{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PNYD7CHZMTMYN4K2RCKWNYOA2D","short_pith_number":"pith:PNYD7CHZ","schema_version":"1.0","canonical_sha256":"7b703f88f964d986f15a889566e1c0d0c56c1d4cf83d33faabad2b65cab73014","source":{"kind":"arxiv","id":"1108.2717","version":1},"attestation_state":"computed","paper":{"title":"On four-dimensional 2-handlebodies and three-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ivelina Bobtcheva, Riccardo Piergallini","submitted_at":"2011-08-12T21:01:58Z","abstract_excerpt":"We show that for any n > 3 there exists an equivalence functor from the category of n-fold connected simple coverings of B^3 x [0, 1] branched over ribbon surface tangles up to certain local ribbon moves, to the category Chb^{3+1} of orientable relative 4-dimensional 2-handlebody cobordisms up to 2-deformations. As a consequence, we obtain an equivalence theorem for simple coverings of S^3 branched over links, which provides a complete solution to the long-standing Fox-Montesinos covering moves problem. This last result generalizes to coverings of any degree results by the second author and Ap"},"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":"1108.2717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-08-12T21:01:58Z","cross_cats_sorted":[],"title_canon_sha256":"800d830cfa1ceb5cd37df7c4b3a20bc0e9950d8f564de081d6b60d5065c5f93d","abstract_canon_sha256":"970a58a182e9ee6d8b41eb522855885b481a768553992f9567126ce204574047"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:41.932967Z","signature_b64":"AYbZZ4XwqWS9eK6oOL5NFST42qKm9Uvau4KKkU7xMt3hNFt71BEsyX9pu1lkggMFKG+5wyk/JHqqB1zQvMmUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b703f88f964d986f15a889566e1c0d0c56c1d4cf83d33faabad2b65cab73014","last_reissued_at":"2026-05-18T02:21:41.932542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:41.932542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On four-dimensional 2-handlebodies and three-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ivelina Bobtcheva, Riccardo Piergallini","submitted_at":"2011-08-12T21:01:58Z","abstract_excerpt":"We show that for any n > 3 there exists an equivalence functor from the category of n-fold connected simple coverings of B^3 x [0, 1] branched over ribbon surface tangles up to certain local ribbon moves, to the category Chb^{3+1} of orientable relative 4-dimensional 2-handlebody cobordisms up to 2-deformations. As a consequence, we obtain an equivalence theorem for simple coverings of S^3 branched over links, which provides a complete solution to the long-standing Fox-Montesinos covering moves problem. This last result generalizes to coverings of any degree results by the second author and Ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2717","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":""},"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":"1108.2717","created_at":"2026-05-18T02:21:41.932613+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2717v1","created_at":"2026-05-18T02:21:41.932613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2717","created_at":"2026-05-18T02:21:41.932613+00:00"},{"alias_kind":"pith_short_12","alias_value":"PNYD7CHZMTMY","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PNYD7CHZMTMYN4K2","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PNYD7CHZ","created_at":"2026-05-18T12:26:39.201973+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/PNYD7CHZMTMYN4K2RCKWNYOA2D","json":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D.json","graph_json":"https://pith.science/api/pith-number/PNYD7CHZMTMYN4K2RCKWNYOA2D/graph.json","events_json":"https://pith.science/api/pith-number/PNYD7CHZMTMYN4K2RCKWNYOA2D/events.json","paper":"https://pith.science/paper/PNYD7CHZ"},"agent_actions":{"view_html":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D","download_json":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D.json","view_paper":"https://pith.science/paper/PNYD7CHZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2717&json=true","fetch_graph":"https://pith.science/api/pith-number/PNYD7CHZMTMYN4K2RCKWNYOA2D/graph.json","fetch_events":"https://pith.science/api/pith-number/PNYD7CHZMTMYN4K2RCKWNYOA2D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D/action/storage_attestation","attest_author":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D/action/author_attestation","sign_citation":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D/action/citation_signature","submit_replication":"https://pith.science/pith/PNYD7CHZMTMYN4K2RCKWNYOA2D/action/replication_record"}},"created_at":"2026-05-18T02:21:41.932613+00:00","updated_at":"2026-05-18T02:21:41.932613+00:00"}