{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YYSJTX7NQ2K4O4YI6LRFRY7NSS","short_pith_number":"pith:YYSJTX7N","schema_version":"1.0","canonical_sha256":"c62499dfed8695c77308f2e258e3ed94941e2db71d47d6cf2ad3fa93e3132005","source":{"kind":"arxiv","id":"1505.01476","version":1},"attestation_state":"computed","paper":{"title":"The Structure of Motivic Homotopy Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bogdan Gheorghe, Daniel C. Isaksen","submitted_at":"2015-05-06T19:51:58Z","abstract_excerpt":"We study the stable motivic homotopy groups $\\pi_{s,w}$ of the 2-completion of the motivic sphere spectrum over $\\mathbb{C}$. When arranged in the $(s,w)$-plane, these groups break into four different regions: a vanishing region, an $\\eta$-local region that is entirely known, a $\\tau$-local region that is identical to classical stable homotopy groups, and a region that is not well-understood."},"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":"1505.01476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-05-06T19:51:58Z","cross_cats_sorted":[],"title_canon_sha256":"093af37da34bb577e54fab38d3863f897f92bc2d79f60a700cf050814f22e858","abstract_canon_sha256":"11242d95de3329f8294ac24aaa2b229fc2a7239e5e00cf0dda2c47c7444730ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:49.163453Z","signature_b64":"zR8D81Oba32zpcD5AgvYF1ln5VJ9J/3EgaUzevvu4sn6rCWt+3gYEfKsm50w103qmLFYPQ2bmXTxIWsiE1KcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c62499dfed8695c77308f2e258e3ed94941e2db71d47d6cf2ad3fa93e3132005","last_reissued_at":"2026-05-18T02:16:49.162724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:49.162724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Structure of Motivic Homotopy Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bogdan Gheorghe, Daniel C. Isaksen","submitted_at":"2015-05-06T19:51:58Z","abstract_excerpt":"We study the stable motivic homotopy groups $\\pi_{s,w}$ of the 2-completion of the motivic sphere spectrum over $\\mathbb{C}$. When arranged in the $(s,w)$-plane, these groups break into four different regions: a vanishing region, an $\\eta$-local region that is entirely known, a $\\tau$-local region that is identical to classical stable homotopy groups, and a region that is not well-understood."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01476","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":"1505.01476","created_at":"2026-05-18T02:16:49.162847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.01476v1","created_at":"2026-05-18T02:16:49.162847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01476","created_at":"2026-05-18T02:16:49.162847+00:00"},{"alias_kind":"pith_short_12","alias_value":"YYSJTX7NQ2K4","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YYSJTX7NQ2K4O4YI","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YYSJTX7N","created_at":"2026-05-18T12:29:52.810259+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/YYSJTX7NQ2K4O4YI6LRFRY7NSS","json":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS.json","graph_json":"https://pith.science/api/pith-number/YYSJTX7NQ2K4O4YI6LRFRY7NSS/graph.json","events_json":"https://pith.science/api/pith-number/YYSJTX7NQ2K4O4YI6LRFRY7NSS/events.json","paper":"https://pith.science/paper/YYSJTX7N"},"agent_actions":{"view_html":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS","download_json":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS.json","view_paper":"https://pith.science/paper/YYSJTX7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.01476&json=true","fetch_graph":"https://pith.science/api/pith-number/YYSJTX7NQ2K4O4YI6LRFRY7NSS/graph.json","fetch_events":"https://pith.science/api/pith-number/YYSJTX7NQ2K4O4YI6LRFRY7NSS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS/action/storage_attestation","attest_author":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS/action/author_attestation","sign_citation":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS/action/citation_signature","submit_replication":"https://pith.science/pith/YYSJTX7NQ2K4O4YI6LRFRY7NSS/action/replication_record"}},"created_at":"2026-05-18T02:16:49.162847+00:00","updated_at":"2026-05-18T02:16:49.162847+00:00"}