MrlyProd
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The wiki, the notes, the claims and the papers.
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A design is a rule on the corners of a cube.
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The Rust crates do the arithmetic, the browser only paints.
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Newest claim
Proved For every base b >= 3 the integers with no two equal adjacent base-b digits are the accepted words of a (b+1)-state automaton read from the units digit whose state is the last digit read; they hold exactly (b-1)^L integers of L digits, form no digit design since 1 and b lie in the set and b + 1 does not, have no digit allowed in every state and no reset word, and their automaton completed with a sink synchronizes on the word 00. Witness: notes/adjacent.md, section The automaton.
Latest papers
A Power Saving for the Digit Sum on Missing Digits
On the integers whose base-b digits avoid a fixed set, keeping two consecutive digits and the one-step certificate (W), the Mobius and von Mangoldt functions modulated by the digit sum, e(alpha s_b(n)), save a power of x against the count of the set whenever (b - 1) alpha is not an integer, with an explicit exponent, an effective constant and no L-function; (W) holds at every one-missing-digit set from base 92317, and the primes of the set then equidistribute by digit sum modulo every q coprime to b - 1. The power is tiny, delta_0 >= 4.678 * 10^-9 at 92317 for every alpha with norm((b - 1) alpha) >= 0.2: the point is the mechanism.
2026-10-05
The Exact Fragility of Fractal Sparse Arrays
From order 2 on, a sensor of a fractal sparse array is essential exactly when every base-M digit of its position has a partner in the generator at a lag that no other pair makes, so the fragility is exactly (u/L)^r; from order 2 on, the bound of Cohen and Eldar is attained exactly when every sensor of the generator has such a partner, which is the strong converse of their Theorem 5, and the power bound of Yang and coauthors exactly when every essential sensor does.
2026-10-05
Spectral Measures from Tiling Levels
For an integer base and a digit set whose every level tiles the integers, the self-similar measure is spectral when the number of digits is a prime power or a product of two primes; at base 12 the digits {0, 1, 8, 9} give such a measure with an explicit spectrum though they are no multiple of a complementing set; and at five digits containing 0, with levels that are sets, the measure is spectral if and only if every level tiles, so {0, 1, 3, 5, 6} gives a spectral measure at no integer base.
2026-10-05
What is MrlyMath
A design is a rule on the corners of a cube: a code says which of the eight corners are filled. The Kronecker product grows that rule into itself, level by level, and the object it converges to is a fractal - the Sierpinski carpet and the Menger sponge are two of them.
Everything else is measurement. Count the fills, the voids and the exposed faces; cut the solid with a plane; join the filled cells into a graph and read its spectrum; collect the integer sequences the counts write down. The Rust crates do the arithmetic, the browser only paints, and a claim is either proved, checked over a stated finite domain, or labelled a conjecture.