proposed
reason
Candidate claim vc_12af1cc9b921f09c imported from artifact packet cap_61973ee16b553d57
finding type
open_question
proposed confidence
0.99
confidence basis
agent-imported candidate claim; reviewer acceptance required
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
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewadd a finding
acceptedErdős Problem #602 remains OPEN. Statement: Does every almost-disjoint family of countably infinite sets whose pairwise intersections all have size ≠ 1 have Property B? Formally: let `α` be any type, let `(A_i)_{i ∈ I}` be a family of countably infinite subsets of `α` such that for all `i ≠ j`, the intersection `A_i ∩ A_j` is finite and `|A_i ∩ A_j| ≠ 1`. Does there exist a 2-colouring `f : α → Fin 2` such that no `A_i` is monochromatic? This is an open question about Property B for almost-disjoint families with a forbidden intersection size of 1. **Note:** This generalises the formulation in which the ground set is `ℕ`. Since every countably infinite set is in bijection with `ℕ`, the two formulations are equivalent, but working over an arbitrary ground type makes the statement apply immediately to, e.g., almost-disjoint families of countable subsets of an uncountable space. Topics: combinatorics, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
- id
- vpr_9e9795d3da08cb2b
- frontier
- Erdős problems frontier
- kind
- finding.add
- created
- 2026-05-30
- findings
- +1
- state
- null → 961886d1
accept gate
1 of 4 on record- —
- signature
- reviewer:erdos-db-trust · no key registered on this bundle
- ✓
- chain
- null → 961886d1
- —
- witness
- no verifier attachment on record for this target
- —
- grade
- in state · unreviewed
timeline
- 2026-05-30proposeproposed · finding.addagent:erdos-spine-ingest
vpr_9e9795d3da08cb2bCandidate claim vc_12af1cc9b921f09c imported from artifact packet cap_61973ee16b553d57 - 2026-05-30acceptfinding.assertedreviewer:erdos-db-trust
null→961886d1vev_9c2cdd208d629732Candidate claim vc_12af1cc9b921f09c imported from artifact packet cap_61973ee16b553d57
provenance
proposed by
agent:erdos-spine-ingest
actor type
agent
created at
2026-05-30
target type
finding
affected
inspect finding →Erdős Problem #602 remains OPEN. Statement: Does every almost-disjoint family of countably infinite sets whose pairwise intersections all have size ≠ 1 have Property B? Formally: let `α` be any type, let `(A_i)_{i ∈ I}` be a family of countably infinite subsets of `α` such that for all `i ≠ j`, the intersection `A_i ∩ A_j` is finite and `|A_i ∩ A_j| ≠ 1`. Does there exist a 2-colouring `f : α → Fin 2` such that no `A_i` is monochromatic? This is an open question about Property B for almost-disjoint families with a forbidden intersection size of 1. **Note:** This generalises the formulation in which the ground set is `ℕ`. Since every countably infinite set is in bijection with `ℕ`, the two formulations are equivalent, but working over an arbitrary ground type makes the statement apply immediately to, e.g., almost-disjoint families of countable subsets of an uncountable space. Topics: combinatorics, set theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
vf_15940eef97d062eaDiff
Read-only frontier; diff not recomputed.
Review chain
- 01requestopen review →
Change request
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
- 02packetopen the campaign →
Diff packet
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
- 03checksinspect checks →
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- 04reviewread queue →
Reviewer decision
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- 05acceptedinspect events →
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Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.