{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X7IFNGQRWFXJS3UNAYF22I4RYA","short_pith_number":"pith:X7IFNGQR","canonical_record":{"source":{"id":"1410.3901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-15T01:05:11Z","cross_cats_sorted":[],"title_canon_sha256":"b0390cc55aac2c233f457dda54901ac9eb5b598fdc75aa1af10852452179cc0f","abstract_canon_sha256":"973bfc4155b2bd99af6c164b117228e9554049f0d0159849388901c1c9beaf89"},"schema_version":"1.0"},"canonical_sha256":"bfd0569a11b16e996e8d060bad2391c0315e145d43bd8182a8c9ffcc01106a97","source":{"kind":"arxiv","id":"1410.3901","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3901","created_at":"2026-05-18T02:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3901v2","created_at":"2026-05-18T02:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3901","created_at":"2026-05-18T02:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"X7IFNGQRWFXJ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7IFNGQRWFXJS3UN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7IFNGQR","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X7IFNGQRWFXJS3UNAYF22I4RYA","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-15T01:05:11Z","cross_cats_sorted":[],"title_canon_sha256":"b0390cc55aac2c233f457dda54901ac9eb5b598fdc75aa1af10852452179cc0f","abstract_canon_sha256":"973bfc4155b2bd99af6c164b117228e9554049f0d0159849388901c1c9beaf89"},"schema_version":"1.0"},"canonical_sha256":"bfd0569a11b16e996e8d060bad2391c0315e145d43bd8182a8c9ffcc01106a97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:54.678429Z","signature_b64":"4/rhHMxyQhB1/DQBbFLJHCvVNMI5/8B0FNod8tz2ZI8iGyvxiYXyCV4D0JNbDVvH5OcXflrzfx3R5mech6wCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfd0569a11b16e996e8d060bad2391c0315e145d43bd8182a8c9ffcc01106a97","last_reissued_at":"2026-05-18T02:30:54.677891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:54.677891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3901","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":"2026-05-18T02:30:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wuDnbmu1b4V8D+K1eXUFmhyE4B2G7OOMygYvu1O/Ag0MjkF6m7hxGih6+8wzbXq6VMxJqB2g7eVuwqhXBvVaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:36:37.828087Z"},"content_sha256":"9de24b05af53a620c2531390955f7e3377da4733bb3b5d74a4521d245cf2c705","schema_version":"1.0","event_id":"sha256:9de24b05af53a620c2531390955f7e3377da4733bb3b5d74a4521d245cf2c705"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X7IFNGQRWFXJS3UNAYF22I4RYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue Coincidences and Multiplicity Free Spherical Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mark Colarusso, Sam Evens","submitted_at":"2014-10-15T01:05:11Z","abstract_excerpt":"In recent work, we related the structure of subvarieties of $n\\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\\mathbb{C})$-orbits on the flag variety of $\\mathfrak{gl}(n,\\mathbb{C})$. In the first part of this paper, we extend these results to the complex orthogonal Lie algebra $\\mathfrak{g}=\\mathfrak{so}(n,\\mathbb{C})$. In the second part of the paper, we use these results to study the geometry and invariant theory of the $K$-action on $\\mathfrak{g}$, in the cases where $(\\mathfrak{g}, K)$ is $(\\mathfrak{gl}(n,\\mathbb{C}), GL(n-1,\\mathbb{C}))$ or $(\\mathfrak{so}(n,\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3901","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":"2026-05-18T02:30:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofzx9Jw7CCL1art61/c5eSh9ymv2eAeQRK0pzaoy9ruUWwDq4lGl+adVFyN39Adsf4ay2S2IH0s/+Pok/q3JCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:36:37.828728Z"},"content_sha256":"f3315d1870a8b8b59e9a78a8ccc8680dac6886b3461a5d622e83e8a8a5895b3b","schema_version":"1.0","event_id":"sha256:f3315d1870a8b8b59e9a78a8ccc8680dac6886b3461a5d622e83e8a8a5895b3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7IFNGQRWFXJS3UNAYF22I4RYA/bundle.json","state_url":"https://pith.science/pith/X7IFNGQRWFXJS3UNAYF22I4RYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7IFNGQRWFXJS3UNAYF22I4RYA/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":"2026-05-26T01:36:37Z","links":{"resolver":"https://pith.science/pith/X7IFNGQRWFXJS3UNAYF22I4RYA","bundle":"https://pith.science/pith/X7IFNGQRWFXJS3UNAYF22I4RYA/bundle.json","state":"https://pith.science/pith/X7IFNGQRWFXJS3UNAYF22I4RYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7IFNGQRWFXJS3UNAYF22I4RYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X7IFNGQRWFXJS3UNAYF22I4RYA","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":"973bfc4155b2bd99af6c164b117228e9554049f0d0159849388901c1c9beaf89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-15T01:05:11Z","title_canon_sha256":"b0390cc55aac2c233f457dda54901ac9eb5b598fdc75aa1af10852452179cc0f"},"schema_version":"1.0","source":{"id":"1410.3901","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3901","created_at":"2026-05-18T02:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3901v2","created_at":"2026-05-18T02:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3901","created_at":"2026-05-18T02:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"X7IFNGQRWFXJ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7IFNGQRWFXJS3UN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7IFNGQR","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:f3315d1870a8b8b59e9a78a8ccc8680dac6886b3461a5d622e83e8a8a5895b3b","target":"graph","created_at":"2026-05-18T02:30:54Z","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 recent work, we related the structure of subvarieties of $n\\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\\mathbb{C})$-orbits on the flag variety of $\\mathfrak{gl}(n,\\mathbb{C})$. In the first part of this paper, we extend these results to the complex orthogonal Lie algebra $\\mathfrak{g}=\\mathfrak{so}(n,\\mathbb{C})$. In the second part of the paper, we use these results to study the geometry and invariant theory of the $K$-action on $\\mathfrak{g}$, in the cases where $(\\mathfrak{g}, K)$ is $(\\mathfrak{gl}(n,\\mathbb{C}), GL(n-1,\\mathbb{C}))$ or $(\\mathfrak{so}(n,\\ma","authors_text":"Mark Colarusso, Sam Evens","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-15T01:05:11Z","title":"Eigenvalue Coincidences and Multiplicity Free Spherical Pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3901","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":"sha256:9de24b05af53a620c2531390955f7e3377da4733bb3b5d74a4521d245cf2c705","target":"record","created_at":"2026-05-18T02:30:54Z","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":"973bfc4155b2bd99af6c164b117228e9554049f0d0159849388901c1c9beaf89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-15T01:05:11Z","title_canon_sha256":"b0390cc55aac2c233f457dda54901ac9eb5b598fdc75aa1af10852452179cc0f"},"schema_version":"1.0","source":{"id":"1410.3901","kind":"arxiv","version":2}},"canonical_sha256":"bfd0569a11b16e996e8d060bad2391c0315e145d43bd8182a8c9ffcc01106a97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfd0569a11b16e996e8d060bad2391c0315e145d43bd8182a8c9ffcc01106a97","first_computed_at":"2026-05-18T02:30:54.677891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:54.677891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/rhHMxyQhB1/DQBbFLJHCvVNMI5/8B0FNod8tz2ZI8iGyvxiYXyCV4D0JNbDVvH5OcXflrzfx3R5mech6wCDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:54.678429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3901","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9de24b05af53a620c2531390955f7e3377da4733bb3b5d74a4521d245cf2c705","sha256:f3315d1870a8b8b59e9a78a8ccc8680dac6886b3461a5d622e83e8a8a5895b3b"],"state_sha256":"f9c3f097ea43e06fa631b3fcc64df9bc76fe9a8a731396f0e13f15924320bd89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rO3oimgc9eAwiVGp5YLpD6BRXJzLkYoTTHMvCI+Joil2mt3UUAurA7ewYmNgezvtcEM6lAFbCz3wykOQheUbAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:36:37.832971Z","bundle_sha256":"91a4ff0c0fc179c762f76078e5273fd2558737174cb974084ec0d480d92e2eb5"}}