{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:4HHYVSK6KNHPM4LVXIUMAFSJWC","short_pith_number":"pith:4HHYVSK6","schema_version":"1.0","canonical_sha256":"e1cf8ac95e534ef67175ba28c01649b092c5e8a76e2d6124b74a5e1d6c2312d0","source":{"kind":"arxiv","id":"math/0602517","version":1},"attestation_state":"computed","paper":{"title":"Infinitely generated Lawson homology groups on some rational projective varieties","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Wenchuan Hu","submitted_at":"2006-02-23T02:25:45Z","abstract_excerpt":"We construct rational projective 4-dimensional varieties with the property that certain Lawson homology groups tensored with Q are infinite dimensional Q-vector spaces. More generally, each pair of integers p and k, with k\\geq 0, p>0, we find a projective variety Y, such that L_pH_{2p+k}(Y) is infinitely generated. We also construct two singular rational projective 3-dimensional varieties Y and Y' with the same homeomorphism type but different Lawson homology groups, specifically L_1H_3(Y) is not isomorphic to L_1H_3(Y')even up to torsion."},"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":"math/0602517","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-02-23T02:25:45Z","cross_cats_sorted":[],"title_canon_sha256":"5512a53e60a74f983b3c6b72f9b2f81d55c942a43e83316c1c191cd8bfb6e42b","abstract_canon_sha256":"6ac91b1fa606b9fd22e72e39ab1c74485387e01a637b5b65ea85bea701bdf71f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:53:25.959685Z","signature_b64":"G/mL544Eiwc2T5cdtQQ7ZPoXJAKg01h1t3L6U5DmjSEfGJzXlGk5dCZynHaxJgeNll1AFCKed91OMUMHasWRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1cf8ac95e534ef67175ba28c01649b092c5e8a76e2d6124b74a5e1d6c2312d0","last_reissued_at":"2026-07-04T14:53:25.959306Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:53:25.959306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely generated Lawson homology groups on some rational projective varieties","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Wenchuan Hu","submitted_at":"2006-02-23T02:25:45Z","abstract_excerpt":"We construct rational projective 4-dimensional varieties with the property that certain Lawson homology groups tensored with Q are infinite dimensional Q-vector spaces. More generally, each pair of integers p and k, with k\\geq 0, p>0, we find a projective variety Y, such that L_pH_{2p+k}(Y) is infinitely generated. We also construct two singular rational projective 3-dimensional varieties Y and Y' with the same homeomorphism type but different Lawson homology groups, specifically L_1H_3(Y) is not isomorphic to L_1H_3(Y')even up to torsion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602517","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0602517/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":"math/0602517","created_at":"2026-07-04T14:53:25.959368+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0602517v1","created_at":"2026-07-04T14:53:25.959368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602517","created_at":"2026-07-04T14:53:25.959368+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HHYVSK6KNHP","created_at":"2026-07-04T14:53:25.959368+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HHYVSK6KNHPM4LV","created_at":"2026-07-04T14:53:25.959368+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HHYVSK6","created_at":"2026-07-04T14:53:25.959368+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/4HHYVSK6KNHPM4LVXIUMAFSJWC","json":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC.json","graph_json":"https://pith.science/api/pith-number/4HHYVSK6KNHPM4LVXIUMAFSJWC/graph.json","events_json":"https://pith.science/api/pith-number/4HHYVSK6KNHPM4LVXIUMAFSJWC/events.json","paper":"https://pith.science/paper/4HHYVSK6"},"agent_actions":{"view_html":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC","download_json":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC.json","view_paper":"https://pith.science/paper/4HHYVSK6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0602517&json=true","fetch_graph":"https://pith.science/api/pith-number/4HHYVSK6KNHPM4LVXIUMAFSJWC/graph.json","fetch_events":"https://pith.science/api/pith-number/4HHYVSK6KNHPM4LVXIUMAFSJWC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC/action/storage_attestation","attest_author":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC/action/author_attestation","sign_citation":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC/action/citation_signature","submit_replication":"https://pith.science/pith/4HHYVSK6KNHPM4LVXIUMAFSJWC/action/replication_record"}},"created_at":"2026-07-04T14:53:25.959368+00:00","updated_at":"2026-07-04T14:53:25.959368+00:00"}