{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DNHCQG2IKYLY4NNGUMNS6MYGXI","short_pith_number":"pith:DNHCQG2I","schema_version":"1.0","canonical_sha256":"1b4e281b4856178e35a6a31b2f3306ba3ffb920715c169cd18f7bdd6a5b00cfb","source":{"kind":"arxiv","id":"1307.6831","version":2},"attestation_state":"computed","paper":{"title":"Secondary characteristic classes and the Euler class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Aravind Asok, Jean Fasel","submitted_at":"2013-07-25T18:15:59Z","abstract_excerpt":"We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We show that if X is a smooth affine scheme of dimension d over a field k of finite 2-cohomological dimension (with char(k) $\\neq$ 2) and E is a rank d vector bundle over X, vanishing of the Chow-Witt theoretic Euler class of E is equivalent to vanishing of its top Chern class and these higher classes. We then derive some consequences of our main theorem when k is of small 2-cohomological dimension."},"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":"1307.6831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-25T18:15:59Z","cross_cats_sorted":["math.AC","math.AT","math.KT"],"title_canon_sha256":"2cfa58873a390dedcfcd5db051817c48fdb5ac7127199f6bc5436f208ad83452","abstract_canon_sha256":"90ba087a5371dc8be369c77302c7e4cc358966903b9f141fd1b5f216ef388ba1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:08.654896Z","signature_b64":"GW9dZJ0K/aYCXoIFh9fo3OhiOVhnebriY+qCT5FnmbkqKZNojbhhKPgyW5+k9hCt18sg5L6bYTotKdaeKiwvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b4e281b4856178e35a6a31b2f3306ba3ffb920715c169cd18f7bdd6a5b00cfb","last_reissued_at":"2026-05-18T02:19:08.654451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:08.654451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Secondary characteristic classes and the Euler class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Aravind Asok, Jean Fasel","submitted_at":"2013-07-25T18:15:59Z","abstract_excerpt":"We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We show that if X is a smooth affine scheme of dimension d over a field k of finite 2-cohomological dimension (with char(k) $\\neq$ 2) and E is a rank d vector bundle over X, vanishing of the Chow-Witt theoretic Euler class of E is equivalent to vanishing of its top Chern class and these higher classes. We then derive some consequences of our main theorem when k is of small 2-cohomological dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6831","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":""},"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":"1307.6831","created_at":"2026-05-18T02:19:08.654518+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.6831v2","created_at":"2026-05-18T02:19:08.654518+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6831","created_at":"2026-05-18T02:19:08.654518+00:00"},{"alias_kind":"pith_short_12","alias_value":"DNHCQG2IKYLY","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DNHCQG2IKYLY4NNG","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DNHCQG2I","created_at":"2026-05-18T12:27:43.054852+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/DNHCQG2IKYLY4NNGUMNS6MYGXI","json":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI.json","graph_json":"https://pith.science/api/pith-number/DNHCQG2IKYLY4NNGUMNS6MYGXI/graph.json","events_json":"https://pith.science/api/pith-number/DNHCQG2IKYLY4NNGUMNS6MYGXI/events.json","paper":"https://pith.science/paper/DNHCQG2I"},"agent_actions":{"view_html":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI","download_json":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI.json","view_paper":"https://pith.science/paper/DNHCQG2I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.6831&json=true","fetch_graph":"https://pith.science/api/pith-number/DNHCQG2IKYLY4NNGUMNS6MYGXI/graph.json","fetch_events":"https://pith.science/api/pith-number/DNHCQG2IKYLY4NNGUMNS6MYGXI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/action/storage_attestation","attest_author":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/action/author_attestation","sign_citation":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/action/citation_signature","submit_replication":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/action/replication_record"}},"created_at":"2026-05-18T02:19:08.654518+00:00","updated_at":"2026-05-18T02:19:08.654518+00:00"}