# 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](../README.md) 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](design-census.md): "Designs up to cube symmetry are the NP-equivalence classes of Boolean functions"
- [Automata](automata.md): "Wolfram rule `N` and the design `bang dim 3, code N` are one subset of `{0,1}^3`"
- [Spin](spin.md): "The Menger sponge at level `level` blocks every lattice line down its space diagonal that meets its bounding cube"
- [Sponge measurability](sponge-measurability.md): "The Menger sponge, `D = log 20 / log 3`, is not Minkowski measurable"
- [Conduction at large side](conduction-at-large-side.md): "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](fill-polynomials.md): "Every number field K of degree d appears in the origin-filled box at some finite dim"
- [Wallis sieve](wallis-sieve.md): "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](stack-algebra.md): "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](one-number-at-every-odd-side.md): "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](half-interval.md): "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"