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

Evidence atom

back to sources

{"artifact_id":"va_9bc926d75e4e3881","artifact_packet_id":"cap_61973ee16b553d57","candidate_claim_id":"vc_0bd9cabd429a45df"}

id: vea_2d04f7e9b0610635
frontier: Erdős problems frontier
source: vs_5be9ca91f7fa2c5d
finding: vf_e98c39e418546862

evidence boundary

supports

computational

finding binding

bound

open_question

Erdős Problem #41 remains OPEN. Statement: Let `A ⊆ ℕ` be an infinite set such that the triple sums `a + b + c` are all distinct for `a, b, c` in `A` (aside from the trivial coincidences). Is it true that `liminf n → ∞ |A ∩ {1, …, N}| / N^(1/3) = 0`? Topics: number theory, sidon sets, additive combinatorics. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.

source binding

source-bound

cap_61973ee16b553d57 · vc_0bd9cabd429a45df

vs_5be9ca91f7fa2c5d

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_0bd9cabd429a45df"}

locator

span:0

extraction method

artifact_to_state_import

support relation

supports

condition refs

vcnd_40c1e536a56513c3

caveats

No caveats recorded.

Review, event, and evaluation records

events

vev_d65a0901b38a0c9efinding.asserted
Candidate claim vc_0bd9cabd429a45df imported from artifact packet cap_61973ee16b553d57
reviewer:erdos-db-trust · 2026-05-30

reviewable changes

vpr_ca899487ad1138b1finding.note
SEMANTIC-EDGE DRAFT -> Erdos #241 (vf_18e6a86bd3459220) [specializes, confidence 0.78]: Problem 241 studies the maximum size of B_3 sets (distinct triple sums) in {1,...,N}, the n=3 instance of the general distinct-n-fold-sum (B_n) condition of Problem 41. -- 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_d84e0b19d435c614finding.add
Candidate claim vc_0bd9cabd429a45df imported from artifact packet cap_61973ee16b553d57
applied · agent:erdos-spine-ingest · 2026-05-30
vpr_f4aba4355af4a871finding.note
SEMANTIC-EDGE DRAFT -> Erdos #44 (vf_a357c9d8ac3d6b26) [generalizes, confidence 0.8]: Problem 41 (sets whose n-fold sums are all distinct, i.e. B_n sets) is the order-n generalization of Sidon sets (B_2), and Problem 44 is the n=2 Sidon size 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_ffca4a68f090582cfinding.note
SEMANTIC-EDGE DRAFT -> Erdos #30 (vf_04c2ff267458866e) [generalizes, confidence 0.75]: B_n sets (distinct n-tuple sums) in Problem 41 generalize Sidon sets, whose maximum size h(N) is the subject of Problem 30; the n=2 case recovers 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

evaluations

No evaluation rows are attached.

computational

open_question

cap_61973ee16b553d57 · vc_0bd9cabd429a45df

1 events

Review, event, and evaluation records

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