{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7UDBSJCOWIG4BO4LPESDCCVBEB","short_pith_number":"pith:7UDBSJCO","schema_version":"1.0","canonical_sha256":"fd0619244eb20dc0bb8b7924310aa120537a9532aec1c96f618c46539e5ab18c","source":{"kind":"arxiv","id":"1304.0808","version":3},"attestation_state":"computed","paper":{"title":"Essential Circles and Gromov-Hausdorff Convergence of Covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Conrad Plaut, Jay Wilkins","submitted_at":"2013-04-02T22:30:35Z","abstract_excerpt":"We give various applications of essential circles (introduced in an earlier paper by the authors) in a compact geodesic space X. Essential circles completely determine the homotopy critical spectrum of X, which we show is precisely 2/3 the covering spectrum of Sormani-Wei. We use finite collections of essential circles to define \"circle covers,\" which extend and contain as special cases the delta-covers of Sormani and Wei (equivalently the epsilon-covers of the authors); the constructions are metric adaptations of those utilized by Berestovskii-Plaut in the construction of entourage covers of "},"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":"1304.0808","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-02T22:30:35Z","cross_cats_sorted":[],"title_canon_sha256":"e03a53ac61ac03d3b28e94d57a33882ed6fd50525a900a4d9f7c5455b0160195","abstract_canon_sha256":"cebed50a78a8b922a01c4dafc2edda79ed752422d3cc0fab770de57b262c1ee0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:33.418767Z","signature_b64":"ct3iOjqo3szkV3NWFw2NBFe+hXM6JHfShgOD5/ZA/XSl5q3XKQtp7gynvnCqi8GX4VRnOvyf/Iwf08rbiLa5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd0619244eb20dc0bb8b7924310aa120537a9532aec1c96f618c46539e5ab18c","last_reissued_at":"2026-05-18T03:01:33.418324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:33.418324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Essential Circles and Gromov-Hausdorff Convergence of Covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Conrad Plaut, Jay Wilkins","submitted_at":"2013-04-02T22:30:35Z","abstract_excerpt":"We give various applications of essential circles (introduced in an earlier paper by the authors) in a compact geodesic space X. Essential circles completely determine the homotopy critical spectrum of X, which we show is precisely 2/3 the covering spectrum of Sormani-Wei. We use finite collections of essential circles to define \"circle covers,\" which extend and contain as special cases the delta-covers of Sormani and Wei (equivalently the epsilon-covers of the authors); the constructions are metric adaptations of those utilized by Berestovskii-Plaut in the construction of entourage covers of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0808","kind":"arxiv","version":3},"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":"1304.0808","created_at":"2026-05-18T03:01:33.418395+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.0808v3","created_at":"2026-05-18T03:01:33.418395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0808","created_at":"2026-05-18T03:01:33.418395+00:00"},{"alias_kind":"pith_short_12","alias_value":"7UDBSJCOWIG4","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"7UDBSJCOWIG4BO4L","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"7UDBSJCO","created_at":"2026-05-18T12:27:36.564083+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/7UDBSJCOWIG4BO4LPESDCCVBEB","json":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB.json","graph_json":"https://pith.science/api/pith-number/7UDBSJCOWIG4BO4LPESDCCVBEB/graph.json","events_json":"https://pith.science/api/pith-number/7UDBSJCOWIG4BO4LPESDCCVBEB/events.json","paper":"https://pith.science/paper/7UDBSJCO"},"agent_actions":{"view_html":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB","download_json":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB.json","view_paper":"https://pith.science/paper/7UDBSJCO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.0808&json=true","fetch_graph":"https://pith.science/api/pith-number/7UDBSJCOWIG4BO4LPESDCCVBEB/graph.json","fetch_events":"https://pith.science/api/pith-number/7UDBSJCOWIG4BO4LPESDCCVBEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB/action/storage_attestation","attest_author":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB/action/author_attestation","sign_citation":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB/action/citation_signature","submit_replication":"https://pith.science/pith/7UDBSJCOWIG4BO4LPESDCCVBEB/action/replication_record"}},"created_at":"2026-05-18T03:01:33.418395+00:00","updated_at":"2026-05-18T03:01:33.418395+00:00"}