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

Evidence atom

back to sources

{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_89b416683da0c721"}

id: vea_6f200e7a4a7c9737
frontier: Erdős problems frontier
source: vs_aaf421202e7e6a3c
finding: vf_62546627839c96be

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #274 remains OPEN. Statement: Does there exist a group `G` with an exact covering by more than one cosets of different sizes? (i.e. each element is contained in exactly one of the cosets.) Topics: group theory, covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_89b416683da0c721

vs_aaf421202e7e6a3c

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_89b416683da0c721"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_83ed709a010743c2

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_ff80d7a757196a45finding.asserted
Candidate claim vc_89b416683da0c721 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_42dfe3716fb7a0c0finding.note
SEMANTIC-EDGE DRAFT -> Erdos #275 (vf_eb851957b3e6491f) [related, confidence 0.55]: Both concern exact/disjoint covering systems of congruences, with 274 lifting the disjoint-covering notion to general groups. -- 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_63e562b601ecd4a2finding.note
SEMANTIC-EDGE DRAFT -> Erdos #7 (vf_6e126f3f5046840d) [generalizes, confidence 0.6]: Problem 274's exact coverings of a group generalize covering systems of congruences (the integers with subgroups nZ), of which 7's odd-moduli covering is a special instance. -- 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_8ee83e9d9a2693bdfinding.add
Candidate claim vc_89b416683da0c721 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_89b416683da0c721

1 events

Review, event, and evaluation records

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