{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:K2EQJFX7CC55GRSXYGNM5S7UHN","short_pith_number":"pith:K2EQJFX7","schema_version":"1.0","canonical_sha256":"56890496ff10bbd34657c19acecbf43b52f83045f84daf43b0e1c2e8801251b6","source":{"kind":"arxiv","id":"2508.09377","version":2},"attestation_state":"computed","paper":{"title":"Optimal Transport on Lie Group Orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.OC","authors_text":"Bahar Taskesen","submitted_at":"2025-08-12T22:26:23Z","abstract_excerpt":"In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \\textit{symmetry} and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport between measures lying on the same Lie group orbit of the reference distribution. In this setting, the Monge problem admits an explicit upper bound given by an optimization problem over the stabilizer subgroup of the re"},"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":"2508.09377","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-08-12T22:26:23Z","cross_cats_sorted":["math.GR","math.PR"],"title_canon_sha256":"ec0ef95cbbaf5f49cab6a44e46fea92fd0c2e38cd8979a857e64e35ba2ac2e18","abstract_canon_sha256":"76e364e02ca0b6cef658d1266dc6079c83fe6379d376d94c2e4cad82b22e761c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:45.237981Z","signature_b64":"ZIIuBj1IEnraZgPgrvkkjHr8h/SJw/SN+ybtSqvBTC86uKHOH8cyQ+gHPyPDWuz0uVTY75FjGJpCIxK3oVMbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56890496ff10bbd34657c19acecbf43b52f83045f84daf43b0e1c2e8801251b6","last_reissued_at":"2026-05-22T01:03:45.237069Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:45.237069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Transport on Lie Group Orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.OC","authors_text":"Bahar Taskesen","submitted_at":"2025-08-12T22:26:23Z","abstract_excerpt":"In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \\textit{symmetry} and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport between measures lying on the same Lie group orbit of the reference distribution. In this setting, the Monge problem admits an explicit upper bound given by an optimization problem over the stabilizer subgroup of the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.09377","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.09377/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2508.09377","created_at":"2026-05-22T01:03:45.237195+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.09377v2","created_at":"2026-05-22T01:03:45.237195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.09377","created_at":"2026-05-22T01:03:45.237195+00:00"},{"alias_kind":"pith_short_12","alias_value":"K2EQJFX7CC55","created_at":"2026-05-22T01:03:45.237195+00:00"},{"alias_kind":"pith_short_16","alias_value":"K2EQJFX7CC55GRSX","created_at":"2026-05-22T01:03:45.237195+00:00"},{"alias_kind":"pith_short_8","alias_value":"K2EQJFX7","created_at":"2026-05-22T01:03:45.237195+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/K2EQJFX7CC55GRSXYGNM5S7UHN","json":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN.json","graph_json":"https://pith.science/api/pith-number/K2EQJFX7CC55GRSXYGNM5S7UHN/graph.json","events_json":"https://pith.science/api/pith-number/K2EQJFX7CC55GRSXYGNM5S7UHN/events.json","paper":"https://pith.science/paper/K2EQJFX7"},"agent_actions":{"view_html":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN","download_json":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN.json","view_paper":"https://pith.science/paper/K2EQJFX7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.09377&json=true","fetch_graph":"https://pith.science/api/pith-number/K2EQJFX7CC55GRSXYGNM5S7UHN/graph.json","fetch_events":"https://pith.science/api/pith-number/K2EQJFX7CC55GRSXYGNM5S7UHN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN/action/storage_attestation","attest_author":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN/action/author_attestation","sign_citation":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN/action/citation_signature","submit_replication":"https://pith.science/pith/K2EQJFX7CC55GRSXYGNM5S7UHN/action/replication_record"}},"created_at":"2026-05-22T01:03:45.237195+00:00","updated_at":"2026-05-22T01:03:45.237195+00:00"}