{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:WKBL2ZO2UTBGQE4MJ63LYU4OIG","short_pith_number":"pith:WKBL2ZO2","canonical_record":{"source":{"id":"1205.1279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-07T04:03:08Z","cross_cats_sorted":["math.AT","math.GR","math.KT"],"title_canon_sha256":"928ce5824c5aaa38bff91aeca1d91c34867ca41f3fe9d444ec6a36afd5543991","abstract_canon_sha256":"fa5ec1b486c743beeec3c6550631f078fa0d8cf7aa39e2c4e9489f4dd07058e7"},"schema_version":"1.0"},"canonical_sha256":"b282bd65daa4c268138c4fb6bc538e418a5af031ef65495cbbdd92635f5871b3","source":{"kind":"arxiv","id":"1205.1279","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1279","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1279v1","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1279","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"WKBL2ZO2UTBG","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WKBL2ZO2UTBGQE4M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WKBL2ZO2","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:WKBL2ZO2UTBGQE4MJ63LYU4OIG","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-07T04:03:08Z","cross_cats_sorted":["math.AT","math.GR","math.KT"],"title_canon_sha256":"928ce5824c5aaa38bff91aeca1d91c34867ca41f3fe9d444ec6a36afd5543991","abstract_canon_sha256":"fa5ec1b486c743beeec3c6550631f078fa0d8cf7aa39e2c4e9489f4dd07058e7"},"schema_version":"1.0"},"canonical_sha256":"b282bd65daa4c268138c4fb6bc538e418a5af031ef65495cbbdd92635f5871b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:11.623464Z","signature_b64":"V0CnPxBdjjEbhAgYk2F8V3dBCyjiIg9lhdGhs3k3ohMMeJeperbfP0TK3cIJM65rbFzshvmYJsoON8e00ntEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b282bd65daa4c268138c4fb6bc538e418a5af031ef65495cbbdd92635f5871b3","last_reissued_at":"2026-05-18T03:56:11.622963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:11.622963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1279","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":"2026-05-18T03:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h0I0zNWl2fXbOaohdB8PknRxJPsaxtelJqXafdH11n860WsYjqHWL7C13i7Du+V31Iror46dd8pow1stXUK/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:59:45.684254Z"},"content_sha256":"aa6f4fae4d8486639fa392ffc6e22bc00eb947b478cb4082862507bee6ba5994","schema_version":"1.0","event_id":"sha256:aa6f4fae4d8486639fa392ffc6e22bc00eb947b478cb4082862507bee6ba5994"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:WKBL2ZO2UTBGQE4MJ63LYU4OIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Serre-Godeaux varieties and the etale index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR","math.KT"],"primary_cat":"math.AG","authors_text":"Benjamin Antieau, Ben Williams","submitted_at":"2012-05-07T04:03:08Z","abstract_excerpt":"We use the Serre-Godeaux varieties of finite groups, projective representation theory, the twisted Atiyah-Segal completion theorem, and our previous work on the topological period-index problem to compute the etale index of Brauer classes alpha in some specific examples. In particular, these computations show that the etale index of alpha differs from the period of alpha in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Serre-Godeaux varieties in terms of projective representation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1279","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":"2026-05-18T03:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oIMSa0sW9BmtiKjQlUL8zHNW2ovUlj5aFtWQn1OT/11F+qrLYHJv/pp9myOZDobvp0FQacAMZ08L90buBcDODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:59:45.684827Z"},"content_sha256":"f6e5bced9e4532522d19e46545de27c0b005f54b9ad25d1e14d1ed695f413438","schema_version":"1.0","event_id":"sha256:f6e5bced9e4532522d19e46545de27c0b005f54b9ad25d1e14d1ed695f413438"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKBL2ZO2UTBGQE4MJ63LYU4OIG/bundle.json","state_url":"https://pith.science/pith/WKBL2ZO2UTBGQE4MJ63LYU4OIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKBL2ZO2UTBGQE4MJ63LYU4OIG/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":"2026-06-07T11:59:45Z","links":{"resolver":"https://pith.science/pith/WKBL2ZO2UTBGQE4MJ63LYU4OIG","bundle":"https://pith.science/pith/WKBL2ZO2UTBGQE4MJ63LYU4OIG/bundle.json","state":"https://pith.science/pith/WKBL2ZO2UTBGQE4MJ63LYU4OIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKBL2ZO2UTBGQE4MJ63LYU4OIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:WKBL2ZO2UTBGQE4MJ63LYU4OIG","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":"fa5ec1b486c743beeec3c6550631f078fa0d8cf7aa39e2c4e9489f4dd07058e7","cross_cats_sorted":["math.AT","math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-07T04:03:08Z","title_canon_sha256":"928ce5824c5aaa38bff91aeca1d91c34867ca41f3fe9d444ec6a36afd5543991"},"schema_version":"1.0","source":{"id":"1205.1279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1279","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1279v1","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1279","created_at":"2026-05-18T03:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"WKBL2ZO2UTBG","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"WKBL2ZO2UTBGQE4M","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"WKBL2ZO2","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:f6e5bced9e4532522d19e46545de27c0b005f54b9ad25d1e14d1ed695f413438","target":"graph","created_at":"2026-05-18T03:56:11Z","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 use the Serre-Godeaux varieties of finite groups, projective representation theory, the twisted Atiyah-Segal completion theorem, and our previous work on the topological period-index problem to compute the etale index of Brauer classes alpha in some specific examples. In particular, these computations show that the etale index of alpha differs from the period of alpha in general. As an application, we compute the index of unramified classes in the function fields of high-dimensional Serre-Godeaux varieties in terms of projective representation theory.","authors_text":"Benjamin Antieau, Ben Williams","cross_cats":["math.AT","math.GR","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-07T04:03:08Z","title":"Serre-Godeaux varieties and the etale index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1279","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:aa6f4fae4d8486639fa392ffc6e22bc00eb947b478cb4082862507bee6ba5994","target":"record","created_at":"2026-05-18T03:56:11Z","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":"fa5ec1b486c743beeec3c6550631f078fa0d8cf7aa39e2c4e9489f4dd07058e7","cross_cats_sorted":["math.AT","math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-07T04:03:08Z","title_canon_sha256":"928ce5824c5aaa38bff91aeca1d91c34867ca41f3fe9d444ec6a36afd5543991"},"schema_version":"1.0","source":{"id":"1205.1279","kind":"arxiv","version":1}},"canonical_sha256":"b282bd65daa4c268138c4fb6bc538e418a5af031ef65495cbbdd92635f5871b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b282bd65daa4c268138c4fb6bc538e418a5af031ef65495cbbdd92635f5871b3","first_computed_at":"2026-05-18T03:56:11.622963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:11.622963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V0CnPxBdjjEbhAgYk2F8V3dBCyjiIg9lhdGhs3k3ohMMeJeperbfP0TK3cIJM65rbFzshvmYJsoON8e00ntEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:11.623464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa6f4fae4d8486639fa392ffc6e22bc00eb947b478cb4082862507bee6ba5994","sha256:f6e5bced9e4532522d19e46545de27c0b005f54b9ad25d1e14d1ed695f413438"],"state_sha256":"5979eaa6ee8b7c9368776d2197f88f088e547915cb3eb7eeb0ada088d9ab608a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PxFhUyA6IBnKtLkjM4k9CWQykcnnoAs/JZiDAip0jAIzZ003rjFNQXOpc2/UqSmX+WRQRmWHRC7aV6N2Q7CXDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:59:45.687951Z","bundle_sha256":"0626ad81ff9f8e1c9bd2b8009d4e8d9bbd87725079f8a51e065f8715ecb2de52"}}