{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CL3HB4VKA3FSB2GENWQ2MMGRBX","short_pith_number":"pith:CL3HB4VK","canonical_record":{"source":{"id":"1110.4542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-20T14:39:04Z","cross_cats_sorted":["math.AG","math.AT"],"title_canon_sha256":"fe45cb6bb5620f768f2312750739c8b9c34831638cd1d68c4d9dfb7682b3ef4e","abstract_canon_sha256":"4c58b8235ebcc2dab07a7e03bc2f3e17c5de91214ea5d3068e2eeceb69e9cfc9"},"schema_version":"1.0"},"canonical_sha256":"12f670f2aa06cb20e8c46da1a630d10dd0dac8b4598695ffced8a21a848fbff6","source":{"kind":"arxiv","id":"1110.4542","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4542","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4542v2","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4542","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"CL3HB4VKA3FS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CL3HB4VKA3FSB2GE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CL3HB4VK","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CL3HB4VKA3FSB2GENWQ2MMGRBX","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-20T14:39:04Z","cross_cats_sorted":["math.AG","math.AT"],"title_canon_sha256":"fe45cb6bb5620f768f2312750739c8b9c34831638cd1d68c4d9dfb7682b3ef4e","abstract_canon_sha256":"4c58b8235ebcc2dab07a7e03bc2f3e17c5de91214ea5d3068e2eeceb69e9cfc9"},"schema_version":"1.0"},"canonical_sha256":"12f670f2aa06cb20e8c46da1a630d10dd0dac8b4598695ffced8a21a848fbff6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:38.186688Z","signature_b64":"ZUTiYvyBfQ/+855Mvpl4NdCWJ30CUhTy3Fa0n8PIwkCbJisuFRsYvKnF6FUYqvcvQohdVHpUm2EmPVZtSlIWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12f670f2aa06cb20e8c46da1a630d10dd0dac8b4598695ffced8a21a848fbff6","last_reissued_at":"2026-05-18T04:05:38.186085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:38.186085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4542","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUEWQCXRhphDbiJJa5GzS605tNZxvemm9gggrMuLKJYvhjtcpt1vPsA9U0VdZYok1hVEp3C6xuBq187HPT5mBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:55:50.999241Z"},"content_sha256":"901af94f9a1bf6bdf5deb1ab28f742985dc30331b4bb17bf6418f1bf0ca42dd0","schema_version":"1.0","event_id":"sha256:901af94f9a1bf6bdf5deb1ab28f742985dc30331b4bb17bf6418f1bf0ca42dd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CL3HB4VKA3FSB2GENWQ2MMGRBX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-abelian crossed modules and nonabelian cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.NT","authors_text":"Cristian D. Gonz\\'alez-Avil\\'es","submitted_at":"2011-10-20T14:39:04Z","abstract_excerpt":"We extend the work of M.Borovoi on the nonabelian Galois cohomology of linear reductive algebraic groups over number fields to a general base scheme. As an application, we obtain new results on the arithmetic of such groups over global function fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4542","kind":"arxiv","version":2},"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":"2026-05-18T04:05:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hxVV+6Whm3MMzdQl1wFPKMQYwTDEg5kctgQ3oDfb7HiNLSn4ET2RP49UV1AoAgk+HyBLJyFerHTEBlyPdP+VCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:55:50.999699Z"},"content_sha256":"6af57d244f9fee3c82ee90f52dc1c9846e6506bd7454a668dd1e6c93bf88f881","schema_version":"1.0","event_id":"sha256:6af57d244f9fee3c82ee90f52dc1c9846e6506bd7454a668dd1e6c93bf88f881"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CL3HB4VKA3FSB2GENWQ2MMGRBX/bundle.json","state_url":"https://pith.science/pith/CL3HB4VKA3FSB2GENWQ2MMGRBX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CL3HB4VKA3FSB2GENWQ2MMGRBX/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":"2026-06-23T18:55:51Z","links":{"resolver":"https://pith.science/pith/CL3HB4VKA3FSB2GENWQ2MMGRBX","bundle":"https://pith.science/pith/CL3HB4VKA3FSB2GENWQ2MMGRBX/bundle.json","state":"https://pith.science/pith/CL3HB4VKA3FSB2GENWQ2MMGRBX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CL3HB4VKA3FSB2GENWQ2MMGRBX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CL3HB4VKA3FSB2GENWQ2MMGRBX","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":"4c58b8235ebcc2dab07a7e03bc2f3e17c5de91214ea5d3068e2eeceb69e9cfc9","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-20T14:39:04Z","title_canon_sha256":"fe45cb6bb5620f768f2312750739c8b9c34831638cd1d68c4d9dfb7682b3ef4e"},"schema_version":"1.0","source":{"id":"1110.4542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4542","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4542v2","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4542","created_at":"2026-05-18T04:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"CL3HB4VKA3FS","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CL3HB4VKA3FSB2GE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CL3HB4VK","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:6af57d244f9fee3c82ee90f52dc1c9846e6506bd7454a668dd1e6c93bf88f881","target":"graph","created_at":"2026-05-18T04:05:38Z","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 extend the work of M.Borovoi on the nonabelian Galois cohomology of linear reductive algebraic groups over number fields to a general base scheme. As an application, we obtain new results on the arithmetic of such groups over global function fields.","authors_text":"Cristian D. Gonz\\'alez-Avil\\'es","cross_cats":["math.AG","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-20T14:39:04Z","title":"Quasi-abelian crossed modules and nonabelian cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4542","kind":"arxiv","version":2},"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":"sha256:901af94f9a1bf6bdf5deb1ab28f742985dc30331b4bb17bf6418f1bf0ca42dd0","target":"record","created_at":"2026-05-18T04:05:38Z","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":"4c58b8235ebcc2dab07a7e03bc2f3e17c5de91214ea5d3068e2eeceb69e9cfc9","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-20T14:39:04Z","title_canon_sha256":"fe45cb6bb5620f768f2312750739c8b9c34831638cd1d68c4d9dfb7682b3ef4e"},"schema_version":"1.0","source":{"id":"1110.4542","kind":"arxiv","version":2}},"canonical_sha256":"12f670f2aa06cb20e8c46da1a630d10dd0dac8b4598695ffced8a21a848fbff6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12f670f2aa06cb20e8c46da1a630d10dd0dac8b4598695ffced8a21a848fbff6","first_computed_at":"2026-05-18T04:05:38.186085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:38.186085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZUTiYvyBfQ/+855Mvpl4NdCWJ30CUhTy3Fa0n8PIwkCbJisuFRsYvKnF6FUYqvcvQohdVHpUm2EmPVZtSlIWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:38.186688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:901af94f9a1bf6bdf5deb1ab28f742985dc30331b4bb17bf6418f1bf0ca42dd0","sha256:6af57d244f9fee3c82ee90f52dc1c9846e6506bd7454a668dd1e6c93bf88f881"],"state_sha256":"1e01e23991985e4787b147986f3911b7388ad35ecf66ee03000a674c7ba9c9ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0k3jMJRVeE0opa0aI+5lhf110oYr4wLOs6wdeF1utTScvxxi/q7wH/+Mu4sFt//vi4UeFVUxWNkv5y1FaRQzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:55:51.002008Z","bundle_sha256":"c6925bc61fe4deebcfc786140cfcde43fece0d8a28d60f901748d0d59a0c60df"}}