Formal-conjectures Lean proofs (kernel-verified)

{
 "assertion": {
  "direction": null,
  "entities": [],
  "relation": null,
  "text": "The Lean 4 theorem `Erdos1054.f_undefined_at_2` — f 2 = 0  — for the Erdős-1054 function f(n) = least m such that n is a sum of the k smallest divisors of m (some k ≥ 1), f is UNDEFINED at n=2 (junk value 0). Proof: any such sum is 1 + R where the i=0 term is the least divisor 1 and every other term is 0 or a strictly larger divisor (≥ 2), so the sum is never 2. — is formally proven and kernel-verified in formal-conjectures (zero `sorry`, no extra axioms). Verifier: lean4-kernel + Mathlib v4.27.0 (lake build green; `#print axioms` = [propext, Classical.choice, Quot.sound] only — NO sorryAx).",
  "type": "theoretical"
 },
 "conditions": {
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  "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": {
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  "evidence_spans": [
   {
    "artifact_id": "va_f78d5e0808a9ac34",
    "artifact_packet_id": "cap_6fcdb44f3a2ff0c6",
    "candidate_claim_id": "vc_c0bc8dce9a810f0b"
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  ],
  "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"
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 "flags": {
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  "declining": false,
  "gap": false,
  "gravity_well": false,
  "negative_space": false,
  "retracted": false
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 "id": "vf_b8e3badb634a19a0",
 "links": [],
 "previous_version": null,
 "provenance": {
  "authors": [
   {
    "name": "Canopus Lean proof-search adapter",
    "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_6fcdb44f3a2ff0c6 · vc_c0bc8dce9a810f0b",
  "url": "github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/1054.lean",
  "year": null
 },
 "updated": null,
 "version": 1
}