Vela
✦ 5 frontiers

frontiers / frontier

Erdős problems frontier

constellation seal · derived from vfr_37aec80d874a0239
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

Reviewable change

back to review

finding.note

claimed — no verifier run, no signed judgmentopen

Erdős Problem #142 remains OPEN. Statement: Prove an asymptotic formula for $r_k(N)$, the largest possible size of a subset of $\{1, \dots, N\}$ that does not contain any non-trivial $k$-term arithmetic progression. Topics: additive combinatorics, arithmetic progressions. Erdős prize: $10000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003002, A003003, A003004, A003005.

id
vpr_aaefaf3f4cd0ee9c
frontier
Erdős problems frontier
kind
finding.note
created
2026-06-10

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
in state · unreviewed

timeline

  1. 2026-06-10proposeproposed · finding.noteagent — machine actor, no signing keyagent:semantic-edge-extractorvpr_aaefaf3f4cd0ee9cSEMANTIC-EDGE DRAFT -> Erdos #138 (vf_8d5ada8b450f91ca) [related, confidence 0.55]: 142 is the density (Szemeredi) version of avoiding k-term APs while 138 is the coloring (van der Waerden) version of forcing monochromatic APs, two faces of the same arithmetic-progression Ramsey phenomenon. -- 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 #138 (vf_8d5ada8b450f91ca) [related, confidence 0.55]: 142 is the density (Szemeredi) version of avoiding k-term APs while 138 is the coloring (van der Waerden) version of forcing monochromatic APs, two faces of the same arithmetic-progression Ramsey phenomenon. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.

provenance

proposed by

agent — machine actor, no signing keyagent:semantic-edge-extractor

actor type

human

created at

2026-06-10

target type

finding

affected

inspect finding →

Erdős Problem #142 remains OPEN. Statement: Prove an asymptotic formula for $r_k(N)$, the largest possible size of a subset of $\{1, \dots, N\}$ that does not contain any non-trivial $k$-term arithmetic progression. Topics: additive combinatorics, arithmetic progressions. Erdős prize: $10000. Statement is machine-verified in Lean (formal-conjectures). OEIS: A003002, A003003, A003004, A003005.

vf_b66b7c5d84d7554e

Diff

Read-only frontier; diff not recomputed.

Review chain

  1. 01request

    Change request

    Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.

    open review →
  2. 02packet

    Diff packet

    The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.

    open the campaign →
  3. 03checks

    Check output

    Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.

    inspect checks →
  4. 04review

    Reviewer decision

    A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.

    read queue →
  5. 05accepted

    Accepted event

    Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.

    inspect events →

finding.noted · reviewer:will-blair · 1 day

renders the record as of vev_d199cb2e · 1,338 events · hub

Search Vela

Jump to a section, signal, campaign, document, primitive, work path, frontier, record index, atlas, constellation, agent, capability, or full-state search.