{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YLDBKDML3Y6OWFEYRP2JCKEKJE","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":"6123469494dc6ad54076e3758d0ef90eb03f9b8c3d8fabd7bbc7a18d81261a15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-08T16:12:10Z","title_canon_sha256":"a299f16ff28133b6d566c95dc9a38dedcb33c2c40c1ae345f291b3cc31e70b68"},"schema_version":"1.0","source":{"id":"1403.1983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1983","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1983v1","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1983","created_at":"2026-05-18T02:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"YLDBKDML3Y6O","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YLDBKDML3Y6OWFEY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YLDBKDML","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:2dbc1252f48f548c4ed3899f853e8f76700d69660e4c4dcfab3ed2f23b88aad3","target":"graph","created_at":"2026-05-18T02:56:51Z","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":"In this article we study the bordism groups of normally nonsingular maps $f: X \\to Y$ defined on pseudomanifolds $X$ and $Y$. To characterize the bordism of such maps, inspired by the formula given by Stong, we give a general definition of Stiefel-Whitney numbers defined on $X$ and $Y$ using the Wu classes defined by Goresky and Pardon and we show that in several cases the cobordism class of a normally nonsingular map $f:X \\to Y$ guarantees that these numbers are zero.","authors_text":"Alice Kimie Miwa Libardi, Eliris Rizziolli, Jean-Paul Brasselet, Marcelo Saia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-08T16:12:10Z","title":"Cobordism of maps on $Z_2$-Witt spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1983","kind":"arxiv","version":1},"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:b75b1c6518151399d46b405c5d002a890f4a63b49dfdd67f572d2ae0367d263f","target":"record","created_at":"2026-05-18T02:56:51Z","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":"6123469494dc6ad54076e3758d0ef90eb03f9b8c3d8fabd7bbc7a18d81261a15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-08T16:12:10Z","title_canon_sha256":"a299f16ff28133b6d566c95dc9a38dedcb33c2c40c1ae345f291b3cc31e70b68"},"schema_version":"1.0","source":{"id":"1403.1983","kind":"arxiv","version":1}},"canonical_sha256":"c2c6150d8bde3ceb14988bf491288a4930f660840d303e785d4c2487078facec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2c6150d8bde3ceb14988bf491288a4930f660840d303e785d4c2487078facec","first_computed_at":"2026-05-18T02:56:51.134008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:51.134008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tu8Szd8Qg7TjXk2HzvS4XagT4fS3fRmUg5IVdQnuyw9TnoV5kXYRI6HzfN5XILekNqlWgS8b2E42+c/WX8SdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:51.134440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b75b1c6518151399d46b405c5d002a890f4a63b49dfdd67f572d2ae0367d263f","sha256:2dbc1252f48f548c4ed3899f853e8f76700d69660e4c4dcfab3ed2f23b88aad3"],"state_sha256":"0f21726baf18fd36944c472405ed4d509f9009b6faf0e6577fb47901de0296e6"}