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_cb7973c232de2315"}
- id
- vea_b2630dde3ab9fbe0
- frontier
- Erdős problems frontier
- source
- vs_77346ef9f3b7e84b
- finding
- vf_edb314f45838fa69
finding binding
boundopen_question
Erdős Problem #198 has status 'disproved (lean)'. Statement: The answer is no; Erdős and Graham report this was proved by Baumgartner, presumably referring to the paper [Ba75], which does not state this exactly, but the following simple construction is implicit in [Ba75]. Let $P_1,P_2,\ldots$ be an enumeration of all countably many infinite arithmetic progressions. We choose $a_1$ to be the minimal element of $P_1\cap \mathbb{N}$, and in general choose $a_n$ to be an element of $P_n\cap \mathbb{N}$ such that $a_n>2a_{n-1}$. By construction $A=\{a_1 < a_2 < \cdots\}$ contains at least one element from every infinite arithmetic progression, and is a lacunary set, so is certainly Sidon. AlphaProof has found the following explicit construction: $A = \{ (n+1)!+n : n\geq 0\}$. This is a Sidon set, and intersects every arithmetic progression, since for any $a,d\in \mathbb{N}$, $(a+d+1)!+(a+d)\in A$, and $d$ divides $(a+d+1)!+d$. This was formalized in Lean by Alexeev using Aristotle. Topics: additive combinatorics, sidon sets, arithmetic progressions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_cb7973c232de2315
vs_77346ef9f3b7e84b
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_cb7973c232de2315"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_7e847268093b1c19
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_bbe9c37600e79fc2finding.assertedCandidate claim vc_cb7973c232de2315 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_65bc6ffad7c2a755finding.addCandidate claim vc_cb7973c232de2315 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.