Erdős problems frontier

{
 "assertion": {
  "direction": null,
  "entities": [],
  "relation": null,
  "text": "Erdős Problem #12: machine-found Lean proof published by AlphaProof Nexus (DeepMind, arXiv 2605.22763, May 2026). Independently re-verified locally 2026-06-10: full lake build of google-deepmind/alphaproof-nexus-results@0647711a7118 under their pinned toolchain leanprover/lean4:v4.27.0 succeeded (8062 jobs); static scan clean (no sorry, no native_decide, no custom axioms). Artifacts: erdos_12.parts.i.lean sha256:c42238294d8d2d88; erdos_12.parts.ii.lean sha256:f155135c1e845cb3. AI involvement: machine-generated proof, machine-checked (Lean kernel is the referee); statement faithfulness NOT yet independently attested — see paper section 4 for DeepMind's own expert validation.",
  "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": "Manually added finding; requires evidence review before scientific use."
 },
 "confidence": {
  "basis": "operator-supplied frontier prior; review required",
  "extraction_confidence": 1,
  "kind": "frontier_epistemic",
  "method": "expert_judgment",
  "score": 0.9
 },
 "created": "2026-06-10T18:37:54.051771+00:00",
 "evidence": {
  "effect_size": null,
  "evidence_spans": [],
  "method": "manual state transition",
  "model_system": "",
  "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_caaa525f7259eff1",
 "links": [],
 "previous_version": null,
 "provenance": {
  "authors": [
   {
    "name": "agent:nexus-ingest-2026-06-10",
    "orcid": null
   }
  ],
  "citation_count": null,
  "doi": null,
  "extraction": {
   "extracted_at": "2026-06-10T18:37:54.051749+00:00",
   "extractor_version": "vela/0.691.0",
   "method": "manual_curation",
   "model": null,
   "model_version": null
  },
  "journal": null,
  "openalex_id": null,
  "pmc": null,
  "pmid": null,
  "review": {
   "corrections": [],
   "reviewed": false,
   "reviewed_at": null,
   "reviewer": null
  },
  "source_type": "preprint",
  "title": "AlphaProof Nexus results repo (Apache-2.0), arXiv:2605.22763",
  "year": null
 },
 "updated": null,
 "version": 1
}