{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:OXR4WWQWPHZR6TPA6DCZUBZELA","short_pith_number":"pith:OXR4WWQW","schema_version":"1.0","canonical_sha256":"75e3cb5a1679f31f4de0f0c59a0724582a677e0b9a781b2adabb6a21067ee462","source":{"kind":"arxiv","id":"0711.1517","version":2},"attestation_state":"computed","paper":{"title":"Combinatorial polar orderings and recursively orderable arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Emanuele Delucchi, Simona Settepanella","submitted_at":"2007-11-09T18:08:28Z","abstract_excerpt":"Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal complex is particularly easy, called {\\em recursively orderable} arrangements, can therefore be combinatorially defined. We initiate the study of this class, giving a complete characterization in dimension 2"},"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":"0711.1517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-11-09T18:08:28Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"9e5b1e462ffa2d7d05bab73f2da97cc1f4950b39923ad18652e0515dde1ffbf8","abstract_canon_sha256":"ad5909bf4dd3aaa0d6d91b2470ef50405bf841e1f9594d5fbd989ab56b9fe73c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:24.277590Z","signature_b64":"HmP7Wi2vkR+L7Y8or58ejYqVPPOUYCEaFxRKsn6anVJTytvv4Jenq0ASBBPEi3NaMfVk70hOfSKUAdcLdDFyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75e3cb5a1679f31f4de0f0c59a0724582a677e0b9a781b2adabb6a21067ee462","last_reissued_at":"2026-05-18T03:42:24.277172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:24.277172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial polar orderings and recursively orderable arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Emanuele Delucchi, Simona Settepanella","submitted_at":"2007-11-09T18:08:28Z","abstract_excerpt":"Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal complex is particularly easy, called {\\em recursively orderable} arrangements, can therefore be combinatorially defined. We initiate the study of this class, giving a complete characterization in dimension 2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1517","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":"0711.1517","created_at":"2026-05-18T03:42:24.277227+00:00"},{"alias_kind":"arxiv_version","alias_value":"0711.1517v2","created_at":"2026-05-18T03:42:24.277227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.1517","created_at":"2026-05-18T03:42:24.277227+00:00"},{"alias_kind":"pith_short_12","alias_value":"OXR4WWQWPHZR","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"OXR4WWQWPHZR6TPA","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"OXR4WWQW","created_at":"2026-05-18T12:25:55.427421+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/OXR4WWQWPHZR6TPA6DCZUBZELA","json":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA.json","graph_json":"https://pith.science/api/pith-number/OXR4WWQWPHZR6TPA6DCZUBZELA/graph.json","events_json":"https://pith.science/api/pith-number/OXR4WWQWPHZR6TPA6DCZUBZELA/events.json","paper":"https://pith.science/paper/OXR4WWQW"},"agent_actions":{"view_html":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA","download_json":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA.json","view_paper":"https://pith.science/paper/OXR4WWQW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0711.1517&json=true","fetch_graph":"https://pith.science/api/pith-number/OXR4WWQWPHZR6TPA6DCZUBZELA/graph.json","fetch_events":"https://pith.science/api/pith-number/OXR4WWQWPHZR6TPA6DCZUBZELA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA/action/storage_attestation","attest_author":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA/action/author_attestation","sign_citation":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA/action/citation_signature","submit_replication":"https://pith.science/pith/OXR4WWQWPHZR6TPA6DCZUBZELA/action/replication_record"}},"created_at":"2026-05-18T03:42:24.277227+00:00","updated_at":"2026-05-18T03:42:24.277227+00:00"}