{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DPJUUYUXNRQ5HOL4QPWFT6KH6R","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":"5cb7b6ae3bfbba07b6529aa234306aa89744853d1c894ae9eba06df36677ef94","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-07T17:33:54Z","title_canon_sha256":"ba0685d61a9dace85df9639d2651c9b04cc13cefc787cc2b1efe2e75dd4406d7"},"schema_version":"1.0","source":{"id":"1805.02631","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02631","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02631v4","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02631","created_at":"2026-05-17T23:46:36Z"},{"alias_kind":"pith_short_12","alias_value":"DPJUUYUXNRQ5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DPJUUYUXNRQ5HOL4","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DPJUUYUX","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:547421525cc1374293a037573b76362548f3a7f6f63db444d0aeae963eb037de","target":"graph","created_at":"2026-05-17T23:46:36Z","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":"We study the geometry of Lie groups $G$ with a continuous Finsler metric, assuming the existence of a subgroup $K$ such that the metric is right-invariant for the action of $K$. We present a systematic study of the metric and geodesic structure of homogeneous spaces $M$ obtained by the quotient $M\\simeq G/K$. Of particular interest are left-invariant metrics of $G$ which are then bi-invariant for the action of $K$. We then focus on the geodesic structure of groups $K$ that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all ot","authors_text":"Gabriel Larotonda","cross_cats":["math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-07T17:33:54Z","title":"The metric geometry of infinite dimensional Lie groups and their homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02631","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":"sha256:6234ef3f9c63cb3fad7d141989176066d83765a610a0d25f71886246025671ad","target":"record","created_at":"2026-05-17T23:46:36Z","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":"5cb7b6ae3bfbba07b6529aa234306aa89744853d1c894ae9eba06df36677ef94","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-07T17:33:54Z","title_canon_sha256":"ba0685d61a9dace85df9639d2651c9b04cc13cefc787cc2b1efe2e75dd4406d7"},"schema_version":"1.0","source":{"id":"1805.02631","kind":"arxiv","version":4}},"canonical_sha256":"1bd34a62976c61d3b97c83ec59f947f47b4cca95f3d08a2059c61d0f455bcd63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bd34a62976c61d3b97c83ec59f947f47b4cca95f3d08a2059c61d0f455bcd63","first_computed_at":"2026-05-17T23:46:36.315787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:36.315787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2RkEPd9p0Fd2fGSawnlYHiKLLBO6OPE3tnamLfgnac06UPujk/t7+ulBwRY1gAUVFTVAUmpAg8+lTllC7SjACw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:36.316306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02631","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6234ef3f9c63cb3fad7d141989176066d83765a610a0d25f71886246025671ad","sha256:547421525cc1374293a037573b76362548f3a7f6f63db444d0aeae963eb037de"],"state_sha256":"c597e99b70eed8e59dc3d192ad00f5195a376b6c8c1780231aca3733fcdbe76c"}