Rational Approximation of Real Constants via Local Mediant Search

This dataset presents the complete hunting table, traceable iteration histories (CSV), and audited source code of the Mediant Hydra v6.0 — a hierarchical greedy algorithm for rational approximation of real numbers. The Hydra combines stochastic three-headed gradient descent, local Stern–Brocot mediant surgery, parametric necromancy of past approximations, and signature-based convergent injection. Eleven constants were hunted: π, e, √2, ln 2, ζ(3), γ, G (Catalan), K₀ (Khinchin), B₂ (Brun), λ (Liouville), and MRB. All fractions are irreducible, all errors independently recalculated, all traces sealed with SHA-3-512.本数据集收录了介数九头蛇（Mediant Hydra）v6.0的完整寻优表、可溯源迭代历史（CSV格式）与经审计的源代码。该算法是一类面向实数有理逼近的分层贪心算法，融合了随机三头梯度下降、局部斯特恩-布罗科介数操作、过往逼近结果的参数化回溯，以及基于签名的收敛注入机制。本次共寻获11个目标常数：圆周率π、自然对数底e、√2、自然对数ln2、黎曼ζ函数值ζ(3)、欧拉-马歇罗尼常数γ、卡特兰常数G（Catalan）、辛钦常数K₀（Khinchin）、布伦常数B₂（Brun）、刘维尔常数λ（Liouville）以及MRB常数。所有生成的分数均为不可约形式，所有误差值均经独立重新计算，所有迭代轨迹均通过SHA-3-512算法完成签名封存。