frontiers / 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

used by 0 · replayed by 2 producers

e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null

Source record

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cap_61973ee16b553d57 · vc_894bfe319d3806af

id: vs_9824de0f244944b1
frontier: Erdős problems frontier
type: synthetic_report

source boundary

frontier-owned

synthetic

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

1 events

2 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

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locator

title:cap_61973ee16b553d57 · vc_894bfe319d3806af

imported

2026-05-30T00:42:06.826507+00:00

extraction mode

artifact_to_state_import

authors

Erdős Open-Problem spine ingest

caveats

source requires human review before being treated as evidence

Bound findings

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.
open_question · vf_2c6d3c9f87b43ccd

Evidence atoms

vea_6e1fc013cd2ec4c1computational · supports
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_894bfe319d3806af"}

Review, event, and evaluation records

events

vev_cb7c269ae2ffb3b4finding.asserted
Candidate claim vc_894bfe319d3806af imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_690ae23d1ab947ecfinding.note
SEMANTIC-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.add
Candidate claim vc_894bfe319d3806af imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.