{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VJ2L53RJIHQM3FCDHH2QTYI52A","short_pith_number":"pith:VJ2L53RJ","schema_version":"1.0","canonical_sha256":"aa74beee2941e0cd944339f509e11dd0259660df57f8d6b78599e5b8d7ee029e","source":{"kind":"arxiv","id":"1312.1103","version":1},"attestation_state":"computed","paper":{"title":"Curvature of Hessian Manfiolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John Armstrong, Shun-ichi Amari","submitted_at":"2013-12-04T10:56:35Z","abstract_excerpt":"We prove that, in dimensions greater than 2, the generic metric is not a Hessian metric and find a curvature condition on Hessian metrics in dimensions greater than 3. In particular we prove that the forms used to define the Pontryagin classes in terms of the curvature vanish on a Hessian manifold. By contrast all analytic Riemannian 2-metrics are Hessian metrics."},"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":"1312.1103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-12-04T10:56:35Z","cross_cats_sorted":[],"title_canon_sha256":"2c95d348c0ac01cc07da8834a1dd854b7042b3f6003c8a6ac77182ae6e9be721","abstract_canon_sha256":"e32118b183aa57c939e9b020e2ff60311ba51f49d8f796f6c8eb52b55a77174d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:34.983323Z","signature_b64":"VBab3EqRLGbmfA3uKL7DK3zZirQfR0SHTXB9rkhKFw8Kf6FKlfkmJ3VdSLbA0oqGpQwxC7bW3oZXzKlx6vNaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa74beee2941e0cd944339f509e11dd0259660df57f8d6b78599e5b8d7ee029e","last_reissued_at":"2026-05-18T03:05:34.982934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:34.982934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Curvature of Hessian Manfiolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"John Armstrong, Shun-ichi Amari","submitted_at":"2013-12-04T10:56:35Z","abstract_excerpt":"We prove that, in dimensions greater than 2, the generic metric is not a Hessian metric and find a curvature condition on Hessian metrics in dimensions greater than 3. In particular we prove that the forms used to define the Pontryagin classes in terms of the curvature vanish on a Hessian manifold. By contrast all analytic Riemannian 2-metrics are Hessian metrics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1103","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1312.1103","created_at":"2026-05-18T03:05:34.982998+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.1103v1","created_at":"2026-05-18T03:05:34.982998+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1103","created_at":"2026-05-18T03:05:34.982998+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJ2L53RJIHQM","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJ2L53RJIHQM3FCD","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJ2L53RJ","created_at":"2026-05-18T12:28:04.890932+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/VJ2L53RJIHQM3FCDHH2QTYI52A","json":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A.json","graph_json":"https://pith.science/api/pith-number/VJ2L53RJIHQM3FCDHH2QTYI52A/graph.json","events_json":"https://pith.science/api/pith-number/VJ2L53RJIHQM3FCDHH2QTYI52A/events.json","paper":"https://pith.science/paper/VJ2L53RJ"},"agent_actions":{"view_html":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A","download_json":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A.json","view_paper":"https://pith.science/paper/VJ2L53RJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.1103&json=true","fetch_graph":"https://pith.science/api/pith-number/VJ2L53RJIHQM3FCDHH2QTYI52A/graph.json","fetch_events":"https://pith.science/api/pith-number/VJ2L53RJIHQM3FCDHH2QTYI52A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A/action/storage_attestation","attest_author":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A/action/author_attestation","sign_citation":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A/action/citation_signature","submit_replication":"https://pith.science/pith/VJ2L53RJIHQM3FCDHH2QTYI52A/action/replication_record"}},"created_at":"2026-05-18T03:05:34.982998+00:00","updated_at":"2026-05-18T03:05:34.982998+00:00"}