{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6QEUUYHT6JTLAIXH2XDPWF4HZC","short_pith_number":"pith:6QEUUYHT","canonical_record":{"source":{"id":"1807.03365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-09T20:01:29Z","cross_cats_sorted":["math.AT","math.GR","math.KT"],"title_canon_sha256":"6706d8534a1d570f75ea1cc9855aaddec097997075651c4124f2302e1e2cbea5","abstract_canon_sha256":"24adf49ba17209ea4495a1ca3fa526ae7a7f4de9683115ba93195eb776c09b42"},"schema_version":"1.0"},"canonical_sha256":"f4094a60f3f266b022e7d5c6fb1787c8a34112f952cad0dd0362562317ccca4e","source":{"kind":"arxiv","id":"1807.03365","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03365","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03365v1","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03365","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"6QEUUYHT6JTL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6QEUUYHT6JTLAIXH","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6QEUUYHT","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6QEUUYHT6JTLAIXH2XDPWF4HZC","target":"record","payload":{"canonical_record":{"source":{"id":"1807.03365","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-09T20:01:29Z","cross_cats_sorted":["math.AT","math.GR","math.KT"],"title_canon_sha256":"6706d8534a1d570f75ea1cc9855aaddec097997075651c4124f2302e1e2cbea5","abstract_canon_sha256":"24adf49ba17209ea4495a1ca3fa526ae7a7f4de9683115ba93195eb776c09b42"},"schema_version":"1.0"},"canonical_sha256":"f4094a60f3f266b022e7d5c6fb1787c8a34112f952cad0dd0362562317ccca4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:10.665465Z","signature_b64":"dU6EXcvQmcRZGeZmX1N0WS/qFk7YE4FTMNiTqwKIE0l+EYL9asSDnsYm4N+ntOojdi1FEdv/b9eceNqi7eviBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4094a60f3f266b022e7d5c6fb1787c8a34112f952cad0dd0362562317ccca4e","last_reissued_at":"2026-05-18T00:11:10.664733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:10.664733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.03365","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2zdfnUpKpwRlCCWkgXogoWdjIDMCWqyYL56owrhl96SU7smjlirkgkKIvQRMmfa5592JIZKrdaKVu6GtV4BCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:06:42.429778Z"},"content_sha256":"b46dabe88dba35747e18110266085d1a0208d76fb9d312a0e5b4a7e92ee9e6b5","schema_version":"1.0","event_id":"sha256:b46dabe88dba35747e18110266085d1a0208d76fb9d312a0e5b4a7e92ee9e6b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6QEUUYHT6JTLAIXH2XDPWF4HZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Affine representability results in A^1-homotopy theory III: finite fields and complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR","math.KT"],"primary_cat":"math.AG","authors_text":"Aravind Asok, Marc Hoyois, Matthias Wendt","submitted_at":"2018-07-09T20:01:29Z","abstract_excerpt":"We give a streamlined proof of ${\\mathbb A}^1$-representability for $G$-torsors under \"isotropic\" reductive groups, extending previous results in this sequence of papers to finite fields. We then analyze a collection of group homomorphisms that yield fiber sequences in ${\\mathbb A}^1$-homotopy theory, and identify the final examples of motivic spheres that arise as homogeneous spaces for reductive groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03365","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2W0n3+bHZtvBv/5zLpTFEKkMst24ErCcYenBSOE7nWMOK2BtzdPhyFcwzMmhLWfPKOzfdSyqzI10uUGAfn+eBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:06:42.430430Z"},"content_sha256":"3246ed41c1a2aec398d33dd9dab2d1329b527789359dc1de72ebb6e8a983d846","schema_version":"1.0","event_id":"sha256:3246ed41c1a2aec398d33dd9dab2d1329b527789359dc1de72ebb6e8a983d846"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QEUUYHT6JTLAIXH2XDPWF4HZC/bundle.json","state_url":"https://pith.science/pith/6QEUUYHT6JTLAIXH2XDPWF4HZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QEUUYHT6JTLAIXH2XDPWF4HZC/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":"2026-05-26T19:06:42Z","links":{"resolver":"https://pith.science/pith/6QEUUYHT6JTLAIXH2XDPWF4HZC","bundle":"https://pith.science/pith/6QEUUYHT6JTLAIXH2XDPWF4HZC/bundle.json","state":"https://pith.science/pith/6QEUUYHT6JTLAIXH2XDPWF4HZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QEUUYHT6JTLAIXH2XDPWF4HZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6QEUUYHT6JTLAIXH2XDPWF4HZC","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":"24adf49ba17209ea4495a1ca3fa526ae7a7f4de9683115ba93195eb776c09b42","cross_cats_sorted":["math.AT","math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-09T20:01:29Z","title_canon_sha256":"6706d8534a1d570f75ea1cc9855aaddec097997075651c4124f2302e1e2cbea5"},"schema_version":"1.0","source":{"id":"1807.03365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03365","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03365v1","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03365","created_at":"2026-05-18T00:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"6QEUUYHT6JTL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6QEUUYHT6JTLAIXH","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6QEUUYHT","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:3246ed41c1a2aec398d33dd9dab2d1329b527789359dc1de72ebb6e8a983d846","target":"graph","created_at":"2026-05-18T00:11:10Z","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":"We give a streamlined proof of ${\\mathbb A}^1$-representability for $G$-torsors under \"isotropic\" reductive groups, extending previous results in this sequence of papers to finite fields. We then analyze a collection of group homomorphisms that yield fiber sequences in ${\\mathbb A}^1$-homotopy theory, and identify the final examples of motivic spheres that arise as homogeneous spaces for reductive groups.","authors_text":"Aravind Asok, Marc Hoyois, Matthias Wendt","cross_cats":["math.AT","math.GR","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-09T20:01:29Z","title":"Affine representability results in A^1-homotopy theory III: finite fields and complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03365","kind":"arxiv","version":1},"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:b46dabe88dba35747e18110266085d1a0208d76fb9d312a0e5b4a7e92ee9e6b5","target":"record","created_at":"2026-05-18T00:11:10Z","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":"24adf49ba17209ea4495a1ca3fa526ae7a7f4de9683115ba93195eb776c09b42","cross_cats_sorted":["math.AT","math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-07-09T20:01:29Z","title_canon_sha256":"6706d8534a1d570f75ea1cc9855aaddec097997075651c4124f2302e1e2cbea5"},"schema_version":"1.0","source":{"id":"1807.03365","kind":"arxiv","version":1}},"canonical_sha256":"f4094a60f3f266b022e7d5c6fb1787c8a34112f952cad0dd0362562317ccca4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4094a60f3f266b022e7d5c6fb1787c8a34112f952cad0dd0362562317ccca4e","first_computed_at":"2026-05-18T00:11:10.664733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:10.664733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dU6EXcvQmcRZGeZmX1N0WS/qFk7YE4FTMNiTqwKIE0l+EYL9asSDnsYm4N+ntOojdi1FEdv/b9eceNqi7eviBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:10.665465Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b46dabe88dba35747e18110266085d1a0208d76fb9d312a0e5b4a7e92ee9e6b5","sha256:3246ed41c1a2aec398d33dd9dab2d1329b527789359dc1de72ebb6e8a983d846"],"state_sha256":"e3df5911689a2b8a1c68f7e7ef3ff397b2e0ffba4d361030cc1dfe73bc92b971"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpLi72hgGqwnE18HQ6o91ttTKLmID1dX41EmcKtOha36ySdE/dSvTz7M3ZsfAHhOkVYk1Nj3QNqMBfjL9ZDABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:06:42.434040Z","bundle_sha256":"3382bb15c90bdabe21078a7e159a3c6b5f4a8b1ab8c62f3b093c8da99ce67f79"}}