{
  "schema": "certiv_public_ai_discovery_dossier_v1",
  "corpus_id": "certiv-ai-discovery-2026-07-16",
  "reviewed_at": "2026-07-16",
  "evidence_boundary": "These are Certiv-authored test dossiers, not author-issued Certiv receipts. A pinned PDF proves file identity only. A passing selected replay records one bounded observation; it does not independently reproduce a paper's central claim or establish truth, novelty, priority, safety, or correct interpretation.",
  "case": {
    "slug": "mathematical-exploration-at-scale",
    "case_type": "reported-discovery",
    "domain": "Mathematics",
    "title": "Mathematical exploration and discovery at scale",
    "authors": {
      "display": "Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao, and Adam Zsolt Wagner",
      "count": 4
    },
    "paper": {
      "arxiv_id": "2511.02864",
      "version": "v3",
      "submitted": "2025-11-03",
      "version_date": "2025-12-22",
      "abs_url": "https://arxiv.org/abs/2511.02864v3",
      "pdf_url": "https://arxiv.org/pdf/2511.02864v3",
      "pdf_sha256": "77b43844077c98c26dfc76ad391cadbbd53d48a1d290ddae575ff4d1bcdef9d2",
      "pdf_bytes": 12141713,
      "pages": 81,
      "extracted_text_bytes": 269596,
      "parser_observations": [
        "Recognized as a PDF and not encrypted.",
        "pdfinfo reported JavaScript: no.",
        "pdfdetach reported no embedded files.",
        "pdftotext completed successfully."
      ]
    },
    "selection_rationale": "A recent 67-problem mathematical study that exposes concrete constructions and makes the gap between checking examples and reproducing a whole study especially visible.",
    "claim": {
      "reported": "The authors report that AlphaEvolve rediscovered many best-known solutions and improved several mathematical constructions across 67 problems.",
      "certiv_observed": "The exact v3 paper was pinned. Selected public verifiers for an Erdős step-function bound and a dimension-11 kissing construction ran successfully in isolation.",
      "not_established": "The 67-problem campaign, system autonomy, comparative preparation time, novelty, generality, and all unselected constructions were not independently reproduced."
    },
    "verification_level": "selected-check-replayed",
    "central_claim_independently_reproduced": false,
    "checks": [
      {
        "id": "pdf-identity",
        "status": "observed",
        "label": "Exact PDF identity",
        "observation": "The downloaded v3 PDF matched the recorded SHA-256, byte count, and page count.",
        "boundary": "This establishes file identity, not mathematical validity."
      },
      {
        "id": "erdos-step-function",
        "status": "passed",
        "label": "Selected Erdős verifier",
        "observation": "Reviewed notebook cells 77–79 accepted the supplied step function and produced C5 ≤ 0.38092303510845016.",
        "boundary": "One construction was checked; the surrounding theorem, comparative literature, and novelty were not adjudicated."
      },
      {
        "id": "kissing-number-11",
        "status": "passed",
        "label": "Selected kissing-number verifier",
        "observation": "Reviewed notebook cells 113–114 accepted the supplied construction showing at least 593 spheres in dimension 11.",
        "boundary": "This validates the supplied witness under the notebook's check, not the paper's full campaign."
      },
      {
        "id": "all-67-problems",
        "status": "not-run",
        "label": "Full study reproduction",
        "observation": "No end-to-end replay of all 67 problems was attempted.",
        "boundary": "The dossier must not be read as 67 independent reproductions."
      }
    ],
    "artifacts": [
      {
        "label": "AlphaEvolve mathematical results repository",
        "url": "https://github.com/google-deepmind/alphaevolve_results",
        "observed_revision": "4226acbf237ff9ad10ba7673a2af127a2d8a5971",
        "sha256": "2cce2543e48c89aa3e91614272a698a0147dd2548ea11cf92f1292b7435d38ff",
        "note": "SHA-256 is for mathematical_results.ipynb at the observed revision. The Certiv cell-selection runner SHA-256 is 82a2424c064ff5a6e2a75d8291c8d9b65577b9d2243580e4e467934fe5f9f73c."
      }
    ],
    "red_team_findings": [
      "Two accepted witnesses cannot support a claim that the entire 67-problem study was reproduced.",
      "The results repository supplies checkable outputs but not the proprietary discovery engine.",
      "Literature comparison and novelty require domain-expert review outside a computational receipt."
    ],
    "certiv_mapping": {
      "inputs": "Exact paper version, repository revision, and notebook hash.",
      "checks": "Two selected witness verifiers with recorded cells and outputs.",
      "receipt_boundary": "selected-check-replayed; full mathematical study not reproduced",
      "missing_for_deeper_verification": "All problem environments, generation system, complete replay plan, and independent mathematical and novelty review."
    },
    "sources": [
      {
        "label": "Exact arXiv record",
        "url": "https://arxiv.org/abs/2511.02864v3"
      },
      {
        "label": "Public results repository",
        "url": "https://github.com/google-deepmind/alphaevolve_results"
      }
    ]
  }
}