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

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{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_f4e6bf184f057992"}

id: vea_dd8e928367596faa
frontier: Erdős problems frontier
source: vs_273245b1d02f8bc5
finding: vf_15dc5ce433b11d94

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #593 remains OPEN. Statement: **Erdős Problem 593 ($500)**: Characterize those finite 3-uniform hypergraphs which appear in every 3-uniform hypergraph of chromatic number $> \aleph_0$. A natural conjectural characterization, recorded here, is that the obligatory finite 3-uniform hypergraphs are exactly the 2-colorable ones (Property B). The forward direction (`IsObligatory → IsTwoColorable`) and converse (`IsTwoColorable → IsObligatory`) are stated as separate variants below; in the graph case ($r = 2$), Erdős–Galvin–Hajnal [EGH75] proved the analogous result (obligatory ⇔ bipartite). Topics: set theory, graph theory, hypergraphs, chromatic number. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_f4e6bf184f057992

vs_273245b1d02f8bc5

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_f4e6bf184f057992"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_8535951d0ec05d59

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_7ec7ca90644b9c13finding.asserted
Candidate claim vc_f4e6bf184f057992 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_618e5e5984daf65efinding.note
SEMANTIC-EDGE DRAFT -> Erdos #564 (vf_8fdce4bf9419e970) [related, confidence 0.5]: Both concern finite 3-uniform hypergraphs as unavoidable substructures under a coloring/chromatic constraint, sharing the 3-uniform hypergraph extremal setting. -- 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_edcceb348c8ac1c3finding.add
Candidate claim vc_f4e6bf184f057992 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_f4e6bf184f057992

1 events

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