frontiers / frontier
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewErdős 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.
A proposal; no authority until an accepted review event.
accept gate
0 of 4 on recordtimeline
vpr_373f28bc2851d658SEMANTIC-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.proposed
reason
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.
provenance
proposed by
agent:semantic-edge-extractor
actor type
human
created at
2026-06-10
target type
finding
affected
inspect finding →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.
vf_e78ce45079841e8aRead-only frontier; diff not recomputed.
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.
A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.
Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.
Jump to a section, signal, campaign, document, primitive, work path, frontier, record index, atlas, constellation, agent, capability, or full-state search.