frontiers / frontier

Formal-conjectures Lean proofs (kernel-verified)

id: vfr_97d7d25957384f80
license: CC-BY-4.0
findings: 2
accepted core: 0
contested: 0
links: 0
sources: 2
evidence: 2
avg conf: 0.99

used by 0 · replayed by 0 · first seat open

e4/4 · finding.asserted · reviewer:will · 2026-06-03 · null→5d1d

Finding bundle

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The Lean 4 theorem `Erdos961.erdos_961.variants.sylvester_schur_1_1` — Erdos961Prop 1 1 (the n=k=1 instance of Sylvester–Schur: every m ≥ 2 has, in {m}, an element that is not 2-smooth) — is formally proven and kernel-verified in formal-conjectures (zero `sorry`, no extra axioms). Verifier: lean4-kernel + Mathlib (lake build green; the declaration's proof term carries no `sorry` and no extra axioms).

id: vf_bc277af6cc7a3216
frontier: Formal-conjectures Lean proofs (kernel-verified)
version: 1
confidence: 0.99

no incoming links yet

file

/frontier/formal-conjectures-lean/at/vev_8a6a56bd6ea7c014permalink · after_hash f6b8ff9379493741…

vf_bc277af6cc7a3216 · formal-conjectures-lean · https://vela-site-next.fly.dev/frontier/formal-conjectures-lean/at/vev_8a6a56bd6ea7c014

cite

raw json · vf_bc277af6cc7a3216 (2.6 KB)

machine twin · index.json

{
 "assertion": {
  "direction": null,
  "entities": [],
  "relation": null,
  "text": "The Lean 4 theorem `Erdos961.erdos_961.variants.sylvester_schur_1_1` — Erdos961Prop 1 1  (the n=k=1 instance of Sylvester–Schur: every m ≥ 2 has, in {m}, an element that is not 2-smooth) — is formally proven and kernel-verified in formal-conjectures (zero `sorry`, no extra axioms). Verifier: lean4-kernel + Mathlib (lake build green; the declaration's proof term carries no `sorry` and no extra axioms).",
  "type": "theoretical"
 },
 "conditions": {
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  "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_370c3b127f446b92",
    "artifact_packet_id": "cap_4af431152a035fa4",
    "candidate_claim_id": "vc_6c8d56f8a59a3179"
   }
  ],
  "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_bc277af6cc7a3216",
 "links": [],
 "previous_version": null,
 "provenance": {
  "authors": [
   {
    "name": "Canopus Lean proof-search adapter",
    "orcid": null
   }
  ],
  "citation_count": null,
  "doi": null,
  "extraction": {
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  "openalex_id": null,
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  "source_type": "model_output",
  "title": "cap_4af431152a035fa4 · vc_6c8d56f8a59a3179",
  "url": "github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/961.lean",
  "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_8a6a56bd6ea7c014

checked byno verifier attachment on record

accepted byno accept signed

history · 1 event

e2/4finding.assertedreviewer:will2026-06-03→f6b8ff9379

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_4af431152a035fa4 · vc_6c8d56f8a59a3179

authors

Canopus Lean proof-search adapter

Source records

source record

synthetic

cap_4af431152a035fa4 · vc_6c8d56f8a59a3179

vs_94dd1c5ae2f69a7c

title:cap_4af431152a035fa4 · vc_6c8d56f8a59a3179

artifact_to_state_import

Evidence atoms

vea_b53ceae60594ba42computational · supports
{"artifact_id":"va_370c3b127f446b92","artifact_packet_id":"cap_4af431152a035fa4","candidate_claim_id":"vc_6c8d56f8a59a3179"}
vs_94dd1c5ae2f69a7c · span:0 · artifact_to_state_import

Typed links

outgoing

No outgoing links.

incoming

No incoming links.

Review, event, and evaluation records

events

vev_8a6a56bd6ea7c014finding.asserted
Candidate claim vc_6c8d56f8a59a3179 imported from artifact packet cap_4af431152a035fa4
reviewer:will · 2026-06-03

reviewable changes

vpr_46edf17cebcd34d7finding.add
Candidate claim vc_6c8d56f8a59a3179 imported from artifact packet cap_4af431152a035fa4
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_4af431152a035fa4 · vc_6c8d56f8a59a3179

Evidence atoms

Typed links

Review, event, and evaluation records

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