{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VB57DEALJAEJ6DXPRDMLS47ZEU","short_pith_number":"pith:VB57DEAL","canonical_record":{"source":{"id":"1410.7950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-10-29T12:09:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"b37634187f5711108930d1d046f5ad5f045b35ac9eda1a85dc72260232985086","abstract_canon_sha256":"87be852277979083e03aa987d7d80a35416abd5b8b40373d09de6f0bd0e41ccc"},"schema_version":"1.0"},"canonical_sha256":"a87bf1900b48089f0eef88d8b973f925134d91165440d944d186132e1dc99435","source":{"kind":"arxiv","id":"1410.7950","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7950","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7950v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7950","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"VB57DEALJAEJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VB57DEALJAEJ6DXP","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VB57DEAL","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VB57DEALJAEJ6DXPRDMLS47ZEU","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-10-29T12:09:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"b37634187f5711108930d1d046f5ad5f045b35ac9eda1a85dc72260232985086","abstract_canon_sha256":"87be852277979083e03aa987d7d80a35416abd5b8b40373d09de6f0bd0e41ccc"},"schema_version":"1.0"},"canonical_sha256":"a87bf1900b48089f0eef88d8b973f925134d91165440d944d186132e1dc99435","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:07.771358Z","signature_b64":"6u8bu+VPQmLUYa7cHxy6sNrVt/6TCP/HjWIH/81vYXyzRs9hLRe15C+CDjTfZLCsvVcs+FU+Jotgy3n/YpmQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a87bf1900b48089f0eef88d8b973f925134d91165440d944d186132e1dc99435","last_reissued_at":"2026-05-18T02:39:07.770754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:07.770754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7950","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":"2026-05-18T02:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u5N9qHlP85JGzSB+KXOoJcRsH8P5k5G9/v5ahZOIAd4Afo8vJU3haULyKPRi8h5rO2AVFbbQv9efUcUtVoIuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:13:42.489906Z"},"content_sha256":"aae4339f7ff355c25a9ec9bf51ececf1c23f1cef8a44cb00794852bb71834fdb","schema_version":"1.0","event_id":"sha256:aae4339f7ff355c25a9ec9bf51ececf1c23f1cef8a44cb00794852bb71834fdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VB57DEALJAEJ6DXPRDMLS47ZEU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic Mackey Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.SG","authors_text":"Francois Ziegler","submitted_at":"2014-10-29T12:09:07Z","abstract_excerpt":"Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup. In this paper, we develop the attendant imprimitivity theorem and Mackey analysis in the full generality needed to deal with arbitrary closed normal subgroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7950","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":"2026-05-18T02:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+gKQ/MLPvGMhquS6W8k/2jIT5XJ+vCB8NnDkWNrl4+a56eYIwwouqC8C2rdZCCq9E+NgPbt38VTNR25kXLDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:13:42.490404Z"},"content_sha256":"1b5db38f0f6889c847c4a6fe9275c5844ec7a8bdb5931817ad4b764077aa483a","schema_version":"1.0","event_id":"sha256:1b5db38f0f6889c847c4a6fe9275c5844ec7a8bdb5931817ad4b764077aa483a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VB57DEALJAEJ6DXPRDMLS47ZEU/bundle.json","state_url":"https://pith.science/pith/VB57DEALJAEJ6DXPRDMLS47ZEU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VB57DEALJAEJ6DXPRDMLS47ZEU/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":"2026-06-24T05:13:42Z","links":{"resolver":"https://pith.science/pith/VB57DEALJAEJ6DXPRDMLS47ZEU","bundle":"https://pith.science/pith/VB57DEALJAEJ6DXPRDMLS47ZEU/bundle.json","state":"https://pith.science/pith/VB57DEALJAEJ6DXPRDMLS47ZEU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VB57DEALJAEJ6DXPRDMLS47ZEU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VB57DEALJAEJ6DXPRDMLS47ZEU","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":"87be852277979083e03aa987d7d80a35416abd5b8b40373d09de6f0bd0e41ccc","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-10-29T12:09:07Z","title_canon_sha256":"b37634187f5711108930d1d046f5ad5f045b35ac9eda1a85dc72260232985086"},"schema_version":"1.0","source":{"id":"1410.7950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7950","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7950v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7950","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"VB57DEALJAEJ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VB57DEALJAEJ6DXP","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VB57DEAL","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:1b5db38f0f6889c847c4a6fe9275c5844ec7a8bdb5931817ad4b764077aa483a","target":"graph","created_at":"2026-05-18T02:39:07Z","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":"Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup. In this paper, we develop the attendant imprimitivity theorem and Mackey analysis in the full generality needed to deal with arbitrary closed normal subgroups.","authors_text":"Francois Ziegler","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-10-29T12:09:07Z","title":"Symplectic Mackey Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7950","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:aae4339f7ff355c25a9ec9bf51ececf1c23f1cef8a44cb00794852bb71834fdb","target":"record","created_at":"2026-05-18T02:39:07Z","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":"87be852277979083e03aa987d7d80a35416abd5b8b40373d09de6f0bd0e41ccc","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2014-10-29T12:09:07Z","title_canon_sha256":"b37634187f5711108930d1d046f5ad5f045b35ac9eda1a85dc72260232985086"},"schema_version":"1.0","source":{"id":"1410.7950","kind":"arxiv","version":1}},"canonical_sha256":"a87bf1900b48089f0eef88d8b973f925134d91165440d944d186132e1dc99435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a87bf1900b48089f0eef88d8b973f925134d91165440d944d186132e1dc99435","first_computed_at":"2026-05-18T02:39:07.770754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:07.770754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6u8bu+VPQmLUYa7cHxy6sNrVt/6TCP/HjWIH/81vYXyzRs9hLRe15C+CDjTfZLCsvVcs+FU+Jotgy3n/YpmQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:07.771358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aae4339f7ff355c25a9ec9bf51ececf1c23f1cef8a44cb00794852bb71834fdb","sha256:1b5db38f0f6889c847c4a6fe9275c5844ec7a8bdb5931817ad4b764077aa483a"],"state_sha256":"9e94e6b3ed37d9b0ddc45d1deac852ce0367fc4e787d3fc4d93fd7ae3d5126a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZptZtZ3a3N7cY8f2gJ2gCSwtW5SBS0CvsGcY/2208kk/cPL9ZyJ7oMlIxrPiIcKC7TmnROuEWerkX+qB4E+3CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:13:42.492980Z","bundle_sha256":"f11f2a36ee7d2043cfe941ad221bd32a17d4a97de551df0bced04812f2b3c5bb"}}