mobius-designs

• Regenerates every number on mobius: the Mobius meter M_F(base^level) = sum of mu(n) over the digit-restricted set S_F up to base^level, measured against the set's own counting function A_F(base^level).
• The census covers every digit set F with 2 <= |F| <= base - 1 at base 3, 4, 5, the full-set control column at base 3, 4, 5, 10 (the Mertens function), and the ten base-10 Kempner columns that exclude one digit.
• Restricted families are enumerated in ascending numeric order, length by length, and mu is computed by exact factorization: trial division below 1024, deterministic Miller-Rabin on the twelve witnesses 2..37, Pollard-Brent rho on the survivors; every integer is exact, no floats touch a count.
• Control and Kempner columns come from a linear Euler sieve for mu to 3^17 = 129140163; one family (base 3, F = {1,2}, level 16) is computed by both methods and asserted equal at every level.
• The digit-scaling identities are asserted, not assumed: every census family whose digits share a factor a > 1 is recomputed as the a-twist of its primitive family and asserted equal at every level, and the count identity A_(aF')(base^level) = A_(F')(base^level) - 1 when {0,1} is inside F' (else equal) is asserted with it.
• Depths per family class: level 24 at (base,fill) = (3,2), 22 at (4,2), 14 at (4,3), 21 at (5,2), 13 at (5,3), 11 at (5,4), 8 at base 10; controls run to 3^17, 4^13, 5^11, 10^8.
• Prints one row line per family per level with exact A, M, the cut exponent theta = log|M|/log A, the running maximum Mmax = max |M_F(x)| over x <= base^level, and thetamax = log(Mmax)/log A; one slope line per family with the final theta, thetamax and the drift of thetamax over the last five levels; one distribution line per base sorted by the generator itself; one band line with the census-wide extremes of thetamax, its deviation from 1/2, the drifts, the cut exponents, and the controls.

RUN

• CARGO_BUILD_JOBS=4 cargo run --release -p mobius-designs
• About five minutes on six threads; prints only, writes nothing.
• cargo test -p mobius-designs pins mu against the sieve to 50000, the Miller-Rabin witnesses against six strong pseudoprimes, the two meter methods against each other, the scaled-family identities at depth 8, the counting closed forms, the ascending enumeration order, the running maximum against a prefix recount, and the Mertens anchors -1, 1, 2, -23, -48 at 10^1..10^5.

WITNESSES

• mobius.md the base-3 series table (M_{0,1}(3^24) = -1886, running max 3296), the final-checkpoint table of all 38 families, the Kempner table at 10^8, and every thetamax and drift; the page tables are extracted by script from this generator's printed rows.
• mobius.md the identity checks: the eight scaled families equal their primitive twists at every level, M vanishes identically on F = {0,4} at base 5, and the base-4 pair reads 34/-34 with shared Mmax = 1553 at level 22.
• mobius.md the controls: M(3^17) = -1423, M(4^13) = 329, M(5^11) = 617, and -1, 1, 2, -23, -48, 212, 1037, 1928 at 10^1..10^8, which is A084237.
• research/claims/ the digit-restricted Mobius meter and exponent rows.