{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BE42XQEWDFCEYLIE4I7CW6YLUB","short_pith_number":"pith:BE42XQEW","schema_version":"1.0","canonical_sha256":"0939abc09619444c2d04e23e2b7b0ba04c13e3c816f525a608d67e49fcede1a4","source":{"kind":"arxiv","id":"1610.09547","version":2},"attestation_state":"computed","paper":{"title":"Geodesic orbit metrics in compact homogeneous manifolds with equivalent isotropy submodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nikolaos Panagiotis Souris","submitted_at":"2016-10-29T17:47:47Z","abstract_excerpt":"A geodesic orbit manifold (GO manifold) is a Riemannian manifold (M,g) with the property that any geodesic in M is an orbit of a one-parameter subgroup of a group G of isometries of (M,g). The metric g is then called a G-GO metric in M. For an arbitrary compact homogeneous manifold M=G/H, we simplify the general problem of determining the G-GO metrics in M. In particular, if the isotropy representation of H induces equivalent irreducible submodules in the tangent space of M, we obtain algebraic conditions, under which, any G-GO metric in M admits a reduced form. As an application we determine "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.09547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-29T17:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"99b5b568c53bace21d69e78fa224c1a71616e48bb32383f702e592ff58a53f4d","abstract_canon_sha256":"9d3587b61ab7d583c3729eef38a48863f1b480cf4f112e98de504736d5e899ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:37.286157Z","signature_b64":"HKjsRoy7LzDFkokQ7NCUdcR+HMbkx1vAlfQSQnQuNJMFeBTdWnyi0EjlF8xCSXHm2Fj0AlFdog/XzY9Erhw5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0939abc09619444c2d04e23e2b7b0ba04c13e3c816f525a608d67e49fcede1a4","last_reissued_at":"2026-05-18T00:00:37.285727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:37.285727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geodesic orbit metrics in compact homogeneous manifolds with equivalent isotropy submodules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nikolaos Panagiotis Souris","submitted_at":"2016-10-29T17:47:47Z","abstract_excerpt":"A geodesic orbit manifold (GO manifold) is a Riemannian manifold (M,g) with the property that any geodesic in M is an orbit of a one-parameter subgroup of a group G of isometries of (M,g). The metric g is then called a G-GO metric in M. For an arbitrary compact homogeneous manifold M=G/H, we simplify the general problem of determining the G-GO metrics in M. In particular, if the isotropy representation of H induces equivalent irreducible submodules in the tangent space of M, we obtain algebraic conditions, under which, any G-GO metric in M admits a reduced form. As an application we determine "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09547","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.09547","created_at":"2026-05-18T00:00:37.285802+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.09547v2","created_at":"2026-05-18T00:00:37.285802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09547","created_at":"2026-05-18T00:00:37.285802+00:00"},{"alias_kind":"pith_short_12","alias_value":"BE42XQEWDFCE","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BE42XQEWDFCEYLIE","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BE42XQEW","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB","json":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB.json","graph_json":"https://pith.science/api/pith-number/BE42XQEWDFCEYLIE4I7CW6YLUB/graph.json","events_json":"https://pith.science/api/pith-number/BE42XQEWDFCEYLIE4I7CW6YLUB/events.json","paper":"https://pith.science/paper/BE42XQEW"},"agent_actions":{"view_html":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB","download_json":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB.json","view_paper":"https://pith.science/paper/BE42XQEW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.09547&json=true","fetch_graph":"https://pith.science/api/pith-number/BE42XQEWDFCEYLIE4I7CW6YLUB/graph.json","fetch_events":"https://pith.science/api/pith-number/BE42XQEWDFCEYLIE4I7CW6YLUB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB/action/storage_attestation","attest_author":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB/action/author_attestation","sign_citation":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB/action/citation_signature","submit_replication":"https://pith.science/pith/BE42XQEWDFCEYLIE4I7CW6YLUB/action/replication_record"}},"created_at":"2026-05-18T00:00:37.285802+00:00","updated_at":"2026-05-18T00:00:37.285802+00:00"}