{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:3I75XIRPBSXYWYQ6YDLURV7H2P","short_pith_number":"pith:3I75XIRP","canonical_record":{"source":{"id":"0812.3989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-20T18:28:45Z","cross_cats_sorted":["math.RT","math.SG"],"title_canon_sha256":"12bc05f6e88d6742c646bb9d4afcac813f5e6376a4ed3fbcc7e6ebc8c29630b1","abstract_canon_sha256":"4d3085966501be84b6dea7b0c2becb575a983e6901b03818470102f7b53950ef"},"schema_version":"1.0"},"canonical_sha256":"da3fdba22f0caf8b621ec0d748d7e7d3c3f9bb05a9daf9631749be655469f295","source":{"kind":"arxiv","id":"0812.3989","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3989","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3989v2","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3989","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"3I75XIRPBSXY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3I75XIRPBSXYWYQ6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3I75XIRP","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:3I75XIRPBSXYWYQ6YDLURV7H2P","target":"record","payload":{"canonical_record":{"source":{"id":"0812.3989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-20T18:28:45Z","cross_cats_sorted":["math.RT","math.SG"],"title_canon_sha256":"12bc05f6e88d6742c646bb9d4afcac813f5e6376a4ed3fbcc7e6ebc8c29630b1","abstract_canon_sha256":"4d3085966501be84b6dea7b0c2becb575a983e6901b03818470102f7b53950ef"},"schema_version":"1.0"},"canonical_sha256":"da3fdba22f0caf8b621ec0d748d7e7d3c3f9bb05a9daf9631749be655469f295","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:21.474178Z","signature_b64":"k5J7Z9cKKg/9KBxWVi9Zkc+kmQE3T0MYZAHnTV6rFSo2ojacGCWEmdpcGryPhl3E9mdUYBDI9fDiH+8rlpMHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da3fdba22f0caf8b621ec0d748d7e7d3c3f9bb05a9daf9631749be655469f295","last_reissued_at":"2026-05-18T03:45:21.473443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:21.473443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.3989","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":"2026-05-18T03:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4bSIYuf0BTEHY6nK+3976DpIVqk4YuQzWtp73q8ot/0FKTM3pfTY3tCtdMIDbARgSqwOKiaEzPcK4G1pU1oHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:13:29.734049Z"},"content_sha256":"a882fb631b8d259d6d90e2dcdaa3305dcb51ea2455a1114b60e51207de822852","schema_version":"1.0","event_id":"sha256:a882fb631b8d259d6d90e2dcdaa3305dcb51ea2455a1114b60e51207de822852"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:3I75XIRPBSXYWYQ6YDLURV7H2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric quantization for proper moment maps: the Vergne conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SG"],"primary_cat":"math.DG","authors_text":"Weiping Zhang (CIM), Xiaonan Ma (IMJ)","submitted_at":"2008-12-20T18:28:45Z","abstract_excerpt":"We establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3989","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":"2026-05-18T03:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SvtdHaa/oqoLdKb+CZGpDteD8nWas8JsTSp4VdhJST03Ig2DQwy6BSf4pQumPZdOzj13zuelpAZe4HZeY/ZGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:13:29.734436Z"},"content_sha256":"979ee007b66d9ef718b9f56c0a75fcee20ed1ab2a4a9a7ca88b029c2ebc1d8ee","schema_version":"1.0","event_id":"sha256:979ee007b66d9ef718b9f56c0a75fcee20ed1ab2a4a9a7ca88b029c2ebc1d8ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3I75XIRPBSXYWYQ6YDLURV7H2P/bundle.json","state_url":"https://pith.science/pith/3I75XIRPBSXYWYQ6YDLURV7H2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3I75XIRPBSXYWYQ6YDLURV7H2P/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":"2026-06-27T12:13:29Z","links":{"resolver":"https://pith.science/pith/3I75XIRPBSXYWYQ6YDLURV7H2P","bundle":"https://pith.science/pith/3I75XIRPBSXYWYQ6YDLURV7H2P/bundle.json","state":"https://pith.science/pith/3I75XIRPBSXYWYQ6YDLURV7H2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3I75XIRPBSXYWYQ6YDLURV7H2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:3I75XIRPBSXYWYQ6YDLURV7H2P","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":"4d3085966501be84b6dea7b0c2becb575a983e6901b03818470102f7b53950ef","cross_cats_sorted":["math.RT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-20T18:28:45Z","title_canon_sha256":"12bc05f6e88d6742c646bb9d4afcac813f5e6376a4ed3fbcc7e6ebc8c29630b1"},"schema_version":"1.0","source":{"id":"0812.3989","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3989","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3989v2","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3989","created_at":"2026-05-18T03:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"3I75XIRPBSXY","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"3I75XIRPBSXYWYQ6","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"3I75XIRP","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:979ee007b66d9ef718b9f56c0a75fcee20ed1ab2a4a9a7ca88b029c2ebc1d8ee","target":"graph","created_at":"2026-05-18T03:45:21Z","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 establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map.","authors_text":"Weiping Zhang (CIM), Xiaonan Ma (IMJ)","cross_cats":["math.RT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-20T18:28:45Z","title":"Geometric quantization for proper moment maps: the Vergne conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3989","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:a882fb631b8d259d6d90e2dcdaa3305dcb51ea2455a1114b60e51207de822852","target":"record","created_at":"2026-05-18T03:45:21Z","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":"4d3085966501be84b6dea7b0c2becb575a983e6901b03818470102f7b53950ef","cross_cats_sorted":["math.RT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-20T18:28:45Z","title_canon_sha256":"12bc05f6e88d6742c646bb9d4afcac813f5e6376a4ed3fbcc7e6ebc8c29630b1"},"schema_version":"1.0","source":{"id":"0812.3989","kind":"arxiv","version":2}},"canonical_sha256":"da3fdba22f0caf8b621ec0d748d7e7d3c3f9bb05a9daf9631749be655469f295","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da3fdba22f0caf8b621ec0d748d7e7d3c3f9bb05a9daf9631749be655469f295","first_computed_at":"2026-05-18T03:45:21.473443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:21.473443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k5J7Z9cKKg/9KBxWVi9Zkc+kmQE3T0MYZAHnTV6rFSo2ojacGCWEmdpcGryPhl3E9mdUYBDI9fDiH+8rlpMHBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:21.474178Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3989","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a882fb631b8d259d6d90e2dcdaa3305dcb51ea2455a1114b60e51207de822852","sha256:979ee007b66d9ef718b9f56c0a75fcee20ed1ab2a4a9a7ca88b029c2ebc1d8ee"],"state_sha256":"686598780d59752c80bb4b9e400792b1185c2f344a6cedc5c15a8959fb31be9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ct6H9IMbxgDHdISQMeJQ/7CdEqcv/HzRNoIzOfs7esQy6qxeMkaIlqMHDmjK38nM1mEmMqFOzU0zIBPChANDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:13:29.736298Z","bundle_sha256":"61e96b91d2c721db54a324dfded1f014560a90ae8e8fc62e92be2d1519861b75"}}