frontiers / frontier

Additive combinatorics: Sidon sets and N(h,k) bounds

id: vfr_496956067dc5ad79
license: CC-BY-4.0
findings: 22
accepted core: 1
contested: 1
links: 0
sources: 22
evidence: 22
avg conf: 0.83

used by 1 · replayed by 1 producer · second seat open

e33/33 · finding.asserted · reviewer:will · 2026-06-03 · null→e123

Finding bundle

back to state

OEIS A309370 a(10) >= 66: a verified Sidon set of 66 distinct binary vectors in {0,1}^10 (componentwise integer addition into {0,1,2}^10; all 2211 pairwise sums a+b (a<=b) distinct), improving the live OEIS public lower bound a(10) >= 63 by +3 and the prior local best 65 by +1. Found by an Opus-4.8 Canopus-loop proposer (no-context arm, local search); re-verified from scratch by verify_construction.verify_sidon (frozen gate). Witness sha256:6a358e229f98b723…

id: vf_c9ab5970cdbcb6af
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
version: 1
confidence: 0.99

no incoming links yet

file

/frontier/sidon-sets/at/vev_d30acf067ad58787permalink · after_hash e1233eb78b69ec3f…

vf_c9ab5970cdbcb6af · sidon-sets · snapshot sha256:8badc78d64f9cdb5b9e9594b0e2855d9295d4b99abf972db104f3b417fa630af · https://vela-site-next.fly.dev/frontier/sidon-sets/at/vev_d30acf067ad58787

cite

raw json · vf_c9ab5970cdbcb6af (2.5 KB)

machine twin · index.json

{
 "assertion": {
  "direction": null,
  "entities": [],
  "relation": null,
  "text": "OEIS A309370 a(10) >= 66: a verified Sidon set of 66 distinct binary vectors in {0,1}^10 (componentwise integer addition into {0,1,2}^10; all 2211 pairwise sums a+b (a<=b) distinct), improving the live OEIS public lower bound a(10) >= 63 by +3 and the prior local best 65 by +1. Found by an Opus-4.8 Canopus-loop proposer (no-context arm, local search); re-verified from scratch by verify_construction.verify_sidon (frozen gate). Witness sha256:6a358e229f98b723…",
  "type": "theoretical"
 },
 "conditions": {
  "age_group": null,
  "cell_type": null,
  "clinical_trial": false,
  "concentration_range": null,
  "duration": null,
  "human_data": false,
  "in_vitro": false,
  "in_vivo": false,
  "species_unverified": [],
  "species_verified": [],
  "text": "Agent-imported candidate claim; scope requires review."
 },
 "confidence": {
  "basis": "agent-imported candidate claim; reviewer acceptance required",
  "extraction_confidence": 0.7,
  "kind": "frontier_epistemic",
  "method": "expert_judgment",
  "score": 0.99
 },
 "created": "2026-06-03T12:00:00+00:00",
 "evidence": {
  "effect_size": null,
  "evidence_spans": [
   {
    "artifact_id": "va_6a358e229f98b723",
    "artifact_packet_id": "cap_087198a92d1e30a2",
    "candidate_claim_id": "vc_5aab0a22f7cdebf1"
   }
  ],
  "method": "ScienceClaw-shaped artifact packet import",
  "model_system": "agent artifact packet",
  "p_value": null,
  "replicated": false,
  "replication_count": null,
  "sample_size": null,
  "species": null,
  "type": "computational"
 },
 "flags": {
  "contested": false,
  "declining": false,
  "gap": false,
  "gravity_well": false,
  "negative_space": false,
  "retracted": false
 },
 "id": "vf_c9ab5970cdbcb6af",
 "links": [],
 "previous_version": null,
 "provenance": {
  "authors": [
   {
    "name": "Canopus Sidon proposer (Opus 4.8)",
    "orcid": null
   }
  ],
  "citation_count": null,
  "doi": null,
  "extraction": {
   "extracted_at": "2026-06-03T12:00:00+00:00",
   "extractor_version": "vela/0.691.0",
   "method": "artifact_to_state_import",
   "model": "agent:canopus-lean-2026-06-03",
   "model_version": null
  },
  "journal": null,
  "openalex_id": null,
  "pmc": null,
  "pmid": null,
  "publisher": "artifact packet",
  "review": {
   "corrections": [],
   "reviewed": false,
   "reviewed_at": null,
   "reviewer": null
  },
  "source_type": "model_output",
  "title": "cap_087198a92d1e30a2 · vc_5aab0a22f7cdebf1",
  "url": "https://oeis.org/A309370",
  "year": null
 },
 "updated": null,
 "version": 1
}

Unsealed — 0 attachment(s) on record, awaiting independent verification.

0 attachments · 0 distinct checker actors · 0 methods

blame · custody trail

produced byreviewer:willfinding.asserted · 2026-06-03vev_d30acf067ad58787

checked byno verifier attachment on record

accepted byno accept signed

history · 1 event

e33/33finding.assertedreviewer:will2026-06-03→e1233eb78b

record state

frontier-owned

Review status

unreviewed

finding statement

finding type

theoretical

No entity list is declared.

evidence

source-bound

1 atoms

computational · ScienceClaw-shaped artifact packet import · agent artifact packet

proof impact

packet context

1 events

1 reviewable changes and 0 evaluation records are attached to this finding id.

evidence

method

ScienceClaw-shaped artifact packet import

evidence type

computational

system

agent artifact packet

evidence spans

span recorded

conditions

species_unverified
species_verified
text: Agent-imported candidate claim; scope requires review.

provenance

source title

cap_087198a92d1e30a2 · vc_5aab0a22f7cdebf1

authors

Canopus Sidon proposer (Opus 4.8)

Source records

source record

synthetic

cap_087198a92d1e30a2 · vc_5aab0a22f7cdebf1

vs_04f529aaefba1005

title:cap_087198a92d1e30a2 · vc_5aab0a22f7cdebf1

artifact_to_state_import

Evidence atoms

vea_260ba1d40fa518abcomputational · supports
{"artifact_id":"va_6a358e229f98b723","artifact_packet_id":"cap_087198a92d1e30a2","candidate_claim_id":"vc_5aab0a22f7cdebf1"}
vs_04f529aaefba1005 · span:0 · artifact_to_state_import

Typed links

outgoing

No outgoing links.

incoming

No incoming links.

Review, event, and evaluation records

events

vev_d30acf067ad58787finding.asserted
Candidate claim vc_5aab0a22f7cdebf1 imported from artifact packet cap_087198a92d1e30a2
reviewer:will · 2026-06-03

reviewable changes

vpr_1879d8894dd07e64finding.add
Candidate claim vc_5aab0a22f7cdebf1 imported from artifact packet cap_087198a92d1e30a2
applied · agent:canopus-lean-2026-06-03 · 2026-06-03

evaluations

No evaluation record targets this finding id.

Review status

theoretical

1 atoms

1 events

Source records

cap_087198a92d1e30a2 · vc_5aab0a22f7cdebf1

Evidence atoms

Typed links

Review, event, and evaluation records

Search Vela