{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KGEXDMBC4YXNZSNUMNIFRSD3KC","short_pith_number":"pith:KGEXDMBC","schema_version":"1.0","canonical_sha256":"518971b022e62edcc9b4635058c87b50a8f2dcfc468b257c28578fca4633ee24","source":{"kind":"arxiv","id":"1802.01538","version":1},"attestation_state":"computed","paper":{"title":"Some remarks on PL collapsible covers of 2-dimensional polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Eugenio Borghini","submitted_at":"2018-02-05T18:05:42Z","abstract_excerpt":"We analyze the topology and geometry of a polyhedron of dimension 2 according to the minimum size of a cover by PL collapsible polyhedra. We provide partial characterizations of the polyhedra of dimension 2 that can be decomposed as the union of two PL collapsible subpolyhedra in terms of their simple homotopy type and certain local properties. In the process, a special class of polyhedra of dimension 2 appears naturally. We give a combinatorial description of the spaces in this class, which includes all closed surfaces and the complexes associated to one-relator presentations."},"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":"1802.01538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-02-05T18:05:42Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"04646e3c1af3e821840e1c74d88dce0594d539048e109f4eb594786d419db433","abstract_canon_sha256":"8ce26594395c76ba1f204914472cf2f6e970b91bc2f03620b0b8be58bcdddfb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:25.623098Z","signature_b64":"83VH8/nHCNS4XJaaVe4QAjpIjfzbH9gEKtaLRtMT9EZpxzGsyFAHD0SxZEea4mPZK7VqARdIh+6ERi318/sEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"518971b022e62edcc9b4635058c87b50a8f2dcfc468b257c28578fca4633ee24","last_reissued_at":"2026-05-18T00:24:25.622616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:25.622616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some remarks on PL collapsible covers of 2-dimensional polyhedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Eugenio Borghini","submitted_at":"2018-02-05T18:05:42Z","abstract_excerpt":"We analyze the topology and geometry of a polyhedron of dimension 2 according to the minimum size of a cover by PL collapsible polyhedra. We provide partial characterizations of the polyhedra of dimension 2 that can be decomposed as the union of two PL collapsible subpolyhedra in terms of their simple homotopy type and certain local properties. In the process, a special class of polyhedra of dimension 2 appears naturally. We give a combinatorial description of the spaces in this class, which includes all closed surfaces and the complexes associated to one-relator presentations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01538","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":"1802.01538","created_at":"2026-05-18T00:24:25.622696+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01538v1","created_at":"2026-05-18T00:24:25.622696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01538","created_at":"2026-05-18T00:24:25.622696+00:00"},{"alias_kind":"pith_short_12","alias_value":"KGEXDMBC4YXN","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KGEXDMBC4YXNZSNU","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KGEXDMBC","created_at":"2026-05-18T12:32:33.847187+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/KGEXDMBC4YXNZSNUMNIFRSD3KC","json":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC.json","graph_json":"https://pith.science/api/pith-number/KGEXDMBC4YXNZSNUMNIFRSD3KC/graph.json","events_json":"https://pith.science/api/pith-number/KGEXDMBC4YXNZSNUMNIFRSD3KC/events.json","paper":"https://pith.science/paper/KGEXDMBC"},"agent_actions":{"view_html":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC","download_json":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC.json","view_paper":"https://pith.science/paper/KGEXDMBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01538&json=true","fetch_graph":"https://pith.science/api/pith-number/KGEXDMBC4YXNZSNUMNIFRSD3KC/graph.json","fetch_events":"https://pith.science/api/pith-number/KGEXDMBC4YXNZSNUMNIFRSD3KC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC/action/storage_attestation","attest_author":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC/action/author_attestation","sign_citation":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC/action/citation_signature","submit_replication":"https://pith.science/pith/KGEXDMBC4YXNZSNUMNIFRSD3KC/action/replication_record"}},"created_at":"2026-05-18T00:24:25.622696+00:00","updated_at":"2026-05-18T00:24:25.622696+00:00"}