Expected finite k-adic complexity in general integer bases

Lineage and corrections

This event attributed to Oleksiy Babanskyy

Expected finite k-adic complexity in general integer bases evidence for this event

VibeMathed record: Expected finite k-adic complexity in general integer bases evidence for this event

Fixed manuscript, certificates and reproduction instructions evidence for this event

Lin-Xiao-Chen, Question 3.2, printed page 20282 evidence for this event

Expected finite k-adic complexity in general integer bases parent of this event

The manuscript claims $E_N^{k\text{-adic}}<N/2+0.241933621228105$ for every integer $k\ge2$ and $N\ge1$. It gives $E_N^{k\text{-adic}}\le N/2$ for prime-power bases and a strict inequality below $N/2$ for bases with exactly two distinct prime factors. The example $k=30,N=2$ disproves a universal zero-correction bound. Section 1 identifies the standard rational observable with the source question. Written arguments combine classical imports, finite certificates and infinite-tail estimates. The optimal additive constant and finite-length attainment remain open. Constrained FCSR connection integers and rounded register lengths are not identified with this observable. The earlier binary theorem is credited and imported. parent of this event

This event attributed to OpenAI GPT models (versions unspecified)