{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O2XQ2X5KLJULIJQMQBKANWYN4Z","short_pith_number":"pith:O2XQ2X5K","canonical_record":{"source":{"id":"1412.0554","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-26T19:24:30Z","cross_cats_sorted":[],"title_canon_sha256":"a1388fc0d332566126de1410e6f82e9589cba64660892fe29e7a98d5c2432544","abstract_canon_sha256":"70b1aabdd8555805680cff18815ea0101be75f00ba904ccfcb6682e704ff893d"},"schema_version":"1.0"},"canonical_sha256":"76af0d5faa5a68b4260c805406db0de665739fffe77113d57c60051d3e423d4d","source":{"kind":"arxiv","id":"1412.0554","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0554","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0554v3","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0554","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"O2XQ2X5KLJUL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O2XQ2X5KLJULIJQM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O2XQ2X5K","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O2XQ2X5KLJULIJQMQBKANWYN4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0554","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-26T19:24:30Z","cross_cats_sorted":[],"title_canon_sha256":"a1388fc0d332566126de1410e6f82e9589cba64660892fe29e7a98d5c2432544","abstract_canon_sha256":"70b1aabdd8555805680cff18815ea0101be75f00ba904ccfcb6682e704ff893d"},"schema_version":"1.0"},"canonical_sha256":"76af0d5faa5a68b4260c805406db0de665739fffe77113d57c60051d3e423d4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:02.501514Z","signature_b64":"Xt+XBdlGjmSAE7Ki7Qltwem9K6M9Jq1lv1pslKK77tNppAP/MdlTbD3PEwWQyLfdqPEJQDBaTCWuFEYVw609Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76af0d5faa5a68b4260c805406db0de665739fffe77113d57c60051d3e423d4d","last_reissued_at":"2026-05-18T00:41:02.500935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:02.500935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0554","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":"2026-05-18T00:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eVagH6qfq0c2walZGbJivlD6Xvp4lMkwo2pKbkOAgsvLelz836cop8QB+ruSK4GfQ0kafxM0IB8jXKgNH5MVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:22:34.014179Z"},"content_sha256":"a9fc87a03fa72ac0a05dfcc79123bf8c2f4d43d5e7c51b652e7d51891f7655cb","schema_version":"1.0","event_id":"sha256:a9fc87a03fa72ac0a05dfcc79123bf8c2f4d43d5e7c51b652e7d51891f7655cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O2XQ2X5KLJULIJQMQBKANWYN4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomological invariants of algebraic stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roberto Pirisi","submitted_at":"2014-11-26T19:24:30Z","abstract_excerpt":"The purpose of this paper is to lay the foundations of a theory of invariants in \\'etale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get some results regarding Brauer groups of algebraic spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0554","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":"2026-05-18T00:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJWf9oppV8ld6hm+PmAbmf4YDQ0HjJNFizPRtikvxhzOm4qrk2qMktRPs7zYjkTetj3WO40H9OL1+C1q5/YoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:22:34.014772Z"},"content_sha256":"cb2e78e2b1834ef725dc2612a2e095b839d44f49bb2396dc716b5e82d7df0da2","schema_version":"1.0","event_id":"sha256:cb2e78e2b1834ef725dc2612a2e095b839d44f49bb2396dc716b5e82d7df0da2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O2XQ2X5KLJULIJQMQBKANWYN4Z/bundle.json","state_url":"https://pith.science/pith/O2XQ2X5KLJULIJQMQBKANWYN4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O2XQ2X5KLJULIJQMQBKANWYN4Z/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":"2026-06-11T21:22:34Z","links":{"resolver":"https://pith.science/pith/O2XQ2X5KLJULIJQMQBKANWYN4Z","bundle":"https://pith.science/pith/O2XQ2X5KLJULIJQMQBKANWYN4Z/bundle.json","state":"https://pith.science/pith/O2XQ2X5KLJULIJQMQBKANWYN4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O2XQ2X5KLJULIJQMQBKANWYN4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O2XQ2X5KLJULIJQMQBKANWYN4Z","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":"70b1aabdd8555805680cff18815ea0101be75f00ba904ccfcb6682e704ff893d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-26T19:24:30Z","title_canon_sha256":"a1388fc0d332566126de1410e6f82e9589cba64660892fe29e7a98d5c2432544"},"schema_version":"1.0","source":{"id":"1412.0554","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0554","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0554v3","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0554","created_at":"2026-05-18T00:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"O2XQ2X5KLJUL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O2XQ2X5KLJULIJQM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O2XQ2X5K","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:cb2e78e2b1834ef725dc2612a2e095b839d44f49bb2396dc716b5e82d7df0da2","target":"graph","created_at":"2026-05-18T00:41:02Z","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":"The purpose of this paper is to lay the foundations of a theory of invariants in \\'etale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get some results regarding Brauer groups of algebraic spaces.","authors_text":"Roberto Pirisi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-26T19:24:30Z","title":"Cohomological invariants of algebraic stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0554","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:a9fc87a03fa72ac0a05dfcc79123bf8c2f4d43d5e7c51b652e7d51891f7655cb","target":"record","created_at":"2026-05-18T00:41:02Z","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":"70b1aabdd8555805680cff18815ea0101be75f00ba904ccfcb6682e704ff893d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-26T19:24:30Z","title_canon_sha256":"a1388fc0d332566126de1410e6f82e9589cba64660892fe29e7a98d5c2432544"},"schema_version":"1.0","source":{"id":"1412.0554","kind":"arxiv","version":3}},"canonical_sha256":"76af0d5faa5a68b4260c805406db0de665739fffe77113d57c60051d3e423d4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76af0d5faa5a68b4260c805406db0de665739fffe77113d57c60051d3e423d4d","first_computed_at":"2026-05-18T00:41:02.500935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:02.500935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xt+XBdlGjmSAE7Ki7Qltwem9K6M9Jq1lv1pslKK77tNppAP/MdlTbD3PEwWQyLfdqPEJQDBaTCWuFEYVw609Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:02.501514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0554","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9fc87a03fa72ac0a05dfcc79123bf8c2f4d43d5e7c51b652e7d51891f7655cb","sha256:cb2e78e2b1834ef725dc2612a2e095b839d44f49bb2396dc716b5e82d7df0da2"],"state_sha256":"9af033370b96b00899600d71bea73ae03d466402ce35092cc11e6245210002cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVB/TYcBm7ghm/Z1h5gyJjhej+DtJDTS/JSc6uJy2CQ+OeujzDTTTfxk61uayhOEjuqHm2B2d/EPEYIPqdjvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:22:34.019069Z","bundle_sha256":"dd9166474e5f3e8d488eee30096c7eff51cf7b599bdc2943a5b311386d6f0329"}}