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_a5a2f7d21f65aba4"}
- id
- vea_fa5999286c205883
- frontier
- Erdős problems frontier
- source
- vs_a0dcb7cbb55e5682
- finding
- vf_a3424c338522cb4b
finding binding
boundtheoretical
Erdős Problem #884 has been DISPROVED (a counterexample is known). Statement: For a natural number n, let $1 = d_1 < \dotsc < d_{\tau(n)} = n$ denote the divisors of $n$ in increasing order. Does it hold that $\sum_{1 \le i < j \le \tau(n)} \frac{1}{d_j - d_i} \ll 1 + \sum_{1 \le i < \tau(n)} \frac{1}{d_{i + 1} - d_i}$ for $n \to \infty`, i.e. $\sum_{1 \le i < j \le \tau(n)} \frac{1}{d_j - d_i} \in O \left( 1 + \sum_{1 \le i < \tau(n)} \frac{1}{d_{i + 1} - d_i}) \right)$? This conjecture has been **disproved**: - In September 2025, Terence Tao gave a conditional _negative_ answer assuming the prime tuples conjecture, see `erdos_884_false_of_hardy_littlewood` for this implication. - Daniel Larsen subsequently gave an [unconditional disproof](https://github.com/Larsen-Daniel/Erdos-884/blob/main/884.pdf). *Reference:* [erdosproblems.com/884](https://www.erdosproblems.com/884) Topics: number theory, divisors. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
source binding
source-boundcap_61973ee16b553d57 · vc_a5a2f7d21f65aba4
vs_a0dcb7cbb55e5682
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_a5a2f7d21f65aba4"}
locator
span:0
extraction method
artifact_to_state_import
support relation
supports
condition refs
vcnd_c926b47d9f90da46
caveats
No caveats recorded.
Review, event, and evaluation records
2events
vev_915ba328f388440ffinding.assertedCandidate claim vc_a5a2f7d21f65aba4 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30
reviewable changes
vpr_ceb43de800efb758finding.addCandidate claim vc_a5a2f7d21f65aba4 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
evaluations
No evaluation rows are attached.