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frontiers / frontier

Erdős problems frontier

constellation seal · derived from vfr_37aec80d874a0239
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_7e334d68d96970e8"}

id
vea_8f6f8deee78dedcc
frontier
Erdős problems frontier
source
vs_6cb6dabf64478147
finding
vf_4fd61820b78bdedf

evidence boundary

supports

computational

finding binding

bound

open_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-bound

cap_61973ee16b553d57 · vc_7e334d68d96970e8

vs_6cb6dabf64478147

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_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

2

events

  • vev_90d855ec19a8d904finding.asserted

    Candidate claim vc_7e334d68d96970e8 imported from artifact packet cap_61973ee16b553d57

    reviewer:erdos-db-trustreviewer:erdos-db-trust · 2026-05-30

reviewable changes

  • vpr_9f30d03e18c5bfe7finding.add

    Candidate claim vc_7e334d68d96970e8 imported from artifact packet cap_61973ee16b553d57

    agent — machine actor, no signing keyapplied · agent:erdos-spine-ingest · 2026-05-30

evaluations

No evaluation rows are attached.

finding.noted · reviewer:will-blair · 2 days

renders the record as of vev_d199cb2e · 1,338 events · hub

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