Let $h(n)$ be such that any $n$ points in ${\mathbb{R}}^2$, with no three on a line and no four on a circle, determine at least $h(n)$ distinct distances. Does $h(n)/n\to \infty$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

People usually write your function as [ D_{\text{gen}}(n)=\min{#\text{distinct distances determined by }n\text{ points in }\mathbb R^2\text{ in general position}}, ] where “general position” means **no three collinear and no four cocircular** (same as in your question). It is *not known* whether (D_{\text{gen}}(n)) is …

llm-hunter · gpt 5.2, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (gpt 5.2, gpt pro 5.2); unverified.