{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:YYOLVEJWJAMY2PI4JN2LQAIS4S","short_pith_number":"pith:YYOLVEJW","schema_version":"1.0","canonical_sha256":"c61cba913648198d3d1c4b74b80112e48b1ff43133d67b22aec3badd4ef07781","source":{"kind":"arxiv","id":"1901.01629","version":1},"attestation_state":"computed","paper":{"title":"Closed Kac-Rice type formulas on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Beno\\^it Jubin","submitted_at":"2019-01-07T00:06:28Z","abstract_excerpt":"We establish a few formulas that compute the volume of the zero-set (or nodal set) of a function on a compact Riemannian manifold as integrals of functionals of the function and its derivatives."},"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":"1901.01629","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-07T00:06:28Z","cross_cats_sorted":[],"title_canon_sha256":"b065049c4f722139da91b433e89f3d9fc0b717b78cb19c53cbf42e220d76198b","abstract_canon_sha256":"6a54f0776d8d60b83bbc37c178ea441fc292448a32f0ff0727b488d97e81ba79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:51.590391Z","signature_b64":"IA/7UbBXndk2YJngtcOOoCbtNAqQZiVuagKxS7Tn9TUnHj6Jb7ydK48HX7iiSr9H/ScTzTGG3IplybrEnpTECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c61cba913648198d3d1c4b74b80112e48b1ff43133d67b22aec3badd4ef07781","last_reissued_at":"2026-05-17T23:56:51.589833Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:51.589833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed Kac-Rice type formulas on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Beno\\^it Jubin","submitted_at":"2019-01-07T00:06:28Z","abstract_excerpt":"We establish a few formulas that compute the volume of the zero-set (or nodal set) of a function on a compact Riemannian manifold as integrals of functionals of the function and its derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01629","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":"1901.01629","created_at":"2026-05-17T23:56:51.589905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01629v1","created_at":"2026-05-17T23:56:51.589905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01629","created_at":"2026-05-17T23:56:51.589905+00:00"},{"alias_kind":"pith_short_12","alias_value":"YYOLVEJWJAMY","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"YYOLVEJWJAMY2PI4","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"YYOLVEJW","created_at":"2026-05-18T12:33:33.725879+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/YYOLVEJWJAMY2PI4JN2LQAIS4S","json":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S.json","graph_json":"https://pith.science/api/pith-number/YYOLVEJWJAMY2PI4JN2LQAIS4S/graph.json","events_json":"https://pith.science/api/pith-number/YYOLVEJWJAMY2PI4JN2LQAIS4S/events.json","paper":"https://pith.science/paper/YYOLVEJW"},"agent_actions":{"view_html":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S","download_json":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S.json","view_paper":"https://pith.science/paper/YYOLVEJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01629&json=true","fetch_graph":"https://pith.science/api/pith-number/YYOLVEJWJAMY2PI4JN2LQAIS4S/graph.json","fetch_events":"https://pith.science/api/pith-number/YYOLVEJWJAMY2PI4JN2LQAIS4S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S/action/storage_attestation","attest_author":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S/action/author_attestation","sign_citation":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S/action/citation_signature","submit_replication":"https://pith.science/pith/YYOLVEJWJAMY2PI4JN2LQAIS4S/action/replication_record"}},"created_at":"2026-05-17T23:56:51.589905+00:00","updated_at":"2026-05-17T23:56:51.589905+00:00"}