Systematic Survey of G₂ Betti Numbers from Joyce–Karigiannis Constructions on Kreuzer–Skarke Polytopes

Key Points

• To conduct a systematic computational survey of G₂ Betti numbers from specific constructions.
• Utilized the complete Kreuzer–Skarke database for 998 toric Calabi–Yau threefolds.
• Compiled 27,000 entries of G₂ Betti numbers into CSV tables.
• Generated combined JSON metadata for the dataset.
• Analyzed the unique (b₂, b₃) = (27, 451) construction.
• Included Python source code to ensure reproducibility of the findings.
• Acquired G₂ Betti numbers for multiple toric Calabi–Yau threefolds.
• Provided complete CSV data tables with extensive entries.
• Delivered specific metadata detailing the sign distributions.
• Enabled reproducibility through shared Python source code.