Boolean Measures

• Computes seven Boolean complexity measures, s, bs, C, dt, deg, dnf, cnf, on every hyperoctahedral class of designs at dim 3 (22 classes) and dim 4 (402 classes), from the truth-table definitions.
• Diffs the result cell by cell against measures_d3.csv and measures_d4.csv, which travel as data; fits the fill polynomial from rendered odd-side grids and compares it with the closed form.
• Groups the catalog by genus, GF(2) degree, popcount and fill polynomial, and reports which keys determine which measures, with the smallest witness pair at dim 4.
• Checks the pin family, the inequality web, total influence in exact rationals at dim 1..4, and the (s, bs, C) profile of every design at dim 4 plus seeded samples at dim 5.

RUN

• uv run python research/lab/py/boolean-measures/measures.py
• Domain: every design at dim 1..4; at dim 5 a seeded sample of 50000 uniform designs, plus 20000 uniform and 20000 thinned designs; about three seconds.

WITNESSES

• complexity.md:61 286 cells at dim 3 and 5226 at dim 4, zero mismatches.
• complexity.md:66-87 the dim 3 table of 22 classes, printed row by row.
• complexity.md:90-91 genus iso 10, axis 2, comp 10; GF(2) degree histogram -1: 1, 0: 1, 1: 3, 2: 9, 3: 8.
• complexity.md:94-96 the three classes bang dim 3, code 7, bang dim 3, code 31, bang dim 3, code 23 with bs = 2, dt = 3.
• complexity.md:104-118 the pin family, six measures equal r, dnf = 1, cnf = r, at dim 3 and dim 4.
• complexity.md:141-150 fill polynomial 21 of 22 at dim 3, one collision 4k^3 - 4k^2 + k at odd side 2k - 1; at dim 4 183 of 402, 94 shared, 92 groups, 81 split, 279 measure-splits.
• complexity.md:154-164 the witness rows bang dim 4, code 27 and bang dim 4, code 281, six of seven measures split, their ANFs, one of 14 size-two groups splitting bs.
• complexity.md:194-209 C = bs on all 424 classes and on 50000 samples at dim 5; bang dim 4, code 7128 the sole s != bs class, orbit 24; 216 samples at s = 3, bs = 4; deg = s^2 at bang dim 4, code 855 and bang dim 4, code 1911.
• complexity.md:248 P[s(f) = dim] is 1/2, 5/8, 69/128, 18253/32768.
• complexity.md:269-278 no design with one bichromatic edge at dim 3, realised counts 0, 3, 4, 5, 6, 7, 8, 9, 12; influence mean 1/2, 1, 3/2, 2, variance 1/4, 1/4, 3/16, 1/8.
• README.md:50 the dim 4 witness bullet.