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

e1288/1288 · statement.registered · agent:claude-proxy · 2026-06-10 · null→null

Evidence atom

back to sources

{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_207ca3dcc13de126"}

id: vea_c66e10132f67164f
frontier: Erdős problems frontier
source: vs_2c3437c98e238aa9
finding: vf_a357c9d8ac3d6b26

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #44 remains OPEN. Statement: **Erdős Problem 44:** Let N ≥ 1 and `A ⊆ {1,…,N}` be a Sidon set. Is it true that, for any ε > 0, there exist M = M(ε) and `B ⊆ {N+1,…,M}` such that `A ∪ B ⊆ {1,…,M}` is a Sidon set of size at least `(1−ε)M^{1/2}`? This problem asks whether any Sidon set can be extended to achieve a density arbitrarily close to the optimal density for Sidon sets. Topics: number theory, sidon sets, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_207ca3dcc13de126

vs_2c3437c98e238aa9

review context

unverified

1 events

3 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_207ca3dcc13de126"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_05e0784a3791e0c9

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_4d27429cd049bd2bfinding.asserted
Candidate claim vc_207ca3dcc13de126 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_49aaf57d6dd0a317finding.add
Candidate claim vc_207ca3dcc13de126 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_a336726922e97c6ffinding.note
SEMANTIC-EDGE DRAFT -> Erdos #30 (vf_04c2ff267458866e) [specializes, confidence 0.85]: Problem 44 asserts the explicit upper bound (max Sidon set in {1,...,N} is at most 2√N), which is a specific quantitative bound on exactly the function h(N) that Problem 30 studies. -- 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_ec6741d1fdc57665finding.note
SEMANTIC-EDGE DRAFT -> Erdos #155 (vf_55921775986ed4e2) [related, confidence 0.8]: Both concern the maximum size of a Sidon subset of {1,...,N} (44 states the ≤2√N bound, 155 names this maximum F(N)), so 44 is a bound on 155's quantity. -- 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

evaluations

No evaluation rows are attached.

computational

open_question

cap_61973ee16b553d57 · vc_207ca3dcc13de126

1 events

Review, event, and evaluation records

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