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_60d341a4d92f1061"}

id: vea_a1a10b3428719fbe
frontier: Erdős problems frontier
source: vs_4125da217fa2cda3
finding: vf_55921775986ed4e2

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #155 remains OPEN. Statement: Is it true that for every $k \geq 1$ we have $$ F(N + k) \leq F(N) + 1 $$ for all sufficiently large $N$? Topics: additive combinatorics, sidon sets. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: A143824, A227590, A003022.

source binding

source-bound

cap_61973ee16b553d57 · vc_60d341a4d92f1061

vs_4125da217fa2cda3

review context

unverified

1 events

4 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_60d341a4d92f1061"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_aae66b26b89bd1a1

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_2390982777202419finding.asserted
Candidate claim vc_60d341a4d92f1061 imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_1513ee01f8aa68ebfinding.add
Candidate claim vc_60d341a4d92f1061 imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_468558fc79d4b6b8finding.note
SEMANTIC-EDGE DRAFT -> Erdos #30 (vf_04c2ff267458866e) [related, confidence 0.9]: F(N) (largest Sidon subset of {1,...,N}) in 155 is the same extremal quantity as h(N) (max size of a Sidon set in {1,...,N}) in 30, stated under a different name. -- 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_b5c5da2cc23d85d4finding.note
SEMANTIC-EDGE DRAFT -> Erdos #44 (vf_a357c9d8ac3d6b26) [specializes, confidence 0.8]: 44 asserts the specific upper bound F(N) <= 2*sqrt(N) for exactly the largest-Sidon-set quantity F(N) that 155 defines, so 44 is a concrete bound on 155's object. -- 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_d6c26971d940d082finding.note
SEMANTIC-EDGE DRAFT -> Erdos #43 (vf_c89f4d7a1f57556e) [related, confidence 0.9]: 155's F(N) and 43's f(N), both the maximum size of a Sidon set in {1,...,N}, are literally the same function. -- 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_60d341a4d92f1061

1 events

Review, event, and evaluation records

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