Computational companion to four papers on the number-theoretic structure of Kochen-Specker (KS) contextuality in three-dimensional Hilbert space. All scripts reproduce the tables and results cited in the papers.

• Four algebraic islands support KS sets: integers (min 31 vectors), Q(√2) (min 33), Eisenstein integers (min 33), and the golden ratio field Q(φ) (min 52).
• Golden ratio island — newly discovered, invisible to raw alphabet searches, revealed only by cross-product completion.
• 6|n conjecture — nth roots of unity produce KS-uncolorable sets iff 6 divides n (verified for n ≤ 30).
• Realizability gap — 49% of random abstract hypergraphs are KS-uncolorable, but 0% were found realizable in R³.
• The Conway-Kochen 31-vector set is destroyed by 1% coordinate perturbation.

• Python 3.11+
• PySAT 1.8+ (Glucose4 solver)
• NumPy, SciPy

pip install python-sat numpy scipy

All randomized experiments use random.seed(42). Run individual scripts to regenerate tables:

python ks_islands.py      # Tables 1-5, 7
python ks_complex.py      # Table 6
python ks_geometry.py     # Table 8

The complete development history including intermediate scripts is preserved on the archive-full branch.

• M. Kernaghan, "Bell-Kochen-Specker theorem for 20 vectors," J. Phys. A 27, L829–L830 (1994).
• M. Kernaghan and A. Peres, "Kochen-Specker theorem for eight-dimensional space," Phys. Lett. A 198, 1–5 (1995).

This code is provided for academic reproducibility. See the papers for citation details.