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_7e334d68d96970e8"}
- id
- vea_8f6f8deee78dedcc
- frontier
- Erdős problems frontier
- source
- vs_6cb6dabf64478147
- finding
- vf_4fd61820b78bdedf
finding binding
boundopen_question
Erdős Problem #204 has status 'disproved (lean)'. Statement: Are there $n$ such that there is a covering system with moduli the divisors of $n$ which is 'as disjoint as possible'? That is, for all $d\mid n$ with $d>1$ there is an associated $a_d$ such that every integer is congruent to some $a_d\pmod{d}$, and if there is some integer $x$ with $$x\equiv a_d\pmod{d}\textrm{ and }x\equiv a_{d'}\pmod{d'}$$then $(d,d')=1$. The density of such $n$ is zero. Erdős and Graham believed that no such $n$ exist. Adenwalla [Ad25] has proved there are no such $n$. This was formalized by van Doorn in Lean using Aristotle. Topics: covering systems. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_7e334d68d96970e8
vs_6cb6dabf64478147
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_7e334d68d96970e8"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_bf53b00dc5a3c08a
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_90d855ec19a8d904finding.assertedCandidate claim vc_7e334d68d96970e8 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_9f30d03e18c5bfe7finding.addCandidate claim vc_7e334d68d96970e8 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.