mrlybang-density-classes

• A mrlybang code is a set P of parity corners in {0,1}^3; at base base it fills the design F_base(P) = { v in {0..base-1}^3 : v mod 2 in P }.
• Computes the exact rational part delta * zeta(3) of the coprime density of every one of the 255 nonempty codes at every base, as a Mobius bracket times Euler factors.
• Checks the even-base band (8/7)(1 - t/|P|) at even base <= 40 and the same band in dim 2, and the odd-base self-similarity fill_e(base) = fill_P(base/e) at odd base <= 75, both domains the widest the pages claim.
• Sorts every code by its mod-2 difference span H, groups the codes by weight enumerator, takes the design lattice rank and index at base 2, 3, 4, 6, 8, 10, and finds the codes whose even value equals their odd limit.
• Measures the visible fraction by exact enumeration of all fill^level points at that level, against the limit and against the exact finite-level walk factor 1 - (1/8) Sum_t lambda_t^level; every enumerated case is the level the page measured.

RUN

uv run python research/lab/py/mrlybang-density-classes/classes.py

Whole run is under half a minute.

WITNESSES

• coprime.md:227 coprime.md:230 - lattice index in {1, 2, 4, 8} at even base 4, 6, 8, 10; 151 codes full rank at base 2, index 1 or 2, the smallest of size 4.
• coprime.md:228 coprime.md:229 - nine band values 0, 4/7, 16/21, 6/7, 32/35, 20/21, 48/49, 1, 8/7, zero exceptions to (8/7)(1 - t/|P|); carpet 0.712853 and 0.709137, net 0.951771, against 0.713063 and 0.950751.
• coprime.md:231 - the dim 2 parity carpet at every even base, delta * zeta(2) = 8/9, delta = 0.5403796460924681 = 16/(3 pi^2).
• coprime.md:233 coprime.md:234 - zero exceptions to fill_e(base) = fill_P(base/e); 63 weight classes, 6 of them mixing regimes, 4 spanning against not and 2 corrected against no-limit.
• coprime.md:235 - twins 0.707501 and 0.711167 at base 4, splitting at base 3 into 0.698204 against 153/182 and 0.783436 against 51/52.
• coprime.md:237 - 7 codes of lattice rank <= 1 at base 3, 37 codes with a coordinate pinned odd, {110,100} measuring 0.972222 0.994084 0.999979 against the trichotomy's 0.987319.
• coprime.md:238 coprime.md:239 coprime.md:241 coprime.md:245 - class counts 149, 43, 63; the subgroup codes 1 3 5 9 15 17 33 51 65 85 105 129 153 165 195 255, exactly the parity-stable ones; 239 codes with two values, where the page says 240 and counts the empty code.
• coprime.md:240 - void base 3, level 8 measures 0.381949 against limit 0.438808 and finite level 0.380043; tree 0.451821 against 0.452521, tree base 5 0.468340 against 0.468560.
• coprime.md:242 - {111} at base 5 is exactly 0 at every even level and 0.925781 0.952881 0.957167 against 0.958419; axes 0.987338 / 0.739563 against 0.987319 / 0.740489.
• coprime.md:250 to coprime.md:259 - the family table 513/520 27/26 99/182 48/91 at base 3 up to 200981/201096 1331/1330 9559/16758 16456/28861 at base 11; carpet 0.98654 0.99562 0.99810 0.98959 0.99943 with fill_P(base) = 20, 81, 208, 425, 756; net B(9) = 297/304 = 1 - 7/304 and no odd base <= 81 below 1, the page's 20/425 and 1/208 being the carpet's fill, not the net's.
• the claims line (was DISCOVERIES.md:33) the claims line (was DISCOVERIES.md:34) - the band, the lattice indices, the dim 2 constant, the enumerations 0.712853, 0.951771, 0.709137; the trichotomy counts at odd base <= 75, the axes pair, the {111} zeros.