A Constructive Frontier for the Social Golfer Problem

We present constructive lower bounds for the equal-group-size Social Golfer Problem for every ordered parameter pair 2≤ g,p≤50. For each pair we distinguish a literature or elementary lower bound L(g,p), a constructed number of rounds C(g,p), and a proved upper bound U(g,p). Comparison with the literature located through July 25, 2026 identifies 33 cases in which C(g,p) improves a cited published lower bound. None of these constructions attains the upper bound. A further 616 constructions exceed the available comparison value but are not presented as literature improvements because an appropriate published baseline could not be established. The region p>g is determined by the identity W(g,p)=1; the remaining 1,225 values are printed in a six-part numeric atlas. Complete schedules for all 1,225 nontrivial-region cells, separately indexed schedules for the 33 reported improvements, and the full numerical table are provided as supplementary data. The literature comparison is necessarily dated and may omit results published under different terminology or unavailable in indexed sources. The record includes the manuscript, LaTeX source, and supplementary schedules with a standalone Python validator. AI assistance in the research and manuscript drafting is disclosed in the paper. Licenses: the manuscript, LaTeX sources, schedules and original numerical tables are CC BY 4.0. The supplementary Python validator is MIT. These licenses apply to separate components; see LICENSES.txt.