{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V3BKDOH7CR2O6YHHWMNNW2JVQJ","short_pith_number":"pith:V3BKDOH7","schema_version":"1.0","canonical_sha256":"aec2a1b8ff1474ef60e7b31adb69358241befabcb5ff0138738f1ea8e469583b","source":{"kind":"arxiv","id":"1812.03964","version":5},"attestation_state":"computed","paper":{"title":"Periods of Complete Intersection Algebraic Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roberto Villaflor Loyola","submitted_at":"2018-12-10T18:20:16Z","abstract_excerpt":"For every even number $n$, and every $n$-dimensional smooth hypersurface of $\\mathbb{P}^{n+1}$ of degree $d$, we compute the periods of all its $\\frac{n}{2}$-dimensional complete intersection algebraic cycles. Furthermore, we determine the image of the given algebraic cycle under the cycle class map inside the De Rham cohomology group of the corresponding hypersurface in terms of its Griffiths basis and the polarization. As an application, we use this information to address variational Hodge conjecture for a non complete intersection algebraic cycle. We prove that the locus of general hypersur"},"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":"1812.03964","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-10T18:20:16Z","cross_cats_sorted":[],"title_canon_sha256":"abf95e074ce06783db30a04a54ea7d2e461feed305228695ecf09adbdba3029f","abstract_canon_sha256":"baaef06cfce72d3618a69f1e9d9e0ba7edef062c089ae98f888a0ebe1d256604"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:27:17.638877Z","signature_b64":"zKGWKV9Oahlxc1YZiQkoP3TX4cgc/+rVcesvS+GQhmvA/SfKOwWNeagN48x/TSPx7/SFD8cQZR/B1zE9757pBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aec2a1b8ff1474ef60e7b31adb69358241befabcb5ff0138738f1ea8e469583b","last_reissued_at":"2026-07-05T02:27:17.638471Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:27:17.638471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Periods of Complete Intersection Algebraic Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roberto Villaflor Loyola","submitted_at":"2018-12-10T18:20:16Z","abstract_excerpt":"For every even number $n$, and every $n$-dimensional smooth hypersurface of $\\mathbb{P}^{n+1}$ of degree $d$, we compute the periods of all its $\\frac{n}{2}$-dimensional complete intersection algebraic cycles. Furthermore, we determine the image of the given algebraic cycle under the cycle class map inside the De Rham cohomology group of the corresponding hypersurface in terms of its Griffiths basis and the polarization. As an application, we use this information to address variational Hodge conjecture for a non complete intersection algebraic cycle. We prove that the locus of general hypersur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03964","kind":"arxiv","version":5},"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/1812.03964/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":"1812.03964","created_at":"2026-07-05T02:27:17.638529+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.03964v5","created_at":"2026-07-05T02:27:17.638529+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03964","created_at":"2026-07-05T02:27:17.638529+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3BKDOH7CR2O","created_at":"2026-07-05T02:27:17.638529+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3BKDOH7CR2O6YHH","created_at":"2026-07-05T02:27:17.638529+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3BKDOH7","created_at":"2026-07-05T02:27:17.638529+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.03221","citing_title":"On reconstructing subvarieties from their periods","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ","json":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ.json","graph_json":"https://pith.science/api/pith-number/V3BKDOH7CR2O6YHHWMNNW2JVQJ/graph.json","events_json":"https://pith.science/api/pith-number/V3BKDOH7CR2O6YHHWMNNW2JVQJ/events.json","paper":"https://pith.science/paper/V3BKDOH7"},"agent_actions":{"view_html":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ","download_json":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ.json","view_paper":"https://pith.science/paper/V3BKDOH7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.03964&json=true","fetch_graph":"https://pith.science/api/pith-number/V3BKDOH7CR2O6YHHWMNNW2JVQJ/graph.json","fetch_events":"https://pith.science/api/pith-number/V3BKDOH7CR2O6YHHWMNNW2JVQJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ/action/storage_attestation","attest_author":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ/action/author_attestation","sign_citation":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ/action/citation_signature","submit_replication":"https://pith.science/pith/V3BKDOH7CR2O6YHHWMNNW2JVQJ/action/replication_record"}},"created_at":"2026-07-05T02:27:17.638529+00:00","updated_at":"2026-07-05T02:27:17.638529+00:00"}