Claims

A claims file is the dated record of one topic: one line per claim, each with its date, one tag and its witness, the code that computes it or the note section that proves it. Lines are only appended: a correction or a counterexample is a new dated line, never an edit.

Every claim carries one tag, Proved, Verified, Conjecture or Refuted, and the law defines the four.

After the top ten, every claims file is listed with its count of each tag and the date of its newest line.

TOP 10

• Design census: "Designs up to cube symmetry are the NP-equivalence classes of Boolean functions"
• Automata: "Wolfram rule N and the design bang dim 3, code N are one subset of {0,1}^3"
• Spin: "The Menger sponge at level level blocks every lattice line down its space diagonal that meets its bounding cube"
• Sponge measurability: "The Menger sponge, D = log 20 / log 3, is not Minkowski measurable"
• Conduction at large side: "In the continuum, for bang dim 2, code 7 at every odd side and level, the conductance with insulated voids times the conductance with floating perfectly conducting voids is exactly 1"
• Fill polynomials: "Every number field K of degree d appears in the origin-filled box at some finite dim"
• Wallis sieve: "The solid Wallis sieve, which drops the centre cube of every surviving cube cut into (2k+1)^3 at level k, keeps the limit volume prod_{n odd >= 3} (1 - n^(-3)) = pi^(3/2) / (8 |Gamma(7/4 - i sqrt(3)/4)|^2) = 0.948815486"
• The stack algebra: "Stacking is Dirichlet convolution: the u-stack of the v-stack draws the inner scale n at scale kn with weight u(k) v(n), so the composite weight is u * v"
• One number at every odd side: "At an odd prime q, 1 <= p <= q - 1 and a the odd one of p, q - p, the Legendre symbol (a/q) is -1 to the number of odd sides 3 <= N < q at which the first base-N digit of p/q is odd"
• Half interval: "At every prime p >= 94939 the sum of mu(k) over k <= x with p not dividing C(2k,k) is at most C A(x) exp(-c sqrt(log x)) in absolute value"