erdős #188
What is the smallest such that can be red/blue coloured with no pair of red points unit distance apart, and no -term arithmetic progression of blue points with distance ?
Open problem — our best result is machine-sealed: improved bound, reproduced by an independent verifier. The conjecture itself is unsettled.
geometry · open · formalized (Lean) · 2 attempts
use this record
vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
honest null
needs verification
attempted via frontier '?' (transfer_strength=n/a) -> no_progress
No solve/partial on this pass. Transfer into the owned frontier was 'n/a'. Do not re-attack cold; needs a new idea or richer accumulated context.
improved bound
needs verification
erdos_188 (Euclidean Ramsey): verified M=min(s)>=6, tightening the recorded range from [5,10^7] to [6,10^7]. Small concrete bound improvement, airtight, formalizable; not novel-theorem-level.
Independently checked chain lifting the lower bound 5->6. Recorded in the Lean file as [5,10^7].
Opus adversarial synthesis, independent CP check.
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
Interpret the “$k$-term arithmetic progression with distance $1$” as a *unit-step collinear progression* [ x,x+u,x+2u,\dots,x+(k-1)u \quad\text{with }|u|=1, ] often denoted (\ell_k) in Euclidean Ramsey theory.
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
status
open