{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:QNL7PKPTHEQ7BSWHFO4ZEZOCQU","short_pith_number":"pith:QNL7PKPT","schema_version":"1.0","canonical_sha256":"8357f7a9f33921f0cac72bb99265c2851f247ee0cbf370fba7fe3e2b2767d299","source":{"kind":"arxiv","id":"1908.06476","version":2},"attestation_state":"computed","paper":{"title":"Algebraic conditions for the positivity of sectional curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Dan Gregorian Fodor","submitted_at":"2019-08-18T16:55:52Z","abstract_excerpt":"We examine algebraic conditions for the sectional positivity of the Riemann curvature operator. We describe sufficient conditions for dimension $n=4$, and complete characterization for a dense open subset of the space of operators in dimension $4$. We also briefly examine higher-dimentional curvature operators."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.06476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-18T16:55:52Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"d1e386e2a8419c98e8175dc936b30f0353e157119d0b9f936cd4dc276e81feb2","abstract_canon_sha256":"5c6d434bb6f4ffa906031d326556924bd51551b996aa8c26dd8ee7b8d52b64f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:29.335471Z","signature_b64":"2UAXtDkcVMclkW/FtydxZXwPADCLvJFOUeINtS+j6i0XQcA9ULC1zxG2tqdE9u3FLCsI4iZFR494i9jTfV8dCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8357f7a9f33921f0cac72bb99265c2851f247ee0cbf370fba7fe3e2b2767d299","last_reissued_at":"2026-07-04T23:58:29.335100Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:29.335100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic conditions for the positivity of sectional curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Dan Gregorian Fodor","submitted_at":"2019-08-18T16:55:52Z","abstract_excerpt":"We examine algebraic conditions for the sectional positivity of the Riemann curvature operator. We describe sufficient conditions for dimension $n=4$, and complete characterization for a dense open subset of the space of operators in dimension $4$. We also briefly examine higher-dimentional curvature operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06476","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06476/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.06476","created_at":"2026-07-04T23:58:29.335156+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06476v2","created_at":"2026-07-04T23:58:29.335156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06476","created_at":"2026-07-04T23:58:29.335156+00:00"},{"alias_kind":"pith_short_12","alias_value":"QNL7PKPTHEQ7","created_at":"2026-07-04T23:58:29.335156+00:00"},{"alias_kind":"pith_short_16","alias_value":"QNL7PKPTHEQ7BSWH","created_at":"2026-07-04T23:58:29.335156+00:00"},{"alias_kind":"pith_short_8","alias_value":"QNL7PKPT","created_at":"2026-07-04T23:58:29.335156+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU","json":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU.json","graph_json":"https://pith.science/api/pith-number/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/graph.json","events_json":"https://pith.science/api/pith-number/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/events.json","paper":"https://pith.science/paper/QNL7PKPT"},"agent_actions":{"view_html":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU","download_json":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU.json","view_paper":"https://pith.science/paper/QNL7PKPT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06476&json=true","fetch_graph":"https://pith.science/api/pith-number/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/graph.json","fetch_events":"https://pith.science/api/pith-number/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/action/storage_attestation","attest_author":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/action/author_attestation","sign_citation":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/action/citation_signature","submit_replication":"https://pith.science/pith/QNL7PKPTHEQ7BSWHFO4ZEZOCQU/action/replication_record"}},"created_at":"2026-07-04T23:58:29.335156+00:00","updated_at":"2026-07-04T23:58:29.335156+00:00"}