{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NSIWKSNA2D3GCKRAY4W5ZDERWC","short_pith_number":"pith:NSIWKSNA","canonical_record":{"source":{"id":"1207.5071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-20T22:23:44Z","cross_cats_sorted":[],"title_canon_sha256":"7f0f42604dc32fa5f9e87f3ac1aa1243bd1d8b6f0aa221fdd37b362f315710c1","abstract_canon_sha256":"aa365a3a67706efaddba197b4f10de7be90e36d7a8082dca40827a452d7c454f"},"schema_version":"1.0"},"canonical_sha256":"6c916549a0d0f6612a20c72ddc8c91b0b22a207c1e2f2b303365a045872d602d","source":{"kind":"arxiv","id":"1207.5071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5071","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5071v1","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5071","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"NSIWKSNA2D3G","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSIWKSNA2D3GCKRA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSIWKSNA","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NSIWKSNA2D3GCKRAY4W5ZDERWC","target":"record","payload":{"canonical_record":{"source":{"id":"1207.5071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-20T22:23:44Z","cross_cats_sorted":[],"title_canon_sha256":"7f0f42604dc32fa5f9e87f3ac1aa1243bd1d8b6f0aa221fdd37b362f315710c1","abstract_canon_sha256":"aa365a3a67706efaddba197b4f10de7be90e36d7a8082dca40827a452d7c454f"},"schema_version":"1.0"},"canonical_sha256":"6c916549a0d0f6612a20c72ddc8c91b0b22a207c1e2f2b303365a045872d602d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:24.683178Z","signature_b64":"uF77Ru54pYQ9DN6r3cm2IUresIjrvuOzP/tK30rMME9c4V32efMeQqmauc6gc6hQsCv1FSgd2A3VoMH4s1cGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c916549a0d0f6612a20c72ddc8c91b0b22a207c1e2f2b303365a045872d602d","last_reissued_at":"2026-05-18T03:50:24.682401Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:24.682401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.5071","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":"2026-05-18T03:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vbcItlyFBS1EeLSroZgRY0P00FymqDMcsy+DhF+63f4vVK7jD2J1bk9EMMc9CrHf6LVASBFpT6pbETMj4YdEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:21:03.425192Z"},"content_sha256":"9e1d5ca1dfc7268d978b995f5e2ae93b75f80ce7cb8cc5ebd4a2613b705522df","schema_version":"1.0","event_id":"sha256:9e1d5ca1dfc7268d978b995f5e2ae93b75f80ce7cb8cc5ebd4a2613b705522df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NSIWKSNA2D3GCKRAY4W5ZDERWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duflo's conjecture for the branching to the Iwasawa $AN$-subgroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gang Liu","submitted_at":"2012-07-20T22:23:44Z","abstract_excerpt":"The purpose of this paper is to prove Duflo's conjecture for $(G,\\pi, AN)$ where $G$ is a simple Lie group of Hermitian type and $\\pi$ is a discrete series of $G$ and $AN$ is the maximal exponential solvable subgroup for an Iwasawa decomposition $G=KAN$. This is essentially reduced from the following general theorem we prove in this paper: let $G$ be a connected semisimple Lie group . Then a strongly elliptic $G$-coadjoint orbit $\\mathcal{O}$ is holomorphic if and only if $\\text{p}(\\mathcal{O})$ is an open $AN$-coadjoint orbit, where $\\text{p} : \\mathfrak{g}^* \\longrightarrow (\\mathfrak{a}\\opl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5071","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":"2026-05-18T03:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fyArnKmaW4WI1JOflPRR+GCBlP941YmMpr2wr4c4soXjsxd2vvWmmpaOWLtfo61+G/UlCu9a79SU1FXKRjy2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T08:21:03.425552Z"},"content_sha256":"b53baabac4018f375bdaa3a2d1240d320b54c1c3b8da22a38d4223c52c93d638","schema_version":"1.0","event_id":"sha256:b53baabac4018f375bdaa3a2d1240d320b54c1c3b8da22a38d4223c52c93d638"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSIWKSNA2D3GCKRAY4W5ZDERWC/bundle.json","state_url":"https://pith.science/pith/NSIWKSNA2D3GCKRAY4W5ZDERWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSIWKSNA2D3GCKRAY4W5ZDERWC/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":"2026-06-04T08:21:03Z","links":{"resolver":"https://pith.science/pith/NSIWKSNA2D3GCKRAY4W5ZDERWC","bundle":"https://pith.science/pith/NSIWKSNA2D3GCKRAY4W5ZDERWC/bundle.json","state":"https://pith.science/pith/NSIWKSNA2D3GCKRAY4W5ZDERWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSIWKSNA2D3GCKRAY4W5ZDERWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NSIWKSNA2D3GCKRAY4W5ZDERWC","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":"aa365a3a67706efaddba197b4f10de7be90e36d7a8082dca40827a452d7c454f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-20T22:23:44Z","title_canon_sha256":"7f0f42604dc32fa5f9e87f3ac1aa1243bd1d8b6f0aa221fdd37b362f315710c1"},"schema_version":"1.0","source":{"id":"1207.5071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5071","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5071v1","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5071","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"NSIWKSNA2D3G","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSIWKSNA2D3GCKRA","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSIWKSNA","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:b53baabac4018f375bdaa3a2d1240d320b54c1c3b8da22a38d4223c52c93d638","target":"graph","created_at":"2026-05-18T03:50:24Z","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 prove Duflo's conjecture for $(G,\\pi, AN)$ where $G$ is a simple Lie group of Hermitian type and $\\pi$ is a discrete series of $G$ and $AN$ is the maximal exponential solvable subgroup for an Iwasawa decomposition $G=KAN$. This is essentially reduced from the following general theorem we prove in this paper: let $G$ be a connected semisimple Lie group . Then a strongly elliptic $G$-coadjoint orbit $\\mathcal{O}$ is holomorphic if and only if $\\text{p}(\\mathcal{O})$ is an open $AN$-coadjoint orbit, where $\\text{p} : \\mathfrak{g}^* \\longrightarrow (\\mathfrak{a}\\opl","authors_text":"Gang Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-20T22:23:44Z","title":"Duflo's conjecture for the branching to the Iwasawa $AN$-subgroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5071","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":"sha256:9e1d5ca1dfc7268d978b995f5e2ae93b75f80ce7cb8cc5ebd4a2613b705522df","target":"record","created_at":"2026-05-18T03:50:24Z","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":"aa365a3a67706efaddba197b4f10de7be90e36d7a8082dca40827a452d7c454f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-07-20T22:23:44Z","title_canon_sha256":"7f0f42604dc32fa5f9e87f3ac1aa1243bd1d8b6f0aa221fdd37b362f315710c1"},"schema_version":"1.0","source":{"id":"1207.5071","kind":"arxiv","version":1}},"canonical_sha256":"6c916549a0d0f6612a20c72ddc8c91b0b22a207c1e2f2b303365a045872d602d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c916549a0d0f6612a20c72ddc8c91b0b22a207c1e2f2b303365a045872d602d","first_computed_at":"2026-05-18T03:50:24.682401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:24.682401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uF77Ru54pYQ9DN6r3cm2IUresIjrvuOzP/tK30rMME9c4V32efMeQqmauc6gc6hQsCv1FSgd2A3VoMH4s1cGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:24.683178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e1d5ca1dfc7268d978b995f5e2ae93b75f80ce7cb8cc5ebd4a2613b705522df","sha256:b53baabac4018f375bdaa3a2d1240d320b54c1c3b8da22a38d4223c52c93d638"],"state_sha256":"c6a2d9e005acf3b811c6d6c0c6a6a2d38a7724f191f2373fb6a853f55dee5d41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3z7yOq2ZjuTarWNWRTRYdEHkmSyrSRgGBk8geP8nFUllhFz/s6SA2q8oycZ2+DJNPl43QKHDs6pzokvm3zwDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T08:21:03.427459Z","bundle_sha256":"e331f1013c2420dcb501f17e8cc5e08373673397c8c518f5ffae120218169ebf"}}