{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DNHCQG2IKYLY4NNGUMNS6MYGXI","short_pith_number":"pith:DNHCQG2I","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"},"canonical_sha256":"1b4e281b4856178e35a6a31b2f3306ba3ffb920715c169cd18f7bdd6a5b00cfb","source":{"kind":"arxiv","id":"1307.6831","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6831","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6831v2","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6831","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"DNHCQG2IKYLY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DNHCQG2IKYLY4NNG","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DNHCQG2I","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DNHCQG2IKYLY4NNGUMNS6MYGXI","target":"record","payload":{"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"},"canonical_sha256":"1b4e281b4856178e35a6a31b2f3306ba3ffb920715c169cd18f7bdd6a5b00cfb","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"},"source_kind":"arxiv","source_id":"1307.6831","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzMq4DaHpk5YBvZ0AK4fOr3DE5s4Fwe+5PjJJzb/ZfBa/W6z/dlsk2SO7Bw19+155ix3zz03PMqrGAxlicrDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:03:50.219473Z"},"content_sha256":"2a3868a743fd81a3fd408c7a98fb0d2afa2a29a55cf703fc9b764e410a83a25e","schema_version":"1.0","event_id":"sha256:2a3868a743fd81a3fd408c7a98fb0d2afa2a29a55cf703fc9b764e410a83a25e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DNHCQG2IKYLY4NNGUMNS6MYGXI","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XMVuO5cQ5HBk6Kmt8zQB3keNEZmcdrEO/9/IjBdqbTJhRHGXBeAUqJkC4s21w0TXSj0Zv2i3+qdH6+JRWXaoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:03:50.219818Z"},"content_sha256":"a753f225e265f8d7ffc6ce2659a66b80f8149cea7ad6afc13824c7556f6c65f1","schema_version":"1.0","event_id":"sha256:a753f225e265f8d7ffc6ce2659a66b80f8149cea7ad6afc13824c7556f6c65f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/bundle.json","state_url":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T14:03:50Z","links":{"resolver":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI","bundle":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/bundle.json","state":"https://pith.science/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNHCQG2IKYLY4NNGUMNS6MYGXI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DNHCQG2IKYLY4NNGUMNS6MYGXI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"90ba087a5371dc8be369c77302c7e4cc358966903b9f141fd1b5f216ef388ba1","cross_cats_sorted":["math.AC","math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-25T18:15:59Z","title_canon_sha256":"2cfa58873a390dedcfcd5db051817c48fdb5ac7127199f6bc5436f208ad83452"},"schema_version":"1.0","source":{"id":"1307.6831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6831","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6831v2","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6831","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"DNHCQG2IKYLY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DNHCQG2IKYLY4NNG","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DNHCQG2I","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:a753f225e265f8d7ffc6ce2659a66b80f8149cea7ad6afc13824c7556f6c65f1","target":"graph","created_at":"2026-05-18T02:19:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Aravind Asok, Jean Fasel","cross_cats":["math.AC","math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-25T18:15:59Z","title":"Secondary characteristic classes and the Euler class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6831","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2a3868a743fd81a3fd408c7a98fb0d2afa2a29a55cf703fc9b764e410a83a25e","target":"record","created_at":"2026-05-18T02:19:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"90ba087a5371dc8be369c77302c7e4cc358966903b9f141fd1b5f216ef388ba1","cross_cats_sorted":["math.AC","math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-07-25T18:15:59Z","title_canon_sha256":"2cfa58873a390dedcfcd5db051817c48fdb5ac7127199f6bc5436f208ad83452"},"schema_version":"1.0","source":{"id":"1307.6831","kind":"arxiv","version":2}},"canonical_sha256":"1b4e281b4856178e35a6a31b2f3306ba3ffb920715c169cd18f7bdd6a5b00cfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b4e281b4856178e35a6a31b2f3306ba3ffb920715c169cd18f7bdd6a5b00cfb","first_computed_at":"2026-05-18T02:19:08.654451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:08.654451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GW9dZJ0K/aYCXoIFh9fo3OhiOVhnebriY+qCT5FnmbkqKZNojbhhKPgyW5+k9hCt18sg5L6bYTotKdaeKiwvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:08.654896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a3868a743fd81a3fd408c7a98fb0d2afa2a29a55cf703fc9b764e410a83a25e","sha256:a753f225e265f8d7ffc6ce2659a66b80f8149cea7ad6afc13824c7556f6c65f1"],"state_sha256":"f037e89fe4e9de9fe774644ce835fe5fe47f2399181af2c9cb9f1ccd59a72337"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWKQh8aKPSVzJmfmpYdBrQbC1bHQR6iaITbPXMQwWm2Ny//fl+a2Wz9yQGkbJWW1RwjW8qhdUuLHrRRAeRanBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:03:50.221926Z","bundle_sha256":"5da263d4e081f731227fc2369a730ec515ee2d426d353a55d882c22f56c52033"}}