{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XWOOH2C654JU5EUG67LFTQ2IQX","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":"174b32747bfda66212f74b65f629b2af13e105911e345381c7d4e5a91bd22797","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-13T16:42:27Z","title_canon_sha256":"e8e6f125a2fbfd7027c6cb29120c11815ab0f247d217849a07a64043dbc75159"},"schema_version":"1.0","source":{"id":"1003.2725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2725","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2725v2","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2725","created_at":"2026-05-18T04:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"XWOOH2C654JU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XWOOH2C654JU5EUG","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XWOOH2C6","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:71fe63b7689c6157b1ace922443f5d4e10c67cb642890391a7718f3f5dca9918","target":"graph","created_at":"2026-05-18T04:33:49Z","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 complex semisimple Lie group, K a maximal compact subgroup and V an irreducible representation of K. Denote by M the unique closed orbit of G in P(V) and by O its image via the moment map. For any measure on M we construct a map from the Satake compactification of G/K (associated to V) to the Lie algebra of K. For the K-invariant measure, this map is a homeomorphism of the Satake compactification onto the convex envelope of O. For a large class of measures the image of the map is the convex envelope. As an application we get sharp upper bounds for the first eigenvalue of the Laplaci","authors_text":"Alessandro Ghigi, Leonardo Biliotti","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-13T16:42:27Z","title":"Satake-Furstenberg compactifications, the moment map and \\lambda_1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2725","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":"sha256:422e501ea8e71fcc5d2fd8b560e52aaa1a53063d92a9594c7e65a74339d4aee0","target":"record","created_at":"2026-05-18T04:33:49Z","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":"174b32747bfda66212f74b65f629b2af13e105911e345381c7d4e5a91bd22797","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-13T16:42:27Z","title_canon_sha256":"e8e6f125a2fbfd7027c6cb29120c11815ab0f247d217849a07a64043dbc75159"},"schema_version":"1.0","source":{"id":"1003.2725","kind":"arxiv","version":2}},"canonical_sha256":"bd9ce3e85eef134e9286f7d659c34885e8bdf035058a3e7e2fae8c424ead9b9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd9ce3e85eef134e9286f7d659c34885e8bdf035058a3e7e2fae8c424ead9b9f","first_computed_at":"2026-05-18T04:33:49.769666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:49.769666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GaEluizHl6HCN+9/Bm2RKgvAcsrgnKrM99BzfVZPEIpcPBbvnjaqsq8RGT6Lwc+VSyTvS6qKDyyWIr1IQVNdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:49.770142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.2725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:422e501ea8e71fcc5d2fd8b560e52aaa1a53063d92a9594c7e65a74339d4aee0","sha256:71fe63b7689c6157b1ace922443f5d4e10c67cb642890391a7718f3f5dca9918"],"state_sha256":"85daf7f86c6433a853d3f02577ec46883a2f464e4649a3e16bb0896641c99d3e"}