{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:DTIYAYSHQPF2YG3W7WC6HQTYCJ","short_pith_number":"pith:DTIYAYSH","schema_version":"1.0","canonical_sha256":"1cd180624783cbac1b76fd85e3c278127af997f124d0351502cfa202f16ed3f4","source":{"kind":"arxiv","id":"2006.08057","version":7},"attestation_state":"computed","paper":{"title":"$PD_3$-pairs with compressible boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Jonathan A. Hillman","submitted_at":"2020-06-15T00:06:08Z","abstract_excerpt":"We extend work of Turaev and Bleile to relax the $\\pi_1$-injectivity hypothesis in the characterization of the fundamental triples of $PD_3$-pairs with aspherical boundary components. This is further extended to pairs $(P,\\partial{P})$ which also have spherical boundary components and with $c.d.\\pi_1(P)\\leq2$."},"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":"2006.08057","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2020-06-15T00:06:08Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"005af5a1fed1d6a5964363c46367197693d782f52f542cc24d437d673af279d3","abstract_canon_sha256":"436936d9c1249ba703bee8d40501bbf6112712740ae9377d385874281f6439da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:18.644723Z","signature_b64":"ZLMk2pJ69DNPahAS1821sj08B+5TfHLEyQgwqqK4RyBptWLMzETnRjwHeAkmnH4Pk4cBPY74/Wlx4se2xJ2lCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cd180624783cbac1b76fd85e3c278127af997f124d0351502cfa202f16ed3f4","last_reissued_at":"2026-05-17T23:39:18.643801Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:18.643801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$PD_3$-pairs with compressible boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Jonathan A. Hillman","submitted_at":"2020-06-15T00:06:08Z","abstract_excerpt":"We extend work of Turaev and Bleile to relax the $\\pi_1$-injectivity hypothesis in the characterization of the fundamental triples of $PD_3$-pairs with aspherical boundary components. This is further extended to pairs $(P,\\partial{P})$ which also have spherical boundary components and with $c.d.\\pi_1(P)\\leq2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08057","kind":"arxiv","version":7},"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":"2006.08057","created_at":"2026-05-17T23:39:18.643957+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.08057v7","created_at":"2026-05-17T23:39:18.643957+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08057","created_at":"2026-05-17T23:39:18.643957+00:00"},{"alias_kind":"pith_short_12","alias_value":"DTIYAYSHQPF2","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"DTIYAYSHQPF2YG3W","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"DTIYAYSH","created_at":"2026-05-18T12:33:33.725879+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/DTIYAYSHQPF2YG3W7WC6HQTYCJ","json":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ.json","graph_json":"https://pith.science/api/pith-number/DTIYAYSHQPF2YG3W7WC6HQTYCJ/graph.json","events_json":"https://pith.science/api/pith-number/DTIYAYSHQPF2YG3W7WC6HQTYCJ/events.json","paper":"https://pith.science/paper/DTIYAYSH"},"agent_actions":{"view_html":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ","download_json":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ.json","view_paper":"https://pith.science/paper/DTIYAYSH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.08057&json=true","fetch_graph":"https://pith.science/api/pith-number/DTIYAYSHQPF2YG3W7WC6HQTYCJ/graph.json","fetch_events":"https://pith.science/api/pith-number/DTIYAYSHQPF2YG3W7WC6HQTYCJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ/action/storage_attestation","attest_author":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ/action/author_attestation","sign_citation":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ/action/citation_signature","submit_replication":"https://pith.science/pith/DTIYAYSHQPF2YG3W7WC6HQTYCJ/action/replication_record"}},"created_at":"2026-05-17T23:39:18.643957+00:00","updated_at":"2026-05-17T23:39:18.643957+00:00"}