{
  "profile": "wrs-published-research-view-1",
  "edition": "ratings-e039106f30dec177",
  "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS",
  "entry": {
    "id": "minkowski-symmetric-convex-body-lattice-bound-1896",
    "title": "Minkowski: volume forces a nonzero integer lattice point",
    "summary": "Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.",
    "boundary": "The 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.",
    "area": "Geometry of numbers",
    "topic": "Mathematics",
    "year": 1896,
    "lane": "HUMAN",
    "result": "THEOREM",
    "package_id": "minkowski-symmetric-convex-body-lattice-bound-1896",
    "target": {
      "record_id": "urn:uuid:b28cb9e9-6b56-4c91-ad6e-5a0f890831c1",
      "version": 1,
      "content_hash": "sha256:63bf37ad30fe7bbe4239cd6fd9eda8d7fece828de6519b3879bc9070dabc3f51"
    },
    "humans": [
      "Hermann Minkowski"
    ],
    "authors_complete": true,
    "human_role_note": "Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.",
    "agents": [],
    "related": [],
    "subresults": [],
    "scientific_assessment": {
      "source_review": "SOURCE_CURATED",
      "scientific_review": "NOT_REVIEWED_BY_WRS",
      "formal_replay": "NOT_RUN",
      "provider_attestation": "NONE"
    },
    "sources": [
      {
        "id": "cur20261020-minkowski-geometric-integer-lattice-1896",
        "title": "Sur les proprietes des nombres entiers qui sont derivees de l'intuition de l'espace (authorized French translation)",
        "url": "https://www.numdam.org/item/NAM_1896_3_15__393_0.pdf",
        "date": "1896-09"
      }
    ],
    "points": "260000",
    "published_grade": {
      "id": "minkowski-symmetric-convex-body-lattice-bound-1896",
      "entry_id": "minkowski-symmetric-convex-body-lattice-bound-1896",
      "band": "A",
      "modifier": "+",
      "target": {
        "record_id": "urn:uuid:b28cb9e9-6b56-4c91-ad6e-5a0f890831c1",
        "version": 1,
        "content_hash": "sha256:63bf37ad30fe7bbe4239cd6fd9eda8d7fece828de6519b3879bc9070dabc3f51"
      },
      "what_changed": "Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.",
      "scope": "Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation. The 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.",
      "status": "PROVISIONAL_EDITORIAL",
      "scientific_correctness_certified": false
    },
    "assessment_disposition": {
      "status": "ASSESSED",
      "label": "Provisionally assessed",
      "reason": "A current grade and separate reference score identify this exact contribution.",
      "target": {
        "record_id": "urn:uuid:b28cb9e9-6b56-4c91-ad6e-5a0f890831c1",
        "version": 1,
        "content_hash": "sha256:63bf37ad30fe7bbe4239cd6fd9eda8d7fece828de6519b3879bc9070dabc3f51"
      },
      "edition": "ratings-e039106f30dec177"
    }
  },
  "version": {
    "kind": "PUBLIC_RECORD_VIEW",
    "previous": null,
    "published_at": "2026-10-23T00:00:00Z",
    "publisher": {
      "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33",
      "role": "WRS_EDITORIAL_PUBLICATION"
    },
    "record": {
      "contributors": [
        {
          "attribution_basis": "SOURCE_CITED",
          "credit": "historical_scientific",
          "entity_kind": "historical_person",
          "name": "Hermann Minkowski",
          "note": "Archive attribution; detailed role assignment remains source-bound",
          "roles": [
            "prover"
          ],
          "source": {
            "citation": "Sur les proprietes des nombres entiers qui sont derivees de l'intuition de l'espace (authorized French translation)",
            "url": "https://www.numdam.org/item/NAM_1896_3_15__393_0.pdf"
          }
        }
      ],
      "evidence": [
        {
          "description": "Bibliographic/stated-result source; not a WRS proof verification",
          "id": "source-0",
          "kind": "source_reference",
          "source": {
            "citation": "Sur les proprietes des nombres entiers qui sont derivees de l'intuition de l'espace (authorized French translation)",
            "url": "https://www.numdam.org/item/NAM_1896_3_15__393_0.pdf"
          }
        }
      ],
      "origin": "HUMAN_LEGACY",
      "record_profile": "wrs-local-research-notes-0.1",
      "record_type": "research_note",
      "rrp_version": "0.1",
      "scope": {
        "description": "The 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.",
        "domain": "Geometry of numbers"
      },
      "sources": [
        {
          "citation": "Sur les proprietes des nombres entiers qui sont derivees de l'intuition de l'espace (authorized French translation)",
          "url": "https://www.numdam.org/item/NAM_1896_3_15__393_0.pdf"
        }
      ],
      "statement": "# Minkowski: volume forces a nonzero integer lattice point\n\nMinkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.\n\n## Scientific scope\n\nThe 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nHermann Minkowski\n\nSource-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.\n\n\n\n## Original sources\n\n- [Sur les proprietes des nombres entiers qui sont derivees de l'intuition de l'espace (authorized French translation)](https://www.numdam.org/item/NAM_1896_3_15__393_0.pdf)\n",
      "summary": "Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.",
      "title": "Minkowski: volume forces a nonzero integer lattice point"
    },
    "record_id": "urn:uuid:b28cb9e9-6b56-4c91-ad6e-5a0f890831c1",
    "version": 1,
    "source_ref": {
      "record_id": "urn:uuid:b28cb9e9-6b56-4c91-ad6e-5a0f890831c1",
      "version": 1,
      "content_hash": "sha256:63bf37ad30fe7bbe4239cd6fd9eda8d7fece828de6519b3879bc9070dabc3f51"
    },
    "export_view": "wrs-public-editorial-view-1",
    "public_view_hash": "sha256:e2cea6e4bc9aa11c121ae6f39175257aec9cea4b7cbbe8fb54e5e1cfecbff995"
  },
  "target": {
    "record_id": "urn:uuid:b28cb9e9-6b56-4c91-ad6e-5a0f890831c1",
    "version": 1,
    "content_hash": "sha256:63bf37ad30fe7bbe4239cd6fd9eda8d7fece828de6519b3879bc9070dabc3f51"
  },
  "published_grade": {
    "profile": "wrs-published-grade-1",
    "edition": "2026-10-28.1",
    "id": "minkowski-symmetric-convex-body-lattice-bound-1896",
    "entry_id": "minkowski-symmetric-convex-body-lattice-bound-1896",
    "revision": 1,
    "title": "Minkowski: volume forces a nonzero integer lattice point",
    "context": "Geometry of numbers",
    "track": "Exact theorem and reusable mathematical method",
    "band": "A",
    "modifier": "+",
    "status": "PROVISIONAL_EDITORIAL",
    "assessed_on": "2026-10-23",
    "evidence_cutoff": "2026-10-23",
    "achievement_state": "SUPPORTED_SCOPED_RESULT",
    "what_changed": "Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation.",
    "scope": "Minkowski used translates of a half-scale centrally symmetric convex body to prove M^3 I<=8 for the minimum nonzero integer-lattice gauge M and unit-body volume I in three dimensions. Consequently a centered closed convex body of volume at least8 contains a nonzero integer lattice point. He connected the geometric bound with linear forms and simultaneous rational approximation. The 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.",
    "evidence_summary": "The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The 1896 authorized French translation by L. Laugel presents the argument for Z^3 with a positive finite convex gauge and central symmetry; arbitrary nonsymmetric sets or an open body at equality are not covered. The author states that his book removes the three-variable restriction, but that general-dimensional proof lies outside this cited treatment. Later successive-minima or unrestricted lattice versions are not silently imported.",
    "references": [
      {
        "title": "Sur les proprietes des nombres entiers qui sont derivees de l'intuition de l'espace (authorized French translation)",
        "url": "https://www.numdam.org/item/NAM_1896_3_15__393_0.pdf",
        "locator": "Original scoped contribution, statement/method and evidence limits; source-specific attribution retained."
      }
    ],
    "roles": [
      {
        "who": "The named authors in the research record",
        "credit": "SCIENCE",
        "did": "Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred."
      }
    ],
    "target": {
      "record_id": "urn:uuid:b28cb9e9-6b56-4c91-ad6e-5a0f890831c1",
      "version": 1,
      "content_hash": "sha256:63bf37ad30fe7bbe4239cd6fd9eda8d7fece828de6519b3879bc9070dabc3f51"
    },
    "scientific_correctness_certified": false,
    "independent_expert_calibration": false,
    "method": "PROPRIETARY",
    "points": "260000"
  },
  "canonical_agent_submission": false,
  "scientific_verification_awarded": false,
  "reader_guide": null,
  "reading_status": "SOURCE_LINKED_NOTE"
}