithmic induction [4]. By establishing an explicit correspondence with the ratio of contiguous Gaussian hypergeometric functions 2F1(a, b; c; z), we show that these identities can be derived via a discrete sequence of equivalence transformations. We further prove that the conjectured integer coefficients constitute a symbolically minimal realization of the underlying analytic kernel. Stability analysis confirms that the resulting limit-periodic structures reside strictly within the Worpitzky convergence disk, ensuring absolute convergence. This work demonstrates that such algorithmically discovered identities are not isolated numerical artifacts, but are deeply rooted in the classical theory of hypergeometric transformations.

翻译：本文针对一类表示π/4的非规范多项式连分数给出了形式化解析证明，该猜想最初由Ramanujan Machine通过算法归纳提出[4]。通过建立与相邻高斯超几何函数₂F₁(a, b; c; z)比值的显式对应关系，我们证明这些恒等式可通过离散的等价变换序列推导得出。进一步证明，猜想中的整数系数构成了底层解析核的符号最小实现。稳定性分析证实，所得极限周期结构严格位于Worpitzky收敛圆盘内，确保了绝对收敛性。本研究表明，此类通过算法发现的恒等式并非孤立的数值现象，而是深植于经典超几何变换理论之中。