We report a new computational lower bound improving the best published result due to Wróblewski (1984): f(3) ≥ 3.0084928720. The construction is Wróblewski's recursive pairing of Behrend sphere blocks, implemented as a Python script that embeds, compiles, and calls a C kernel at runtime; the C kernel uses unsigned __int128 arithmetic and OpenMP parallelism for node enumeration, while Python arbitrary-precision integers handle all shift computation. The 3-AP-free property is guaranteed by Wróblewski's pairing theorem and requires no computational verification. A conservative floating-point error analysis, explicitly separating denominator rounding and summation error, confirms that the computed value exceeds Wróblewski's bound by a factor exceeding 10¹⁵ relative to a conservative total IEEE 754 error bound. Two independent implementations (single-threaded and 12-core OpenMP) produce matching node counts and matching harmonic sums to the reported precision. Full source code, checkpoint data, checksums, and citation metadata are provided as supplementary material in the Zenodo deposit.