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_9a744c7bc1866dd5"}

id: vea_5f9b9b02f1500b54
frontier: Erdős problems frontier
source: vs_6d1990743b238628
finding: vf_6f307ef73915ae96

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #3 remains OPEN. Statement: If $A \subset \mathbb{N} has $\sum_{n \in A}\frac 1 n = \infty$, then must $A$ contain arbitrarily long arithmetic progressions? Topics: number theory, additive combinatorics, arithmetic progressions. Erdős prize: $5000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003002, A003003, A003004, A003005.

source binding

source-bound

cap_61973ee16b553d57 · vc_9a744c7bc1866dd5

vs_6d1990743b238628

review context

unverified

1 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_9a744c7bc1866dd5"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_a7c45792fad7c993

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_9271a70d4a2f21e0finding.asserted
Candidate claim vc_9a744c7bc1866dd5 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_455114364d12c5b5finding.note
SEMANTIC-EDGE DRAFT -> Erdos #219 (vf_0cf052d918abf92d) [depends_on, confidence 0.6]: P3 (does divergent reciprocal sum force arbitrarily long APs) applied to the primes yields long prime APs (P219), the famous special case resolved by Green-Tao. -- 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_ff085c96f9ced1b1finding.add
Candidate claim vc_9a744c7bc1866dd5 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.

computational

open_question

cap_61973ee16b553d57 · vc_9a744c7bc1866dd5

1 events

Review, event, and evaluation records

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