{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VVUSJ7K5OEN6TQYN4CAU6P4JOD","short_pith_number":"pith:VVUSJ7K5","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"},"canonical_sha256":"ad6924fd5d711be9c30de0814f3f8970e3994ca9684311896229d66ee09d553a","source":{"kind":"arxiv","id":"1801.08471","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08471","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08471v3","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08471","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"VVUSJ7K5OEN6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VVUSJ7K5OEN6TQYN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VVUSJ7K5","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VVUSJ7K5OEN6TQYN4CAU6P4JOD","target":"record","payload":{"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"},"canonical_sha256":"ad6924fd5d711be9c30de0814f3f8970e3994ca9684311896229d66ee09d553a","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"},"source_kind":"arxiv","source_id":"1801.08471","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPwM9BIWkrYA0mnrLEIlksGD/Ksecf04FkFMlutcQo1aYvAOb121Fu13C50e8eBMU7A4S6mFh0r3I8lsvkJWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:06:27.041833Z"},"content_sha256":"bb8a01e33183fbd46fe9bbfe76f88c02487b9cbe00f7630b9ba48f4f15cfeff6","schema_version":"1.0","event_id":"sha256:bb8a01e33183fbd46fe9bbfe76f88c02487b9cbe00f7630b9ba48f4f15cfeff6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VVUSJ7K5OEN6TQYN4CAU6P4JOD","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UeSv4Comhd/6mc6tiGb3nG8LldC1OrZkQf/4C55L0JS2s9lgygQZJy3xwMZ0/SdKfVXuUQKK8GU25ThODLpsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:06:27.042176Z"},"content_sha256":"c33b6352e4732f3522d595d5d493ccf58998bb8c61fe76da647c53ec28ac0244","schema_version":"1.0","event_id":"sha256:c33b6352e4732f3522d595d5d493ccf58998bb8c61fe76da647c53ec28ac0244"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/bundle.json","state_url":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T13:06:27Z","links":{"resolver":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD","bundle":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/bundle.json","state":"https://pith.science/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVUSJ7K5OEN6TQYN4CAU6P4JOD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VVUSJ7K5OEN6TQYN4CAU6P4JOD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2403934e4411bee73fdb8ba9f0375220aa23e64221788c4168075b014a00b623","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-25T16:16:18Z","title_canon_sha256":"61819d7e5b5d2314152b005103a8522c299dbb77cbe7cedd4f8545ad3b37a969"},"schema_version":"1.0","source":{"id":"1801.08471","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08471","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08471v3","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08471","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"VVUSJ7K5OEN6","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VVUSJ7K5OEN6TQYN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VVUSJ7K5","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:c33b6352e4732f3522d595d5d493ccf58998bb8c61fe76da647c53ec28ac0244","target":"graph","created_at":"2026-05-17T23:50:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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).","authors_text":"Tom Bachmann","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-25T16:16:18Z","title":"Affine Grassmannians in A^1-algebraic topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08471","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bb8a01e33183fbd46fe9bbfe76f88c02487b9cbe00f7630b9ba48f4f15cfeff6","target":"record","created_at":"2026-05-17T23:50:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2403934e4411bee73fdb8ba9f0375220aa23e64221788c4168075b014a00b623","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-25T16:16:18Z","title_canon_sha256":"61819d7e5b5d2314152b005103a8522c299dbb77cbe7cedd4f8545ad3b37a969"},"schema_version":"1.0","source":{"id":"1801.08471","kind":"arxiv","version":3}},"canonical_sha256":"ad6924fd5d711be9c30de0814f3f8970e3994ca9684311896229d66ee09d553a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad6924fd5d711be9c30de0814f3f8970e3994ca9684311896229d66ee09d553a","first_computed_at":"2026-05-17T23:50:34.244661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:34.244661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jkYbyOFqwsfcH8ExBdX9gqhmGs9MQKXh3Kd0zohc49FctRCjmB/WostTj7FBlxDmYdsi0NO0HRHvGt1+yJ8nDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:34.245187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08471","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb8a01e33183fbd46fe9bbfe76f88c02487b9cbe00f7630b9ba48f4f15cfeff6","sha256:c33b6352e4732f3522d595d5d493ccf58998bb8c61fe76da647c53ec28ac0244"],"state_sha256":"6b2647b7ae6cc89b1fee15daf8676cbea86ff661782f5378afaf1c0681d41777"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJpiV1f3JA00oBk5otyIclnMZQ/emSJEH6JAistXH863NuEr7i5CWx9cSfgp7eSs5cYnob9bf5wyhIN2EEoEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:06:27.044176Z","bundle_sha256":"c026248fb72d861b670f0acb85ff2b155fb69ff1b7c764115d120e191758bdc6"}}