evidence boundary
supportsfrontiers / 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
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_12af1cc9b921f09c"}
- id
- vea_24fa371bb1a64f71
- frontier
- Erdős problems frontier
- source
- vs_94976a32819c07b4
- finding
- vf_15940eef97d062ea
finding binding
boundopen_question
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.
source binding
source-boundcap_61973ee16b553d57 · vc_12af1cc9b921f09c
vs_94976a32819c07b4
review context
unverified1 events
1 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_12af1cc9b921f09c"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_12c40b94393fffc1
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_9c2cdd208d629732finding.assertedCandidate claim vc_12af1cc9b921f09c imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_9e9795d3da08cb2bfinding.addCandidate claim vc_12af1cc9b921f09c imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.