frontiers / frontier
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewErdős Problem #289 remains OPEN. Statement: Is it true that, for all sufficiently large $k$, there exists finite intervals $I_1, \dotsc, I_k \subset \mathbb{N}$ with $|I_i| \geq 2$ for $1 \leq i \leq k$ such that $$ 1 = \sum_{i=1}^k \sum_{n \in I_i} \frac{1}{n}. $$ Topics: number theory, unit fractions. Erdős prize: no. 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_cea8a84628903867SEMANTIC-EDGE DRAFT -> Erdos #295 (vf_12edf5d520c20c45) [depends_on, confidence 0.7]: Problem 295 is stated as a helper lemma producing a run n_1<...<n_k of integers above N with reciprocal sum a prescribed value, the existence ingredient needed to build the k intervals in 289. -- 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 #295 (vf_12edf5d520c20c45) [depends_on, confidence 0.7]: Problem 295 is stated as a helper lemma producing a run n_1<...<n_k of integers above N with reciprocal sum a prescribed value, the existence ingredient needed to build the k intervals in 289. -- 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 #289 remains OPEN. Statement: Is it true that, for all sufficiently large $k$, there exists finite intervals $I_1, \dotsc, I_k \subset \mathbb{N}$ with $|I_i| \geq 2$ for $1 \leq i \leq k$ such that $$ 1 = \sum_{i=1}^k \sum_{n \in I_i} \frac{1}{n}. $$ Topics: number theory, unit fractions. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.
vf_e03590a9131c59a7Read-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.