proposed
reason
Candidate claim vc_faa0e419bc15b452 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 #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.
- id
- vpr_3ff1e076ad56c4c7
- frontier
- Erdős problems frontier
- kind
- finding.add
- created
- 2026-05-30
- findings
- +1
- state
- null → c8124aa2
accept gate
1 of 4 on record- —
- signature
- reviewer:erdos-db-trust · no key registered on this bundle
- ✓
- chain
- null → c8124aa2
- —
- witness
- no verifier attachment on record for this target
- —
- grade
- in state · unreviewed
timeline
- 2026-05-30proposeproposed · finding.addagent:erdos-spine-ingest
vpr_3ff1e076ad56c4c7Candidate claim vc_faa0e419bc15b452 imported from artifact packet cap_61973ee16b553d57 - 2026-05-30acceptfinding.assertedreviewer:erdos-db-trust
null→c8124aa2vev_e57145290618cde7Candidate claim vc_faa0e419bc15b452 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 #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.
vf_113dea72070e740cDiff
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 →
Check output
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- 04reviewread queue →
Reviewer decision
A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.
- 05acceptedinspect events →
Accepted event
Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.