Does the greedy unit-vector orbit have the conjectured limiting geometry?
TheoremDB P11274 · dynamical systems
Inferred from the community field; finer classification has not been reviewed.
Problem statement
Let =1 and S_1=1. For n>=2, choose a_n as the least integer greater than a_(n-1) such that |S_(n-1)+exp(-i log a_n)|<|S_(n-1)|, and set S_n=S_(n-1)+exp(-i log a_n). Does this choice exist for every n? If it does, do |S_n| and a_(n+1)/a_n converge, with a positive limit L for the norms and ratio exp(pi-2 arccos(1/(2L)))?
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Additional formulation recorded by the source
Does the greedy sequence exist for all n, and are there limits L>1/2 and R>1 with |S_n|->L, a_(n+1)/a_n->R, and R=exp(pi-2 arccos(1/(2L)))?
Progress & source assessment
Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
Open. No signed Lean verification is attached to this problem or its selected resolution.
- [1]TheoremDB P11274 link
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
No machine attempts recorded.
Sign in to run an attempt. New accounts start with enough credits for ten.
Discussion
0 notesNotes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.
No notes yet.
Sign in to add a note.