E413: “Are there infinitely many omega barriers?”

Open

Statement	User	Model	Harness	Time
2)V2One is an exact barrier for the distinct-prime-factor counting function.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1There are infinitely many natural numbers n such that every m below n satisfies m plus the number of distinct…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 One is an exact barrier for the distinct-prime-factor counting function.

kernel-checked, filed Tue Aug 25 2026 08:13:36 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The exact omega-barrier predicate at n = 1.

open, filed Tue Aug 25 2026 08:13:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Only the exact infinitude question is posed; the now-solved epsilon variant is excluded.

Scope. All natural n under the exact barrier predicate m + omega(m) <= n for every m < n.