{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VVUSJ7K5OEN6TQYN4CAU6P4JOD","short_pith_number":"pith:VVUSJ7K5","schema_version":"1.0","canonical_sha256":"ad6924fd5d711be9c30de0814f3f8970e3994ca9684311896229d66ee09d553a","source":{"kind":"arxiv","id":"1801.08471","version":3},"attestation_state":"computed","paper":{"title":"Affine Grassmannians in A^1-algebraic topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Tom Bachmann","submitted_at":"2018-01-25T16:16:18Z","abstract_excerpt":"Let k be a field. Denote by Spc(k)_* the unstable, pointed motivic homotopy category and by Omega_Gm: Spc(k)_* \\to Spc(k)_* the Gm-loops functor. For a k-group G, denote by Gr_G the affine Grassmannian of G. If G is isotropic reductive, we provide a canonical motivic equivalence Omega_Gm G = Gr_G. If k is perfect, we use this to compute the motive M(Omega_Gm G) in DM(k, Z)."},"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":"1801.08471","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-25T16:16:18Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"61819d7e5b5d2314152b005103a8522c299dbb77cbe7cedd4f8545ad3b37a969","abstract_canon_sha256":"2403934e4411bee73fdb8ba9f0375220aa23e64221788c4168075b014a00b623"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:34.245187Z","signature_b64":"jkYbyOFqwsfcH8ExBdX9gqhmGs9MQKXh3Kd0zohc49FctRCjmB/WostTj7FBlxDmYdsi0NO0HRHvGt1+yJ8nDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad6924fd5d711be9c30de0814f3f8970e3994ca9684311896229d66ee09d553a","last_reissued_at":"2026-05-17T23:50:34.244661Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:34.244661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine Grassmannians in A^1-algebraic topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Tom Bachmann","submitted_at":"2018-01-25T16:16:18Z","abstract_excerpt":"Let k be a field. Denote by Spc(k)_* the unstable, pointed motivic homotopy category and by Omega_Gm: Spc(k)_* \\to Spc(k)_* the Gm-loops functor. For a k-group G, denote by Gr_G the affine Grassmannian of G. If G is isotropic reductive, we provide a canonical motivic equivalence Omega_Gm G = Gr_G. If k is perfect, we use this to compute the motive M(Omega_Gm G) in DM(k, Z)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08471","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":"1801.08471","created_at":"2026-05-17T23:50:34.244720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.08471v3","created_at":"2026-05-17T23:50:34.244720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08471","created_at":"2026-05-17T23:50:34.244720+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVUSJ7K5OEN6","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVUSJ7K5OEN6TQYN","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVUSJ7K5","created_at":"2026-05-18T12:32:59.047623+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/VVUSJ7K5OEN6TQYN4CAU6P4JOD","json":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD.json","graph_json":"https://pith.science/api/pith-number/VVUSJ7K5OEN6TQYN4CAU6P4JOD/graph.json","events_json":"https://pith.science/api/pith-number/VVUSJ7K5OEN6TQYN4CAU6P4JOD/events.json","paper":"https://pith.science/paper/VVUSJ7K5"},"agent_actions":{"view_html":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD","download_json":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD.json","view_paper":"https://pith.science/paper/VVUSJ7K5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.08471&json=true","fetch_graph":"https://pith.science/api/pith-number/VVUSJ7K5OEN6TQYN4CAU6P4JOD/graph.json","fetch_events":"https://pith.science/api/pith-number/VVUSJ7K5OEN6TQYN4CAU6P4JOD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/action/storage_attestation","attest_author":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/action/author_attestation","sign_citation":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/action/citation_signature","submit_replication":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/action/replication_record"}},"created_at":"2026-05-17T23:50:34.244720+00:00","updated_at":"2026-05-17T23:50:34.244720+00:00"}