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
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_faa0e419bc15b452"}
- id
- vea_1ccdde8a3efa3a49
- frontier
- Erdős problems frontier
- source
- vs_3f32584d880f00bd
- finding
- vf_113dea72070e740c
finding binding
boundopen_question
Erdős Problem #331 has status 'disproved (lean)'. Statement: Let $A,B\subseteq \mathbb{N}$ such that for all large $N$$$\lvert A\cap \{1,\ldots,N\}\rvert \gg N^{1/2}$$and$$\lvert B\cap \{1,\ldots,N\}\rvert \gg N^{1/2}.$$ Is it true that there are infinitely many solutions to $a_1-a_2=b_1-b_2\neq 0$ with $a_1,a_2\in A$ and $b_1,b_2\in B$? Ruzsa has observed that there is a simple counterexample: take $A$ to be the set of numbers whose binary representation has only non-zero digits in even places, and $B$ similarly but with non-zero digits only in odd places. It is easy to see $A$ and $B$ both grow like $\gg N^{1/2}$ and yet for any $n\geq 1$ there is exactly one solution to $n=a+b$ with $a\in A$ and $b\in B$. This was formalized in Lean by van Doorn using Aristotle. Topics: number theory, additive combinatorics. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_faa0e419bc15b452
vs_3f32584d880f00bd
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_faa0e419bc15b452"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_661c4778f1c5a1c5
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_e57145290618cde7finding.assertedCandidate claim vc_faa0e419bc15b452 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_3ff1e076ad56c4c7finding.addCandidate claim vc_faa0e419bc15b452 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.