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

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_85c29b02ee61e183"}

id: vea_f8e6bd2ac187675a
frontier: Erdős problems frontier
source: vs_5cb211907c00b136
finding: vf_04c2ff267458866e

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #30 remains OPEN. Statement: Is it true that, for every $\varepsilon > 0$, $h(N) = \sqrt N + O_{\varespilon}(N^\varespilon) Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $1000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, A227590, A003022.

source binding

source-bound

cap_61973ee16b553d57 · vc_85c29b02ee61e183

vs_5cb211907c00b136

review context

unverified

1 events

6 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_85c29b02ee61e183"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_3c002606d1b3602c

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_9af5f03fc20e0006finding.asserted
Candidate claim vc_85c29b02ee61e183 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_26d7c978130b3c2dfinding.add
Candidate claim vc_85c29b02ee61e183 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_393929f7c4c46956finding.note
SEMANTIC-EDGE DRAFT -> Erdos #155 (vf_55921775986ed4e2) [related, confidence 0.9]: P155's F(N) (size of the largest Sidon subset of {1,...,N}) is the same extremal function as P30's h(N). -- 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_3addf64850ce94c5finding.note
SEMANTIC-EDGE DRAFT -> Erdos #44 (vf_a357c9d8ac3d6b26) [related, confidence 0.9]: P44 asserts the explicit upper bound (max Sidon set size in {1,...,N} ≤ 2√N) on exactly the quantity h(N) that P30 defines and studies. -- 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_618905bc6801eeb5finding.note
SEMANTIC-EDGE DRAFT -> Erdos #39 (vf_e78ce45079841e8a) [related, confidence 0.7]: P39 asks for an infinite Sidon set of density N^{1/2-ε}, the infinite analogue of the finite maximal-Sidon-size question in P30, both governed by the √N Sidon 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
vpr_646b595bc51e1a63finding.note
SEMANTIC-EDGE DRAFT -> Erdos #43 (vf_c89f4d7a1f57556e) [related, confidence 0.92]: Both define the maximum size of a Sidon set in {1,...,N} (h(N) in P30, f(N) in P43) — the same extremal quantity under different names. -- 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_c5d1d8466e87d4cffinding.note
SEMANTIC-EDGE DRAFT -> Erdos #241 (vf_18e6a86bd3459220) [generalizes, confidence 0.78]: P241 is the B_3 analogue (all triple sums a+b+c distinct) of the B_2/Sidon (pairwise-sum-distinct) extremal problem P30 studies, generalizing distinct-pairwise-sums to distinct-triple-sums. -- 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.

computational

open_question

cap_61973ee16b553d57 · vc_85c29b02ee61e183

1 events

Review, event, and evaluation records

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