{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HXOKYSAHQAL7R2OFWETMHTDNLK","short_pith_number":"pith:HXOKYSAH","canonical_record":{"source":{"id":"1309.2438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T10:09:05Z","cross_cats_sorted":[],"title_canon_sha256":"f54eb679b842710007b8a3f88b5abfb82917de248d593560019b0bd82738b198","abstract_canon_sha256":"9d9efe3e02bff0936f1a36222eeaa07d8157fc885f4706588a587f87d103bda9"},"schema_version":"1.0"},"canonical_sha256":"3ddcac48078017f8e9c5b126c3cc6d5aa45d41ead9b510b3780a49483ef659fd","source":{"kind":"arxiv","id":"1309.2438","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2438","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2438v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2438","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"HXOKYSAHQAL7","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HXOKYSAHQAL7R2OF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HXOKYSAH","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HXOKYSAHQAL7R2OFWETMHTDNLK","target":"record","payload":{"canonical_record":{"source":{"id":"1309.2438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T10:09:05Z","cross_cats_sorted":[],"title_canon_sha256":"f54eb679b842710007b8a3f88b5abfb82917de248d593560019b0bd82738b198","abstract_canon_sha256":"9d9efe3e02bff0936f1a36222eeaa07d8157fc885f4706588a587f87d103bda9"},"schema_version":"1.0"},"canonical_sha256":"3ddcac48078017f8e9c5b126c3cc6d5aa45d41ead9b510b3780a49483ef659fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.534775Z","signature_b64":"LCWIRVu+URen8Q+bLaRvD/Jsti6Q1wIAiG+pLpVrQb9lzmLeM2vjlNqXI4pdrJDJ3GU2ZhJ3nLfh9Orh1N5lAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ddcac48078017f8e9c5b126c3cc6d5aa45d41ead9b510b3780a49483ef659fd","last_reissued_at":"2026-05-18T00:44:29.534285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.534285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.2438","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":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUlAAAmABK0RPRlgxj3OJIQD6Ik2H7B0NG6oPRwINIzK6HgyzsYBKo4Wj9XO4SWzKCezKvv8nxMVJC+BjgpNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:16:13.588955Z"},"content_sha256":"c162d0ed4e913701a8fa20df9859811d0e46ffbe68120e1710628e6251eedd85","schema_version":"1.0","event_id":"sha256:c162d0ed4e913701a8fa20df9859811d0e46ffbe68120e1710628e6251eedd85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HXOKYSAHQAL7R2OFWETMHTDNLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isotropy in Group Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ehud Meir, Nir Ben David, Yuval Ginosar","submitted_at":"2013-09-10T10:09:05Z","abstract_excerpt":"The analogue of Lagrangians for symplectic forms over finite groups is studied, motivated by the fact that symplectic G-forms with a normal Lagrangian N<G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N. This yields a method to construct groups of central type from such quotients, known as Involutive Yang-Baxter groups. Another motivation for the search of normal Lagrangians comes from a non-commutative generalization of Heisenberg liftings which require normality.\n  Although it is true that symplectic forms over finite nilpotent groups alw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2438","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":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1pyHKFDf7RafPfqDRZTCm27rzbF61PkUYODybVFJ/ONGtD8ZDmRlrb/5+6zHx71GUrq3b6Zny/F9K50tSaxYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:16:13.589295Z"},"content_sha256":"42cb8797622f6f9a9e67ff19daa4a3e365f62cd666b0b99baa39f498b7d4287f","schema_version":"1.0","event_id":"sha256:42cb8797622f6f9a9e67ff19daa4a3e365f62cd666b0b99baa39f498b7d4287f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXOKYSAHQAL7R2OFWETMHTDNLK/bundle.json","state_url":"https://pith.science/pith/HXOKYSAHQAL7R2OFWETMHTDNLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXOKYSAHQAL7R2OFWETMHTDNLK/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":"2026-06-01T16:16:13Z","links":{"resolver":"https://pith.science/pith/HXOKYSAHQAL7R2OFWETMHTDNLK","bundle":"https://pith.science/pith/HXOKYSAHQAL7R2OFWETMHTDNLK/bundle.json","state":"https://pith.science/pith/HXOKYSAHQAL7R2OFWETMHTDNLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXOKYSAHQAL7R2OFWETMHTDNLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HXOKYSAHQAL7R2OFWETMHTDNLK","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":"9d9efe3e02bff0936f1a36222eeaa07d8157fc885f4706588a587f87d103bda9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T10:09:05Z","title_canon_sha256":"f54eb679b842710007b8a3f88b5abfb82917de248d593560019b0bd82738b198"},"schema_version":"1.0","source":{"id":"1309.2438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2438","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2438v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2438","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"HXOKYSAHQAL7","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HXOKYSAHQAL7R2OF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HXOKYSAH","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:42cb8797622f6f9a9e67ff19daa4a3e365f62cd666b0b99baa39f498b7d4287f","target":"graph","created_at":"2026-05-18T00:44:29Z","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 analogue of Lagrangians for symplectic forms over finite groups is studied, motivated by the fact that symplectic G-forms with a normal Lagrangian N<G are in one-to-one correspondence, up to inflation, with bijective 1-cocycle data on the quotients G/N. This yields a method to construct groups of central type from such quotients, known as Involutive Yang-Baxter groups. Another motivation for the search of normal Lagrangians comes from a non-commutative generalization of Heisenberg liftings which require normality.\n  Although it is true that symplectic forms over finite nilpotent groups alw","authors_text":"Ehud Meir, Nir Ben David, Yuval Ginosar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T10:09:05Z","title":"Isotropy in Group Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2438","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:c162d0ed4e913701a8fa20df9859811d0e46ffbe68120e1710628e6251eedd85","target":"record","created_at":"2026-05-18T00:44:29Z","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":"9d9efe3e02bff0936f1a36222eeaa07d8157fc885f4706588a587f87d103bda9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-09-10T10:09:05Z","title_canon_sha256":"f54eb679b842710007b8a3f88b5abfb82917de248d593560019b0bd82738b198"},"schema_version":"1.0","source":{"id":"1309.2438","kind":"arxiv","version":1}},"canonical_sha256":"3ddcac48078017f8e9c5b126c3cc6d5aa45d41ead9b510b3780a49483ef659fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ddcac48078017f8e9c5b126c3cc6d5aa45d41ead9b510b3780a49483ef659fd","first_computed_at":"2026-05-18T00:44:29.534285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:29.534285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCWIRVu+URen8Q+bLaRvD/Jsti6Q1wIAiG+pLpVrQb9lzmLeM2vjlNqXI4pdrJDJ3GU2ZhJ3nLfh9Orh1N5lAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:29.534775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c162d0ed4e913701a8fa20df9859811d0e46ffbe68120e1710628e6251eedd85","sha256:42cb8797622f6f9a9e67ff19daa4a3e365f62cd666b0b99baa39f498b7d4287f"],"state_sha256":"eced3653e29f7a8c14a3f7fc23ec0706401c8fe74d3830ebf35ead42e350bf2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9rxP4cwGvKbsGNfgN8tBn/hdiSZXny6lbfgV9ST9G8voKYkC+gdVyOIqFao44ZD1dIiMw23/Vsh0mpkYS//MDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:16:13.591181Z","bundle_sha256":"8e5878d656eeb29a8be2c475fa4255e240f53e8c27537e83e09c8fd27e5d4568"}}