{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZFWA3WOGUNJCW4MWBQRQWK3VO3","short_pith_number":"pith:ZFWA3WOG","canonical_record":{"source":{"id":"2507.13094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-07-17T13:06:24Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"c695c99a31775974ce1991406e599e8e0e968cffacedce6dc14c8e02028fb3fe","abstract_canon_sha256":"37dff59f51ab4b6c3387d98d5bf9618629c51382de83b72b6e5c470e5f7b97b4"},"schema_version":"1.0"},"canonical_sha256":"c96c0dd9c6a3522b71960c230b2b7576d0716365f372277ee93e9a5cc229b501","source":{"kind":"arxiv","id":"2507.13094","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13094","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13094v1","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13094","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZFWA3WOGUNJC","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZFWA3WOGUNJCW4MW","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZFWA3WOG","created_at":"2026-07-05T11:38:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZFWA3WOGUNJCW4MWBQRQWK3VO3","target":"record","payload":{"canonical_record":{"source":{"id":"2507.13094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-07-17T13:06:24Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"c695c99a31775974ce1991406e599e8e0e968cffacedce6dc14c8e02028fb3fe","abstract_canon_sha256":"37dff59f51ab4b6c3387d98d5bf9618629c51382de83b72b6e5c470e5f7b97b4"},"schema_version":"1.0"},"canonical_sha256":"c96c0dd9c6a3522b71960c230b2b7576d0716365f372277ee93e9a5cc229b501","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:54.614182Z","signature_b64":"4uPsu0RKNs1gAxgfv7uILw5wV2vjb0P6jpUzPHogOP6LRPHok5rr2j/HyVbog6aZN2jsV1BQnImWVVP6O+paAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c96c0dd9c6a3522b71960c230b2b7576d0716365f372277ee93e9a5cc229b501","last_reissued_at":"2026-07-05T11:38:54.613711Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:54.613711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.13094","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrLgZxWgLne6E5W1XKu39h7Orb2eg+YyHnNQMoezA0bNKhURbNuvsevzgL/ZpXv/Dfjl8hPiyRvzCOYVayR2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:49:14.554067Z"},"content_sha256":"79b35b404d6a234bdb1ebc16eeb26888d1ab47ba488e7ca8aa127a9d0215d342","schema_version":"1.0","event_id":"sha256:79b35b404d6a234bdb1ebc16eeb26888d1ab47ba488e7ca8aa127a9d0215d342"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZFWA3WOGUNJCW4MWBQRQWK3VO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unsupervised Ground Metric Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Gabriele Steidl, Janis Auffenberg, Jonas Bresch, Oleh Melnyk","submitted_at":"2025-07-17T13:06:24Z","abstract_excerpt":"Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyr\\'e proposed to simultaneously learn optimal transport (OT) cost matrices between samples and features of the dataset. This leads to the task of finding positive eigenvectors of a certain nonlinear function that maps cost matrices to OT distances. Having this basic idea in mind, we consider both the algorithmic and the modeling part of unsupervised metric learning. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13094","kind":"arxiv","version":1},"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/2507.13094/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AnE1YBqCmHE53fgxbGrdfHlhrKvE7/1WWOSAF+TXOXPBmFzYkJaIyhTrJ5OPZ6ov0oOL5PG3Oug9drpYaDReAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:49:14.558688Z"},"content_sha256":"cf5d4b93b467c714495e87aea4996c535e2f1b18aa522ccb65fd21fa97572d54","schema_version":"1.0","event_id":"sha256:cf5d4b93b467c714495e87aea4996c535e2f1b18aa522ccb65fd21fa97572d54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFWA3WOGUNJCW4MWBQRQWK3VO3/bundle.json","state_url":"https://pith.science/pith/ZFWA3WOGUNJCW4MWBQRQWK3VO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFWA3WOGUNJCW4MWBQRQWK3VO3/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":"2026-08-08T04:49:14Z","links":{"resolver":"https://pith.science/pith/ZFWA3WOGUNJCW4MWBQRQWK3VO3","bundle":"https://pith.science/pith/ZFWA3WOGUNJCW4MWBQRQWK3VO3/bundle.json","state":"https://pith.science/pith/ZFWA3WOGUNJCW4MWBQRQWK3VO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFWA3WOGUNJCW4MWBQRQWK3VO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZFWA3WOGUNJCW4MWBQRQWK3VO3","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":"37dff59f51ab4b6c3387d98d5bf9618629c51382de83b72b6e5c470e5f7b97b4","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-07-17T13:06:24Z","title_canon_sha256":"c695c99a31775974ce1991406e599e8e0e968cffacedce6dc14c8e02028fb3fe"},"schema_version":"1.0","source":{"id":"2507.13094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13094","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13094v1","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13094","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZFWA3WOGUNJC","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZFWA3WOGUNJCW4MW","created_at":"2026-07-05T11:38:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZFWA3WOG","created_at":"2026-07-05T11:38:54Z"}],"graph_snapshots":[{"event_id":"sha256:cf5d4b93b467c714495e87aea4996c535e2f1b18aa522ccb65fd21fa97572d54","target":"graph","created_at":"2026-07-05T11:38:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.13094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in metric learning. Recently, Huizing, Cantini and Peyr\\'e proposed to simultaneously learn optimal transport (OT) cost matrices between samples and features of the dataset. This leads to the task of finding positive eigenvectors of a certain nonlinear function that maps cost matrices to OT distances. Having this basic idea in mind, we consider both the algorithmic and the modeling part of unsupervised metric learning. F","authors_text":"Gabriele Steidl, Janis Auffenberg, Jonas Bresch, Oleh Melnyk","cross_cats":["cs.LG","cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-07-17T13:06:24Z","title":"Unsupervised Ground Metric Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13094","kind":"arxiv","version":1},"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":"sha256:79b35b404d6a234bdb1ebc16eeb26888d1ab47ba488e7ca8aa127a9d0215d342","target":"record","created_at":"2026-07-05T11:38:54Z","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":"37dff59f51ab4b6c3387d98d5bf9618629c51382de83b72b6e5c470e5f7b97b4","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-07-17T13:06:24Z","title_canon_sha256":"c695c99a31775974ce1991406e599e8e0e968cffacedce6dc14c8e02028fb3fe"},"schema_version":"1.0","source":{"id":"2507.13094","kind":"arxiv","version":1}},"canonical_sha256":"c96c0dd9c6a3522b71960c230b2b7576d0716365f372277ee93e9a5cc229b501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c96c0dd9c6a3522b71960c230b2b7576d0716365f372277ee93e9a5cc229b501","first_computed_at":"2026-07-05T11:38:54.613711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:54.613711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4uPsu0RKNs1gAxgfv7uILw5wV2vjb0P6jpUzPHogOP6LRPHok5rr2j/HyVbog6aZN2jsV1BQnImWVVP6O+paAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:54.614182Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79b35b404d6a234bdb1ebc16eeb26888d1ab47ba488e7ca8aa127a9d0215d342","sha256:cf5d4b93b467c714495e87aea4996c535e2f1b18aa522ccb65fd21fa97572d54"],"state_sha256":"8f592c285e00844b97a0305192370fa8dc121217702157095405802d19a14ab7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TNEnqeNHgcyaRuk0qoHJ0o4+k+DKp+IW6EtJzu/cwK8L4FFHsVSmlrR80xV2mTXbY1raeReNwKE4xGg8T8ajCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:49:14.573426Z","bundle_sha256":"bc3600206e3120ca0fe9ccf2e285869f98d4747f79d27b08c8d751c17c1c7bf2"}}