proposed
reason
Candidate claim vc_7b7a1a5f9d4086f8 imported from artifact packet cap_f4e8bcd294c97ba7
finding type
theoretical
proposed confidence
0.95
confidence basis
agent-imported candidate claim; reviewer acceptance required
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
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewadd a finding
openErdős #44 (?, AMS 5 11). STATEMENT: The maximum size of a Sidon set in `{1, ..., N}` is less than or equal to `2 * √N`. FORMAL: maxSidonSubsetCard_icc_bound: ℕ) (hN : 1 ≤ N) : maxSidonSubsetCard (Icc 1 N) ≤ 2 * Real.sqrt N; erdos_44: answer(sorry) ↔ ∀ᵉ (N ≥ (1 : ℕ)) (A ⊆ Finset.Icc 1 N), IsSidon (A : Set ℕ) → ∀ᵉ (ε > (0 : ℝ)), ∃ᵉ (M > N) (B ⊆ Finset.Icc (N + 1) M), IsSidon (A ∪ B : Set ℕ) ∧ (1 - ε) * Real.sqrt M ≤ (A ∪ B).ca KNOWN/REMARKS: # Erdős Problem 44: Extending Sidon Sets *Reference:* erdosproblems.com/44 | **Erdős Problem 44:** Let N ≥ 1 and `A ⊆ {1,…,N}` be a Sidon set. Is it true that, for any ε > 0, there exist M = M(ε) and `B ⊆ {N+1,…,M}` such that `A ∪ B ⊆ {1,…,M}` is a Sidon set of size at least `(1−ε)M^{1/2}`? This problem asks whether any Sidon set can be extended to achieve a density arbitrarily close to the optima RELATED: [] OEIS: []
- id
- vpr_4a729fc90315c745
- frontier
- Erdős problems frontier
- kind
- finding.add
- created
- 2026-06-04
A proposal; no authority until an accepted review event.
accept gate
0 of 4 on record- ·
- signature
- no terminal verdict yet
- ·
- chain
- no state transition yet
- —
- witness
- no verifier attachment on record for this target
- ·
- grade
- target not (yet) in frontier state
timeline
- 2026-06-04proposeproposed · finding.addagent:erdos-deep-ingest
vpr_4a729fc90315c745Candidate claim vc_7b7a1a5f9d4086f8 imported from artifact packet cap_f4e8bcd294c97ba7
provenance
proposed by
agent:erdos-deep-ingest
actor type
agent
created at
2026-06-04
target type
finding
Diff
Read-only frontier; diff not recomputed.
Review chain
- 01requestopen review →
Change request
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
- 02packetopen the campaign →
Diff packet
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
- 03checksinspect checks →
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- 04reviewread queue →
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- 05acceptedinspect events →
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Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.