{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:JAB3LZ54X2SPYZ5E5JTZY77OOC","short_pith_number":"pith:JAB3LZ54","canonical_record":{"source":{"id":"2003.06725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-15T00:17:24Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"97472069a2d2a26e52a0c436ceccd3f994e3832a102dfcf56184f914d0fe4489","abstract_canon_sha256":"6c942276deaea8d7ba6f35ee2ff6705a1858b3a30d77df2b31402b944e769e30"},"schema_version":"1.0"},"canonical_sha256":"4803b5e7bcbea4fc67a4ea679c7fee708cc6ed2b872f5c00bef630b2077add0d","source":{"kind":"arxiv","id":"2003.06725","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.06725","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"2003.06725v2","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.06725","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"JAB3LZ54X2SP","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"pith_short_16","alias_value":"JAB3LZ54X2SPYZ5E","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"pith_short_8","alias_value":"JAB3LZ54","created_at":"2026-07-05T01:43:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:JAB3LZ54X2SPYZ5E5JTZY77OOC","target":"record","payload":{"canonical_record":{"source":{"id":"2003.06725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-15T00:17:24Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"97472069a2d2a26e52a0c436ceccd3f994e3832a102dfcf56184f914d0fe4489","abstract_canon_sha256":"6c942276deaea8d7ba6f35ee2ff6705a1858b3a30d77df2b31402b944e769e30"},"schema_version":"1.0"},"canonical_sha256":"4803b5e7bcbea4fc67a4ea679c7fee708cc6ed2b872f5c00bef630b2077add0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:43:14.409761Z","signature_b64":"uOyWv7BszaiK3EzA/lCnMIx9uKysaCTR8HeBEY1fEyRIMeIXMtsOtHFMVE57JMdEopygcQeEVW14Bh7MGn8NAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4803b5e7bcbea4fc67a4ea679c7fee708cc6ed2b872f5c00bef630b2077add0d","last_reissued_at":"2026-07-05T01:43:14.409277Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:43:14.409277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.06725","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ExKFbi0Apr+20SWmHKLhf6Sd/U/5Ywd7UBALEgmOYuxLyiKTmjVK1uKrHStxVB/gftcH//7S69n0qcocwqdXCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:45:31.802808Z"},"content_sha256":"5146b251d6c264caff40ab8a510ecd1e1b4320a8bce0712a3363a6d8069cade8","schema_version":"1.0","event_id":"sha256:5146b251d6c264caff40ab8a510ecd1e1b4320a8bce0712a3363a6d8069cade8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:JAB3LZ54X2SPYZ5E5JTZY77OOC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wasserstein Distance to Independence Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.OC","authors_text":"Asgar Jamneshan, Bernd Sturmfels, Guido Mont\\'ufar, Lorenzo Venturello, T\\\"urk\\\"u \\\"Ozl\\\"um \\c{C}elik","submitted_at":"2020-03-15T00:17:24Z","abstract_excerpt":"An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball of this polyhedral norm is dual to the Lipschitz polytope. Given any data distribution, we seek to minimize its Wasserstein distance to a fixed independence model. The solution to this optimization problem is a piecewise algebraic function of the data. We compute this function explicitly in small instances, we examine its combinatorial structure and algebraic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.06725","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/2003.06725/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":"2026-07-05T01:43:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WcwKQ7kyzCyirRb3nLMPKnSKcKLqQehYao3ZGsu1wz3Eb3SfqEAx9cLTUuiSTAjPW5jImSkPq4xZ7rbQ3GrTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:45:31.803342Z"},"content_sha256":"dd4c5c1ad36e537592397f27c6b0bd282b1e4e2ba08ed39731a690852be9cf7b","schema_version":"1.0","event_id":"sha256:dd4c5c1ad36e537592397f27c6b0bd282b1e4e2ba08ed39731a690852be9cf7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAB3LZ54X2SPYZ5E5JTZY77OOC/bundle.json","state_url":"https://pith.science/pith/JAB3LZ54X2SPYZ5E5JTZY77OOC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAB3LZ54X2SPYZ5E5JTZY77OOC/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":"2026-08-11T11:45:31Z","links":{"resolver":"https://pith.science/pith/JAB3LZ54X2SPYZ5E5JTZY77OOC","bundle":"https://pith.science/pith/JAB3LZ54X2SPYZ5E5JTZY77OOC/bundle.json","state":"https://pith.science/pith/JAB3LZ54X2SPYZ5E5JTZY77OOC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAB3LZ54X2SPYZ5E5JTZY77OOC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:JAB3LZ54X2SPYZ5E5JTZY77OOC","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":"6c942276deaea8d7ba6f35ee2ff6705a1858b3a30d77df2b31402b944e769e30","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-15T00:17:24Z","title_canon_sha256":"97472069a2d2a26e52a0c436ceccd3f994e3832a102dfcf56184f914d0fe4489"},"schema_version":"1.0","source":{"id":"2003.06725","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.06725","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"arxiv_version","alias_value":"2003.06725v2","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.06725","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"pith_short_12","alias_value":"JAB3LZ54X2SP","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"pith_short_16","alias_value":"JAB3LZ54X2SPYZ5E","created_at":"2026-07-05T01:43:14Z"},{"alias_kind":"pith_short_8","alias_value":"JAB3LZ54","created_at":"2026-07-05T01:43:14Z"}],"graph_snapshots":[{"event_id":"sha256:dd4c5c1ad36e537592397f27c6b0bd282b1e4e2ba08ed39731a690852be9cf7b","target":"graph","created_at":"2026-07-05T01:43:14Z","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/2003.06725/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. Any metric on the set of joint states of the random variables induces a Wasserstein metric on the probability simplex. The unit ball of this polyhedral norm is dual to the Lipschitz polytope. Given any data distribution, we seek to minimize its Wasserstein distance to a fixed independence model. The solution to this optimization problem is a piecewise algebraic function of the data. We compute this function explicitly in small instances, we examine its combinatorial structure and algebraic","authors_text":"Asgar Jamneshan, Bernd Sturmfels, Guido Mont\\'ufar, Lorenzo Venturello, T\\\"urk\\\"u \\\"Ozl\\\"um \\c{C}elik","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-15T00:17:24Z","title":"Wasserstein Distance to Independence Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.06725","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":"sha256:5146b251d6c264caff40ab8a510ecd1e1b4320a8bce0712a3363a6d8069cade8","target":"record","created_at":"2026-07-05T01:43:14Z","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":"6c942276deaea8d7ba6f35ee2ff6705a1858b3a30d77df2b31402b944e769e30","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-03-15T00:17:24Z","title_canon_sha256":"97472069a2d2a26e52a0c436ceccd3f994e3832a102dfcf56184f914d0fe4489"},"schema_version":"1.0","source":{"id":"2003.06725","kind":"arxiv","version":2}},"canonical_sha256":"4803b5e7bcbea4fc67a4ea679c7fee708cc6ed2b872f5c00bef630b2077add0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4803b5e7bcbea4fc67a4ea679c7fee708cc6ed2b872f5c00bef630b2077add0d","first_computed_at":"2026-07-05T01:43:14.409277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:43:14.409277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uOyWv7BszaiK3EzA/lCnMIx9uKysaCTR8HeBEY1fEyRIMeIXMtsOtHFMVE57JMdEopygcQeEVW14Bh7MGn8NAw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:43:14.409761Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.06725","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5146b251d6c264caff40ab8a510ecd1e1b4320a8bce0712a3363a6d8069cade8","sha256:dd4c5c1ad36e537592397f27c6b0bd282b1e4e2ba08ed39731a690852be9cf7b"],"state_sha256":"57b9e2810f375da2aa127a9c508eabdf9ab9050755772d01f4b8e74999ed26f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rOZ+UfjxiZogabSz0BkCu4JApEcxBgyzLWgEaXJOHlQbw1tMjZHb95hZgkyevlMvt0gRQVlE9RUf3kEPERFCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T11:45:31.807203Z","bundle_sha256":"17313b3228c862e4467f79e94dcd768d0b8ecc88c896700001e3ba6fe347e5e1"}}