{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:7RDRYREVXVC2ALQHV4X6CDTDL4","short_pith_number":"pith:7RDRYREV","canonical_record":{"source":{"id":"0907.1177","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-07T10:41:58Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e0f49767b74091f569c20f69db164bba138da2fe2c51676e8931ecae29ebd3e8","abstract_canon_sha256":"03d1d1604f430d1c84463779840045e985c0e53fcc1b3d083494607cf6b72b7e"},"schema_version":"1.0"},"canonical_sha256":"fc471c4495bd45a02e07af2fe10e635f3eca1c7b2b1dcfbb591bb5b7ba528f33","source":{"kind":"arxiv","id":"0907.1177","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1177","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1177v4","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1177","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"7RDRYREVXVC2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7RDRYREVXVC2ALQH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7RDRYREV","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:7RDRYREVXVC2ALQHV4X6CDTDL4","target":"record","payload":{"canonical_record":{"source":{"id":"0907.1177","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-07T10:41:58Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e0f49767b74091f569c20f69db164bba138da2fe2c51676e8931ecae29ebd3e8","abstract_canon_sha256":"03d1d1604f430d1c84463779840045e985c0e53fcc1b3d083494607cf6b72b7e"},"schema_version":"1.0"},"canonical_sha256":"fc471c4495bd45a02e07af2fe10e635f3eca1c7b2b1dcfbb591bb5b7ba528f33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:36.085701Z","signature_b64":"NmOQwHPMPWm71cuHHM4r/xZqoAUR2H2BETqf0ZxpZj+AyBmGFxLHw8avQS01uuRJh64KY/MjVdiI3FQxH9H2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc471c4495bd45a02e07af2fe10e635f3eca1c7b2b1dcfbb591bb5b7ba528f33","last_reissued_at":"2026-05-18T00:12:36.085174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:36.085174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.1177","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WTSPwV1tLpEY24G+lsmMicOIBCvtFlwNqXDLBoK/7yte01LO3fuYg/t0b7swMoORHk27QsMs5C3TMhBe1opQDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:08:57.538249Z"},"content_sha256":"611f8dc4813410b6463288ba3791c0ed56515a3dfedb321d7ba888a1ac88113b","schema_version":"1.0","event_id":"sha256:611f8dc4813410b6463288ba3791c0ed56515a3dfedb321d7ba888a1ac88113b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:7RDRYREVXVC2ALQHV4X6CDTDL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical orbit closures in simple projective spaces and their normalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Jacopo Gandini","submitted_at":"2009-07-07T10:41:58Z","abstract_excerpt":"Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \\subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1177","kind":"arxiv","version":4},"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":"2026-05-18T00:12:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8c19xRfzvSB7qf90UpmjkegFHknazETAeCBnHtKhnxzuy5je9InkspE+U+XaabLSfofP6gqr7RTUzZ1hQsLTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T07:08:57.538974Z"},"content_sha256":"544f49a79a39d57fe81ff0631a9eb636f1b5d896c5dda074586761f64f9b1d89","schema_version":"1.0","event_id":"sha256:544f49a79a39d57fe81ff0631a9eb636f1b5d896c5dda074586761f64f9b1d89"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RDRYREVXVC2ALQHV4X6CDTDL4/bundle.json","state_url":"https://pith.science/pith/7RDRYREVXVC2ALQHV4X6CDTDL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RDRYREVXVC2ALQHV4X6CDTDL4/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":"2026-06-05T07:08:57Z","links":{"resolver":"https://pith.science/pith/7RDRYREVXVC2ALQHV4X6CDTDL4","bundle":"https://pith.science/pith/7RDRYREVXVC2ALQHV4X6CDTDL4/bundle.json","state":"https://pith.science/pith/7RDRYREVXVC2ALQHV4X6CDTDL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RDRYREVXVC2ALQHV4X6CDTDL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:7RDRYREVXVC2ALQHV4X6CDTDL4","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":"03d1d1604f430d1c84463779840045e985c0e53fcc1b3d083494607cf6b72b7e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-07T10:41:58Z","title_canon_sha256":"e0f49767b74091f569c20f69db164bba138da2fe2c51676e8931ecae29ebd3e8"},"schema_version":"1.0","source":{"id":"0907.1177","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1177","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1177v4","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1177","created_at":"2026-05-18T00:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"7RDRYREVXVC2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"7RDRYREVXVC2ALQH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"7RDRYREV","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:544f49a79a39d57fe81ff0631a9eb636f1b5d896c5dda074586761f64f9b1d89","target":"graph","created_at":"2026-05-18T00:12:36Z","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":"Let G be a simply connected semisimple algebraic group over an algebraically closed field k of characteristic 0 and let V be a rational simple G-module of finite dimension. If G/H \\subset P(V) is a spherical orbit and if X is its closure, then we describe the orbits of X and those of its normalization. If moreover the wonderful completion of G/H is strict, then we give necessary and sufficient combinatorial conditions so that the normalization morphism is a homeomorphism. Such conditions are trivially fulfilled if G is simply laced or if H is a symmetric subgroup.","authors_text":"Jacopo Gandini","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-07T10:41:58Z","title":"Spherical orbit closures in simple projective spaces and their normalizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1177","kind":"arxiv","version":4},"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":"sha256:611f8dc4813410b6463288ba3791c0ed56515a3dfedb321d7ba888a1ac88113b","target":"record","created_at":"2026-05-18T00:12:36Z","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":"03d1d1604f430d1c84463779840045e985c0e53fcc1b3d083494607cf6b72b7e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-07-07T10:41:58Z","title_canon_sha256":"e0f49767b74091f569c20f69db164bba138da2fe2c51676e8931ecae29ebd3e8"},"schema_version":"1.0","source":{"id":"0907.1177","kind":"arxiv","version":4}},"canonical_sha256":"fc471c4495bd45a02e07af2fe10e635f3eca1c7b2b1dcfbb591bb5b7ba528f33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc471c4495bd45a02e07af2fe10e635f3eca1c7b2b1dcfbb591bb5b7ba528f33","first_computed_at":"2026-05-18T00:12:36.085174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:36.085174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NmOQwHPMPWm71cuHHM4r/xZqoAUR2H2BETqf0ZxpZj+AyBmGFxLHw8avQS01uuRJh64KY/MjVdiI3FQxH9H2Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:36.085701Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.1177","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:611f8dc4813410b6463288ba3791c0ed56515a3dfedb321d7ba888a1ac88113b","sha256:544f49a79a39d57fe81ff0631a9eb636f1b5d896c5dda074586761f64f9b1d89"],"state_sha256":"1ea151d4591dd717fe37fb269dfa64379e7613aa6c43ec8f37b66696eddff3dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SlEP71WE6dIf6eobH+gE+FP037DlEhxLGehwnNrtV63RYT9v+Ivd62c9uCuxQRe3Vht72BEMvGVL6zmzpEwJDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T07:08:57.543031Z","bundle_sha256":"63dde97ab3dbe7a9976a6041f0883ad36aa75da2d9ee85a96d28c55e2ef763a6"}}