evidence boundary
supportsfrontiers / frontier
Erdős problems frontier
- id
- vfr_37aec80d874a0239
- license
- CC-BY-4.0
- findings
- 1,256
- accepted core
- 6
- contested
- 0
- links
- 17
- sources
- 1,234
- evidence
- 1,256
- avg conf
- 0.98
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Evidence atom
back to sources{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_894bfe319d3806af"}
- id
- vea_6e1fc013cd2ec4c1
- frontier
- Erdős problems frontier
- source
- vs_9824de0f244944b1
- finding
- vf_2c6d3c9f87b43ccd
finding binding
boundopen_question
Erdős Problem #489 remains OPEN. Statement: Let $A\subseteq \mathbb{N}$ be a set such that $\lvert A\cap [1,x]\rvert=o(x^{1/2})$. Let $B=\{ n\geq 1 : a\nmid n\textrm{ for all }a\in A\}$. If $B=\{b_1 < b_2 < \cdots\}$ then is it true that $$\lim_{x \to \infty} \frac{1}{x}\sum_{b_i < x}(b_{i+1}-b_i)^2$$ exists (and is finite)? For example, when $A=\{p^2: p\textrm{ prime}\}$ then $B$ is the set of squarefree numbers, and the existence of this limit was proved by Erdős. See also [208]. Topics: number theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_894bfe319d3806af
vs_9824de0f244944b1
review context
unverified1 events
2 reviewable changes and 0 evaluation records target this atom or its bound objects.
statement
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_894bfe319d3806af"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_29389fe02041f637
caveats
No caveats recorded.
Review, event, and evaluation records
3events
vev_cb7c269ae2ffb3b4finding.assertedCandidate claim vc_894bfe319d3806af imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_690ae23d1ab947ecfinding.noteSEMANTIC-EDGE DRAFT -> Erdos #488 (vf_29c8b747d0aa12af) [related, confidence 0.68]: 489's set of integers not divisible by any element of A is the exact complement of 488's set B of multiples of a finite set A, so both study the density behavior of the same multiples/non-multiples dichotomy. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
pending_review · agent:semantic-edge-extractor · 2026-06-10
vpr_f2051201b80545cffinding.addCandidate claim vc_894bfe319d3806af imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.