E349: “Are all sub-golden geometric floor sequences complete?”

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Statement	User	Model	Harness	Time
2)V2If subset sums of a finite natural set cover [0,L], adjoining a fresh value a at most L+1 extends coverage th…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every positive t and every alpha strictly between one and the golden ratio, is the set of floors floor(t…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 If subset sums of a finite natural set cover [0,L], adjoining a fresh value a at most L+1 extends coverage through L+a.

kernel-checked, filed Tue Aug 25 2026 05:23:08 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every finite set of natural values, fresh natural a, and natural coverage endpoint L.

1) V1 For every positive t and every alpha strictly between one and the golden ratio, is the set of floors floor(t alpha^n) additively complete?

open, filed Tue Aug 25 2026 05:22:44 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The statement inlines the exact FormalConjecturesForMathlib subset-sum and eventual-completeness definitions over integers. The parameter region is nonempty at (1,3/2), and an independent explicit eventual-subset-sum transcription agrees.

Scope. All positive real t and all real alpha with 1 < alpha < (1+sqrt(5))/2.

E349:Erdős Problem #349 “Are all sub-golden geometric floor sequences complete?”

E349: “Are all sub-golden geometric floor sequences complete?”