{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:WJE5HPH4EDQG2WKEQHKSVGITVF","short_pith_number":"pith:WJE5HPH4","schema_version":"1.0","canonical_sha256":"b249d3bcfc20e06d594481d52a9913a94c35fd6ee0bf10bf803a5dca548ce2fd","source":{"kind":"arxiv","id":"1110.0563","version":1},"attestation_state":"computed","paper":{"title":"Strong L-spaces and left orderability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Simon Levine, Sam Lewallen","submitted_at":"2011-10-04T02:09:13Z","abstract_excerpt":"We introduce the notion of a strong L-space, a closed, oriented rational homology 3-sphere whose Heegaard Floer homology can be determined at the chain level. We prove that the fundamental group of a strong L-space is not left-orderable. Examples of strong L-spaces include the double branched covers of alternating links in S^3."},"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":"1110.0563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-10-04T02:09:13Z","cross_cats_sorted":[],"title_canon_sha256":"bee0d46335848956920a28d3f4d4e747792ccebf26697fa583a7aca63d4726ef","abstract_canon_sha256":"e96ad89995ca0c75c7ef02426d496d62569e898ded346e6242453fa6c5571fb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:49.735338Z","signature_b64":"AEPuE1dGhgoVbz40Yz9tAcUXUVeei3bfWUerrr+FyK5NqKilXwRpG/8TIDlfmlVa+xdWKj+KZDGeYsFMS97pBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b249d3bcfc20e06d594481d52a9913a94c35fd6ee0bf10bf803a5dca548ce2fd","last_reissued_at":"2026-05-18T02:52:49.734915Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:49.734915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong L-spaces and left orderability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Adam Simon Levine, Sam Lewallen","submitted_at":"2011-10-04T02:09:13Z","abstract_excerpt":"We introduce the notion of a strong L-space, a closed, oriented rational homology 3-sphere whose Heegaard Floer homology can be determined at the chain level. We prove that the fundamental group of a strong L-space is not left-orderable. Examples of strong L-spaces include the double branched covers of alternating links in S^3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0563","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":"1110.0563","created_at":"2026-05-18T02:52:49.734977+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.0563v1","created_at":"2026-05-18T02:52:49.734977+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0563","created_at":"2026-05-18T02:52:49.734977+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJE5HPH4EDQG","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJE5HPH4EDQG2WKE","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJE5HPH4","created_at":"2026-05-18T12:26:44.992195+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/WJE5HPH4EDQG2WKEQHKSVGITVF","json":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF.json","graph_json":"https://pith.science/api/pith-number/WJE5HPH4EDQG2WKEQHKSVGITVF/graph.json","events_json":"https://pith.science/api/pith-number/WJE5HPH4EDQG2WKEQHKSVGITVF/events.json","paper":"https://pith.science/paper/WJE5HPH4"},"agent_actions":{"view_html":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF","download_json":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF.json","view_paper":"https://pith.science/paper/WJE5HPH4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.0563&json=true","fetch_graph":"https://pith.science/api/pith-number/WJE5HPH4EDQG2WKEQHKSVGITVF/graph.json","fetch_events":"https://pith.science/api/pith-number/WJE5HPH4EDQG2WKEQHKSVGITVF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF/action/storage_attestation","attest_author":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF/action/author_attestation","sign_citation":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF/action/citation_signature","submit_replication":"https://pith.science/pith/WJE5HPH4EDQG2WKEQHKSVGITVF/action/replication_record"}},"created_at":"2026-05-18T02:52:49.734977+00:00","updated_at":"2026-05-18T02:52:49.734977+00:00"}