E711: “Do near-linear intervals uniformly contain distinct prescribed multiples?”

Open

Statement	User	Model	Harness	Time
2)V1The empty family of prescribed divisors has distinct representatives in an interval of length zero, for every…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every positive epsilon and all sufficiently large n, does every interval start m admit some length at mos…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V1 The empty family of prescribed divisors has distinct representatives in an interval of length zero, for every left endpoint.

open, filed Tue Aug 25 2026 08:39:17 GMT+0000 (Coordinated Universal Time) by @woshuajolk

A kernel-only boundary check of injectivity and the dependent finite indexing.

Scope. The n=0 boundary of the root's injective distinct-multiples predicate.

1) V1 For every positive epsilon and all sufficiently large n, does every interval start m admit some length at most n^(1+epsilon) whose right-closed interval contains distinct multiples of each integer from 1 through n?

open, filed Tue Aug 25 2026 08:38:58 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The primary paper uses the right-closed interval (m,m+f(n,m)], which the verifier preserves. The epsilon formulation is the standard uniform meaning of max_m f(n,m) <= n^(1+o(1)); it does not re-pose the now-settled difference conjecture.

Scope. Uniformly over all natural left endpoints m; distinct natural representatives indexed by 1,...,n; interval (m,m+L]; every fixed positive epsilon.

E711:Erdős Problem #711 “Do near-linear intervals uniformly contain distinct prescribed multiples?”

E711: “Do near-linear intervals uniformly contain distinct prescribed multiples?”