{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QN26GMRF2MD64EVYJ33RFEFA4D","short_pith_number":"pith:QN26GMRF","schema_version":"1.0","canonical_sha256":"8375e33225d307ee12b84ef71290a0e0dc1c1369184f78f1700185f5299db6c8","source":{"kind":"arxiv","id":"1211.0076","version":5},"attestation_state":"computed","paper":{"title":"On the homotopy of Q(3) and Q(5) at the prime 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Kyle Ormsby, Mark Behrens","submitted_at":"2012-11-01T02:26:36Z","abstract_excerpt":"We study modular approximations Q(l), l = 3,5, of the K(2)-local sphere at the prime 2 that arise from l-power degree isogenies of elliptic curves. We develop Hopf algebroid level tools for working with Q(l) and record Hill, Hopkins, and Ravenel's computation of the homotopy groups of TMF_0(5). Using these tools and formulas of Mahowald and Rezk for Q(3) we determine the image of Shimomura's 2-primary divided beta-family in the Adams-Novikov spectral sequences for Q(3) and Q(5). Finally, we use low-dimensional computations of the homotopy of Q(3) and Q(5) to explore the role of these spectra a"},"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":"1211.0076","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-11-01T02:26:36Z","cross_cats_sorted":[],"title_canon_sha256":"0fe257b37253499b0d77f67becd011158ac065afcdc5af8297529e08f1d1e628","abstract_canon_sha256":"db9e7b757e0314b48b062e65da79efac3677bfef2a8ed4127290ec53c5985e6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:49.201492Z","signature_b64":"OS66+mhlw0nS4IegufidcU5Bg5Ec6gxMADjsdrzF+/aBaqY9ZDZx7uEgb8xyXpo/oFDnrlDHyH8cBoeNMxl4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8375e33225d307ee12b84ef71290a0e0dc1c1369184f78f1700185f5299db6c8","last_reissued_at":"2026-05-18T00:58:49.200970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:49.200970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the homotopy of Q(3) and Q(5) at the prime 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Kyle Ormsby, Mark Behrens","submitted_at":"2012-11-01T02:26:36Z","abstract_excerpt":"We study modular approximations Q(l), l = 3,5, of the K(2)-local sphere at the prime 2 that arise from l-power degree isogenies of elliptic curves. We develop Hopf algebroid level tools for working with Q(l) and record Hill, Hopkins, and Ravenel's computation of the homotopy groups of TMF_0(5). Using these tools and formulas of Mahowald and Rezk for Q(3) we determine the image of Shimomura's 2-primary divided beta-family in the Adams-Novikov spectral sequences for Q(3) and Q(5). Finally, we use low-dimensional computations of the homotopy of Q(3) and Q(5) to explore the role of these spectra a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0076","kind":"arxiv","version":5},"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":"1211.0076","created_at":"2026-05-18T00:58:49.201052+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.0076v5","created_at":"2026-05-18T00:58:49.201052+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0076","created_at":"2026-05-18T00:58:49.201052+00:00"},{"alias_kind":"pith_short_12","alias_value":"QN26GMRF2MD6","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QN26GMRF2MD64EVY","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QN26GMRF","created_at":"2026-05-18T12:27:18.751474+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/QN26GMRF2MD64EVYJ33RFEFA4D","json":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D.json","graph_json":"https://pith.science/api/pith-number/QN26GMRF2MD64EVYJ33RFEFA4D/graph.json","events_json":"https://pith.science/api/pith-number/QN26GMRF2MD64EVYJ33RFEFA4D/events.json","paper":"https://pith.science/paper/QN26GMRF"},"agent_actions":{"view_html":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D","download_json":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D.json","view_paper":"https://pith.science/paper/QN26GMRF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.0076&json=true","fetch_graph":"https://pith.science/api/pith-number/QN26GMRF2MD64EVYJ33RFEFA4D/graph.json","fetch_events":"https://pith.science/api/pith-number/QN26GMRF2MD64EVYJ33RFEFA4D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D/action/storage_attestation","attest_author":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D/action/author_attestation","sign_citation":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D/action/citation_signature","submit_replication":"https://pith.science/pith/QN26GMRF2MD64EVYJ33RFEFA4D/action/replication_record"}},"created_at":"2026-05-18T00:58:49.201052+00:00","updated_at":"2026-05-18T00:58:49.201052+00:00"}