{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XSWQQ5UH2LYTL57P5WEOW4VNEG","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":"3eacdd78aefcc123eeadcc53ed869b6eae6c2bf3b930ffcf9241f3d37f4a0374","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-06-25T16:05:22Z","title_canon_sha256":"516630080776646d5f0fdb1712397b2dbd10e3120225bdb2dd3f5f1f973baded"},"schema_version":"1.0","source":{"id":"2406.17674","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.17674","created_at":"2026-07-05T10:29:18Z"},{"alias_kind":"arxiv_version","alias_value":"2406.17674v2","created_at":"2026-07-05T10:29:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.17674","created_at":"2026-07-05T10:29:18Z"},{"alias_kind":"pith_short_12","alias_value":"XSWQQ5UH2LYT","created_at":"2026-07-05T10:29:18Z"},{"alias_kind":"pith_short_16","alias_value":"XSWQQ5UH2LYTL57P","created_at":"2026-07-05T10:29:18Z"},{"alias_kind":"pith_short_8","alias_value":"XSWQQ5UH","created_at":"2026-07-05T10:29:18Z"}],"graph_snapshots":[{"event_id":"sha256:102dc5c7bb2f39d7bb6c40d0994f86df4303a0bd8908caf527bbec9886fd18a2","target":"graph","created_at":"2026-07-05T10:29:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.17674/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we study Figalli and Gigli's formulation of optimal transport between non-negative Radon measures in the setting of metric pairs. We carry over classical characterisations of optimal plans to this setting and prove that the resulting spaces of measures, $\\mathcal{M}_p(X,A)$, are complete, separable and geodesic whenever the underlying space, $X$, is so. We also prove that, for $p>1$, $\\mathcal{M}_p(X,A)$ preserves the property of being non-branching, and for $p=2$ it preserves non-negative curvature in the Alexandrov sense. Finally, we prove isometric embeddings of generalised ","authors_text":"Mauricio Che","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-06-25T16:05:22Z","title":"Optimal partial transport for metric pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.17674","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:a87f4029964390ee48f21f2d03b16a860f9b37047b8ffba3e23e617a8229c07e","target":"record","created_at":"2026-07-05T10:29:18Z","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":"3eacdd78aefcc123eeadcc53ed869b6eae6c2bf3b930ffcf9241f3d37f4a0374","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2024-06-25T16:05:22Z","title_canon_sha256":"516630080776646d5f0fdb1712397b2dbd10e3120225bdb2dd3f5f1f973baded"},"schema_version":"1.0","source":{"id":"2406.17674","kind":"arxiv","version":2}},"canonical_sha256":"bcad087687d2f135f7efed88eb72ad21a5304b3dc3b8f6906e468d9b5277a3b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcad087687d2f135f7efed88eb72ad21a5304b3dc3b8f6906e468d9b5277a3b7","first_computed_at":"2026-07-05T10:29:18.538688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:29:18.538688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"whopb4HAroiDyoguJQey+qgnx8QuBTKhz2asV6bkayljY4dfPJulczYnVCuhvlMgSorjrqnXVseH0WUjZhnRDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:29:18.539185Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.17674","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a87f4029964390ee48f21f2d03b16a860f9b37047b8ffba3e23e617a8229c07e","sha256:102dc5c7bb2f39d7bb6c40d0994f86df4303a0bd8908caf527bbec9886fd18a2"],"state_sha256":"fad3997e72f0ef177e8a1bce4603bb0868b5a88e766c2506f36cbbd36f6e1472"}