Supplementary data and verification code for "The Seven Bogeys of Darts: An Arithmetic Anatomy"
收藏资源简介:
Companion archive to the paper "The Seven Bogeys of Darts: An Arithmetic Anatomy" by Frank M. V. Feys, submitted to Discrete Applied Mathematics. The archive contains: - darts_verification.py: A Python script that verifies every numerical claim in the paper (107 checks across 14 sections), including the base-case identity |B| = 12 - 5, the Rigidity Theorem for k = 2, 3, 4, the bijection between B and [49, 60] \ D, the mod-3 partition of the top window, the sideways-miss classification of the twenty doubles, the halving-depth table, the path-multiplicity distribution (max at rho(102) = 322), the trap-count identities on the seven three-dart bogeys with closure-lemma duality, and the comparative-statics ordering across five alternative finish rules. - multi_chart_analysis.py: A detailed report reproducing the multi-chart empirical concordance test (Proposition 37 and Corollary 38) across three independent published checkout charts. - multi_chart_data.json: First-dart data from three checkout charts (William Hill, Darts501, WhichDarts) for every finishable score in [100, 170], with source URLs and access dates. - wh_checkout_chart.json: William Hill's full published checkout chart, including all three dart positions of the primary route for every finishable score. - README.md: Reproduction instructions and a mapping from each verification section to the corresponding proposition number in the paper. All 107 verification checks pass. The multi-chart concordance test achieves per-chart and joint rates of 100% across 3 charts times 64 finishable scores. Requirements: Python 3.6+ (standard library only).



