{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:7UKVG2QWFGJBCDZXTI22PXAJTF","short_pith_number":"pith:7UKVG2QW","canonical_record":{"source":{"id":"1911.00574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-01T20:12:14Z","cross_cats_sorted":[],"title_canon_sha256":"f13a8d5b6a9e3989a0cee0423fe24c6c2f79711218d1a57ec415861a662d0be4","abstract_canon_sha256":"060f236f4031eeca6cf28975e3217bc38545a74e1c6cec206d653f5a564d3016"},"schema_version":"1.0"},"canonical_sha256":"fd15536a162992110f379a35a7dc09997aca5c8ffdfe5bbb8e0b79ea01fa5001","source":{"kind":"arxiv","id":"1911.00574","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.00574","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1911.00574v2","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.00574","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"7UKVG2QWFGJB","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"7UKVG2QWFGJBCDZX","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"7UKVG2QW","created_at":"2026-07-05T02:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:7UKVG2QWFGJBCDZXTI22PXAJTF","target":"record","payload":{"canonical_record":{"source":{"id":"1911.00574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-01T20:12:14Z","cross_cats_sorted":[],"title_canon_sha256":"f13a8d5b6a9e3989a0cee0423fe24c6c2f79711218d1a57ec415861a662d0be4","abstract_canon_sha256":"060f236f4031eeca6cf28975e3217bc38545a74e1c6cec206d653f5a564d3016"},"schema_version":"1.0"},"canonical_sha256":"fd15536a162992110f379a35a7dc09997aca5c8ffdfe5bbb8e0b79ea01fa5001","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:29:52.480773Z","signature_b64":"7lsG2uaCRiG89fgUN4AFCnEq4R9qVpcEmhyRjxx/O3cRLD71H+sFyT8zYQvmJ0iOxAoQlOCrqmre5NsOy9dRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd15536a162992110f379a35a7dc09997aca5c8ffdfe5bbb8e0b79ea01fa5001","last_reissued_at":"2026-07-05T02:29:52.480275Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:29:52.480275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.00574","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":"2026-07-05T02:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jumzqrvoCGKq5+j5LsCXEhSdb5GJ3z/JtKl8Yp6yjYAlBr7fwmMS85M1Ld0LvhEIG1OTUc+FQNZ/XEYjECT8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:07:35.499069Z"},"content_sha256":"10552d60819c31c48b2c2826139b66563d4e191a17ccdd0783a04969d5e9ff1d","schema_version":"1.0","event_id":"sha256:10552d60819c31c48b2c2826139b66563d4e191a17ccdd0783a04969d5e9ff1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:7UKVG2QWFGJBCDZXTI22PXAJTF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local regularity result for an optimal transportation problem with rough measures in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Mellet, M. Molina, P.-E. Jabin","submitted_at":"2019-11-01T20:12:14Z","abstract_excerpt":"We investigate the properties of convex functions in the plane that satisfy a local inequality which generalizes the notion of sub-solution of Monge-Ampere equation for a Monge-Kantorovich problem with quadratic cost between non-absolutely continuous measures. For each measure, we introduce a discrete scale so that the measure behaves as an absolutely continuous measure up to that scale. Our main theorem then proves that such convex functions cannot exhibit any flat part at a scale larger than the corresponding discrete scales on the measures. This, in turn, implies a $C^1$ regularity result u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.00574","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/1911.00574/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":"2026-07-05T02:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c3DgCLAIfqLrDWj61KmYydf5EkDCkzCFLGLgrRqBWgXUXHko4H5O/a8hG5GEZoz9/wPhwM6dIBCiOuLg0p5UAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T09:07:35.499449Z"},"content_sha256":"1652aa03f7e587bdcef7893f93422b31616727059ac20b2d808887558f139bb6","schema_version":"1.0","event_id":"sha256:1652aa03f7e587bdcef7893f93422b31616727059ac20b2d808887558f139bb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UKVG2QWFGJBCDZXTI22PXAJTF/bundle.json","state_url":"https://pith.science/pith/7UKVG2QWFGJBCDZXTI22PXAJTF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UKVG2QWFGJBCDZXTI22PXAJTF/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":"2026-07-07T09:07:35Z","links":{"resolver":"https://pith.science/pith/7UKVG2QWFGJBCDZXTI22PXAJTF","bundle":"https://pith.science/pith/7UKVG2QWFGJBCDZXTI22PXAJTF/bundle.json","state":"https://pith.science/pith/7UKVG2QWFGJBCDZXTI22PXAJTF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UKVG2QWFGJBCDZXTI22PXAJTF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7UKVG2QWFGJBCDZXTI22PXAJTF","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":"060f236f4031eeca6cf28975e3217bc38545a74e1c6cec206d653f5a564d3016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-01T20:12:14Z","title_canon_sha256":"f13a8d5b6a9e3989a0cee0423fe24c6c2f79711218d1a57ec415861a662d0be4"},"schema_version":"1.0","source":{"id":"1911.00574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.00574","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1911.00574v2","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.00574","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"7UKVG2QWFGJB","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"7UKVG2QWFGJBCDZX","created_at":"2026-07-05T02:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"7UKVG2QW","created_at":"2026-07-05T02:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:1652aa03f7e587bdcef7893f93422b31616727059ac20b2d808887558f139bb6","target":"graph","created_at":"2026-07-05T02:29:52Z","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/1911.00574/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the properties of convex functions in the plane that satisfy a local inequality which generalizes the notion of sub-solution of Monge-Ampere equation for a Monge-Kantorovich problem with quadratic cost between non-absolutely continuous measures. For each measure, we introduce a discrete scale so that the measure behaves as an absolutely continuous measure up to that scale. Our main theorem then proves that such convex functions cannot exhibit any flat part at a scale larger than the corresponding discrete scales on the measures. This, in turn, implies a $C^1$ regularity result u","authors_text":"A. Mellet, M. Molina, P.-E. Jabin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-01T20:12:14Z","title":"Local regularity result for an optimal transportation problem with rough measures in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.00574","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":"sha256:10552d60819c31c48b2c2826139b66563d4e191a17ccdd0783a04969d5e9ff1d","target":"record","created_at":"2026-07-05T02:29:52Z","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":"060f236f4031eeca6cf28975e3217bc38545a74e1c6cec206d653f5a564d3016","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-11-01T20:12:14Z","title_canon_sha256":"f13a8d5b6a9e3989a0cee0423fe24c6c2f79711218d1a57ec415861a662d0be4"},"schema_version":"1.0","source":{"id":"1911.00574","kind":"arxiv","version":2}},"canonical_sha256":"fd15536a162992110f379a35a7dc09997aca5c8ffdfe5bbb8e0b79ea01fa5001","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd15536a162992110f379a35a7dc09997aca5c8ffdfe5bbb8e0b79ea01fa5001","first_computed_at":"2026-07-05T02:29:52.480275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:29:52.480275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7lsG2uaCRiG89fgUN4AFCnEq4R9qVpcEmhyRjxx/O3cRLD71H+sFyT8zYQvmJ0iOxAoQlOCrqmre5NsOy9dRCw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:29:52.480773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.00574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10552d60819c31c48b2c2826139b66563d4e191a17ccdd0783a04969d5e9ff1d","sha256:1652aa03f7e587bdcef7893f93422b31616727059ac20b2d808887558f139bb6"],"state_sha256":"0c764b8df701ba13b0db0ad8a5cd5f955d90d632d990931ea37fd074f45008e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NHjOqnfmCwPDHp0w4L4BY3BV1+Ene7mffic5M8bK+2QGMAJnbTqmPP10MW9h3LGtGHLQXYI+QmcttUvIGIqPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T09:07:35.501337Z","bundle_sha256":"c845bf5d1b2f7f050514569dafce3ba8f1564db180441b878c3fecc085fb88dd"}}