{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:KXUKJFOS5WWVRGQI5NF5RLEL7Q","short_pith_number":"pith:KXUKJFOS","canonical_record":{"source":{"id":"math/0309469","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2003-09-30T05:51:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"3cb8974ba8fdce13ec8ef50e4e3fbddabcb4fbaae6ce3fdd408e7277c839525a","abstract_canon_sha256":"0d4aece6ffa493177071082c7cd12659dced3039b11963a8f9f5cf3eaec16c68"},"schema_version":"1.0"},"canonical_sha256":"55e8a495d2edad589a08eb4bd8ac8bfc3e9c93a90c7cb30f64857a2413326e65","source":{"kind":"arxiv","id":"math/0309469","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0309469","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0309469v3","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0309469","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"KXUKJFOS5WWV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"KXUKJFOS5WWVRGQI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"KXUKJFOS","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:KXUKJFOS5WWVRGQI5NF5RLEL7Q","target":"record","payload":{"canonical_record":{"source":{"id":"math/0309469","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.RT","submitted_at":"2003-09-30T05:51:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"3cb8974ba8fdce13ec8ef50e4e3fbddabcb4fbaae6ce3fdd408e7277c839525a","abstract_canon_sha256":"0d4aece6ffa493177071082c7cd12659dced3039b11963a8f9f5cf3eaec16c68"},"schema_version":"1.0"},"canonical_sha256":"55e8a495d2edad589a08eb4bd8ac8bfc3e9c93a90c7cb30f64857a2413326e65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:31.211913Z","signature_b64":"4r8qRfhadmJw7duoboJjAnRbn/dA4hjGrCJ5SeLYwQehtAw7D+Y684OEVNbc7TjfynP59nzXo8fzawOc9l53Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55e8a495d2edad589a08eb4bd8ac8bfc3e9c93a90c7cb30f64857a2413326e65","last_reissued_at":"2026-05-18T01:19:31.211421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:31.211421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0309469","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"frjQ6lzgbXpIikvCFiK4UMZyBbCwRCyhdt1ZBflKS3wBeeU2F43kYxH5JKzBLTd2xThNC/KLBOPeM87XwbJ5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:11:12.093700Z"},"content_sha256":"5b8d179abfeb71e2f81ff8cc8bea9bf06cb7ee51407e049e7bfed1d8edccb325","schema_version":"1.0","event_id":"sha256:5b8d179abfeb71e2f81ff8cc8bea9bf06cb7ee51407e049e7bfed1d8edccb325"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:KXUKJFOS5WWVRGQI5NF5RLEL7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivalence of domains arising from duality of orbits on flag manifolds II","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Toshihiko Matsuki","submitted_at":"2003-09-30T05:51:43Z","abstract_excerpt":"In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity will be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type. This conjecture was proved for closed S in [WZ1,WZ2,FH,M6] and for open S in [M6]. In this paper, we prove the conjecture for all the other orbits when G_R is of non-Hermitian type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309469","kind":"arxiv","version":3},"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":"2026-05-18T01:19:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bEYZ3VvsboaSQB+wCD2DSjJxnLycglm5mZloRz23qnnWZDp6FjmRq6+DFgXIMSKyrl+CTpl1cYPF/Bw7W163Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:11:12.094276Z"},"content_sha256":"dde8123645dc36b4056c3974b3c7cd9feb6969424b1d60a612231e0b56f8c9ce","schema_version":"1.0","event_id":"sha256:dde8123645dc36b4056c3974b3c7cd9feb6969424b1d60a612231e0b56f8c9ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXUKJFOS5WWVRGQI5NF5RLEL7Q/bundle.json","state_url":"https://pith.science/pith/KXUKJFOS5WWVRGQI5NF5RLEL7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXUKJFOS5WWVRGQI5NF5RLEL7Q/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":"2026-05-27T10:11:12Z","links":{"resolver":"https://pith.science/pith/KXUKJFOS5WWVRGQI5NF5RLEL7Q","bundle":"https://pith.science/pith/KXUKJFOS5WWVRGQI5NF5RLEL7Q/bundle.json","state":"https://pith.science/pith/KXUKJFOS5WWVRGQI5NF5RLEL7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXUKJFOS5WWVRGQI5NF5RLEL7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:KXUKJFOS5WWVRGQI5NF5RLEL7Q","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":"0d4aece6ffa493177071082c7cd12659dced3039b11963a8f9f5cf3eaec16c68","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.RT","submitted_at":"2003-09-30T05:51:43Z","title_canon_sha256":"3cb8974ba8fdce13ec8ef50e4e3fbddabcb4fbaae6ce3fdd408e7277c839525a"},"schema_version":"1.0","source":{"id":"math/0309469","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0309469","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0309469v3","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0309469","created_at":"2026-05-18T01:19:31Z"},{"alias_kind":"pith_short_12","alias_value":"KXUKJFOS5WWV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"KXUKJFOS5WWVRGQI","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"KXUKJFOS","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:dde8123645dc36b4056c3974b3c7cd9feb6969424b1d60a612231e0b56f8c9ce","target":"graph","created_at":"2026-05-18T01:19:31Z","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":"In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity will be equal to the Akhiezer-Gindikin domain D if S is of nonholomorphic type. This conjecture was proved for closed S in [WZ1,WZ2,FH,M6] and for open S in [M6]. In this paper, we prove the conjecture for all the other orbits when G_R is of non-Hermitian type.","authors_text":"Toshihiko Matsuki","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2003-09-30T05:51:43Z","title":"Equivalence of domains arising from duality of orbits on flag manifolds II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309469","kind":"arxiv","version":3},"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":"sha256:5b8d179abfeb71e2f81ff8cc8bea9bf06cb7ee51407e049e7bfed1d8edccb325","target":"record","created_at":"2026-05-18T01:19:31Z","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":"0d4aece6ffa493177071082c7cd12659dced3039b11963a8f9f5cf3eaec16c68","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.RT","submitted_at":"2003-09-30T05:51:43Z","title_canon_sha256":"3cb8974ba8fdce13ec8ef50e4e3fbddabcb4fbaae6ce3fdd408e7277c839525a"},"schema_version":"1.0","source":{"id":"math/0309469","kind":"arxiv","version":3}},"canonical_sha256":"55e8a495d2edad589a08eb4bd8ac8bfc3e9c93a90c7cb30f64857a2413326e65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55e8a495d2edad589a08eb4bd8ac8bfc3e9c93a90c7cb30f64857a2413326e65","first_computed_at":"2026-05-18T01:19:31.211421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:31.211421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4r8qRfhadmJw7duoboJjAnRbn/dA4hjGrCJ5SeLYwQehtAw7D+Y684OEVNbc7TjfynP59nzXo8fzawOc9l53Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:31.211913Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0309469","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b8d179abfeb71e2f81ff8cc8bea9bf06cb7ee51407e049e7bfed1d8edccb325","sha256:dde8123645dc36b4056c3974b3c7cd9feb6969424b1d60a612231e0b56f8c9ce"],"state_sha256":"7b243a4eed9fc131d2d85fe785b20a1ab23c3f7143231608936fe2569e1d0c28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6KXum/1XAvzG9f2R/cgWrrUAXn4zWrKR4klvJ7b15ZclIhdn+DcrvooPTmZS4gdmS99EVjpNYEEaD07hKHH3DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:11:12.097234Z","bundle_sha256":"5b298016f8aec00b2921b8074649634bcb581793914341c82b50337a142ce4ef"}}