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_dcaf7eada589de75"}

id: vea_9f53dc3d7b77f3c6
frontier: Erdős problems frontier
source: vs_f8505cd648dc1c23
finding: vf_b691c54cbf309acd

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #189 has status 'disproved (lean)'. Statement: If $\mathbb{R}^2$ is finitely coloured then must there exist some colour class which contains the vertices of a rectangle of every area? Graham, "On Partitions of 𝔼ⁿ", Journal of Combinatorial Theory, Series A 28, 89-91 (1980). (See "Concluding Remarks" on page 96.) Solved (with answer `False`, as formalised below) in: Vjekoslav Kovač, "Coloring and density theorems for configurations of a given volume", 2023 https://arxiv.org/abs/2309.09973 In fact, Kovač's colouring is even Jordan measurable (the topological boundary of each monochromatic region is Lebesgue measurable and has measure zero). This was formalized in Lean by Alexeev and Kovac using Aristotle. Topics: geometry, ramsey theory. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_dcaf7eada589de75

vs_f8505cd648dc1c23

review context

unverified

1 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_dcaf7eada589de75"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_e519e8a0be3991c5

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_160daa5cd32e0949finding.asserted
Candidate claim vc_dcaf7eada589de75 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_ddf4c9af93a361f7finding.add
Candidate claim vc_dcaf7eada589de75 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_dcaf7eada589de75

1 events

Review, event, and evaluation records

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