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

used by 0 · replayed by 2 producers

e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null

Source record

back to sources

cap_61973ee16b553d57 · vc_bc28213ca89ad8f2

id: vs_8984c527502364d1
frontier: Erdős problems frontier
type: synthetic_report

source boundary

frontier-owned

synthetic

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

1 events

3 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

external source

locator

title:cap_61973ee16b553d57 · vc_bc28213ca89ad8f2

imported

2026-05-30T00:42:06.826507+00:00

extraction mode

artifact_to_state_import

authors

Erdős Open-Problem spine ingest

caveats

source requires human review before being treated as evidence

Bound findings

Erdős Problem #39 remains OPEN. Statement: Is there an infinite Sidon set $A\subset \mathbb{N}$ such that $\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon}$ for all $\varepsilon > 0$? Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
open_question · vf_e78ce45079841e8a

Evidence atoms

vea_595d18b995d5da50computational · supports
{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_bc28213ca89ad8f2"}

Review, event, and evaluation records

events

vev_b4de5f6375b94a30finding.asserted
Candidate claim vc_bc28213ca89ad8f2 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_373f28bc2851d658finding.note
SEMANTIC-EDGE DRAFT -> Erdos #30 (vf_04c2ff267458866e) [shares_technique, confidence 0.6]: Both rely on counting-function bounds for Sidon sets in {1,...,N}; the infinite-density question of 39 is governed by the same h(N) ~ √N upper bound estimated in 30. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
pending_review · agent:semantic-edge-extractor · 2026-06-10
vpr_5f72f6958e3d1297finding.add
Candidate claim vc_bc28213ca89ad8f2 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_efcf998e14120ad6finding.note
SEMANTIC-EDGE DRAFT -> Erdos #44 (vf_a357c9d8ac3d6b26) [depends_on, confidence 0.6]: The N^{1/2-ε} density ceiling for an infinite Sidon set in 39 is forced by the finite Sidon upper bound (≈√N) asserted in 44, so 39's obstruction depends on that bound. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
pending_review · agent:semantic-edge-extractor · 2026-06-10

evaluations

No evaluation rows are attached.