{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:72LSPC6RHLC5V3LRCF4FDFMUFF","short_pith_number":"pith:72LSPC6R","canonical_record":{"source":{"id":"1208.4873","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-23T22:09:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e7f8f05b2a8f9102d3be5d8b0bfda138dcdc1a859d831d09f3e29a6f13fbec8d","abstract_canon_sha256":"3fe9f3da1fb6e47cd95a85547217c3487f2f2e420c79221d8f58e8f671aa0b57"},"schema_version":"1.0"},"canonical_sha256":"fe97278bd13ac5daed711178519594297864c88cb6d92f5d35e46b4e1fa9c27e","source":{"kind":"arxiv","id":"1208.4873","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4873","created_at":"2026-05-18T03:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4873v2","created_at":"2026-05-18T03:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4873","created_at":"2026-05-18T03:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"72LSPC6RHLC5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"72LSPC6RHLC5V3LR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"72LSPC6R","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:72LSPC6RHLC5V3LRCF4FDFMUFF","target":"record","payload":{"canonical_record":{"source":{"id":"1208.4873","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-23T22:09:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e7f8f05b2a8f9102d3be5d8b0bfda138dcdc1a859d831d09f3e29a6f13fbec8d","abstract_canon_sha256":"3fe9f3da1fb6e47cd95a85547217c3487f2f2e420c79221d8f58e8f671aa0b57"},"schema_version":"1.0"},"canonical_sha256":"fe97278bd13ac5daed711178519594297864c88cb6d92f5d35e46b4e1fa9c27e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:49.731978Z","signature_b64":"rZoyeb62CSJTuTc/nV1gS+35e0BYEB/jckgke939HMvNpO0fA2Q6RhBd9tawptu8/8ZmKiHsmYEupgzhFgNZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe97278bd13ac5daed711178519594297864c88cb6d92f5d35e46b4e1fa9c27e","last_reissued_at":"2026-05-18T03:16:49.731232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:49.731232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.4873","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":"2026-05-18T03:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6e9XeVM4XP8qEFXR69Qi4GlIzZkJtRO66oNLQEznG00IS5uH5ONjKO3y8pz0kNw2XHmV91k+Mbn7Aw2FWbvFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:30:41.973099Z"},"content_sha256":"28b92eedf1ec4964e3e662c171ffb139ad3969979f8886d3545b518ef6f5aadf","schema_version":"1.0","event_id":"sha256:28b92eedf1ec4964e3e662c171ffb139ad3969979f8886d3545b518ef6f5aadf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:72LSPC6RHLC5V3LRCF4FDFMUFF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A viscosity solution approach to the Monge-Ampere formulation of the Optimal Transportation Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Adam M. Oberman, Brittany D. Froese, Jean-David Benamou","submitted_at":"2012-08-23T22:09:07Z","abstract_excerpt":"In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as applications in diverse areas. Numerical solution techniques for the OT problem remain underdeveloped. The solution is obtained by solving the second boundary value problem for the MA equation, a fully nonlinear elliptic partial differential equation (PDE). Instead of standard boundary conditions the problem has global state constraints. These are reformulated as a tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4873","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":""},"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":"2026-05-18T03:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7S93qAFwoHnIKhHJRt6yeSUtpJUyhXIweIk0jRAdGA02deXmHpKTWn0IGsR5+jLP1/UjpGm/sSIDsLAfTPtLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:30:41.973765Z"},"content_sha256":"85eaff1b0531b053e1af4138002a595c7f7fc6d1beffa783f7f68adea7152d2c","schema_version":"1.0","event_id":"sha256:85eaff1b0531b053e1af4138002a595c7f7fc6d1beffa783f7f68adea7152d2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72LSPC6RHLC5V3LRCF4FDFMUFF/bundle.json","state_url":"https://pith.science/pith/72LSPC6RHLC5V3LRCF4FDFMUFF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72LSPC6RHLC5V3LRCF4FDFMUFF/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":"2026-05-30T23:30:41Z","links":{"resolver":"https://pith.science/pith/72LSPC6RHLC5V3LRCF4FDFMUFF","bundle":"https://pith.science/pith/72LSPC6RHLC5V3LRCF4FDFMUFF/bundle.json","state":"https://pith.science/pith/72LSPC6RHLC5V3LRCF4FDFMUFF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72LSPC6RHLC5V3LRCF4FDFMUFF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:72LSPC6RHLC5V3LRCF4FDFMUFF","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":"3fe9f3da1fb6e47cd95a85547217c3487f2f2e420c79221d8f58e8f671aa0b57","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-23T22:09:07Z","title_canon_sha256":"e7f8f05b2a8f9102d3be5d8b0bfda138dcdc1a859d831d09f3e29a6f13fbec8d"},"schema_version":"1.0","source":{"id":"1208.4873","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4873","created_at":"2026-05-18T03:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4873v2","created_at":"2026-05-18T03:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4873","created_at":"2026-05-18T03:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"72LSPC6RHLC5","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"72LSPC6RHLC5V3LR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"72LSPC6R","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:85eaff1b0531b053e1af4138002a595c7f7fc6d1beffa783f7f68adea7152d2c","target":"graph","created_at":"2026-05-18T03:16:49Z","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"},"paper":{"abstract_excerpt":"In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as applications in diverse areas. Numerical solution techniques for the OT problem remain underdeveloped. The solution is obtained by solving the second boundary value problem for the MA equation, a fully nonlinear elliptic partial differential equation (PDE). Instead of standard boundary conditions the problem has global state constraints. These are reformulated as a tr","authors_text":"Adam M. Oberman, Brittany D. Froese, Jean-David Benamou","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-23T22:09:07Z","title":"A viscosity solution approach to the Monge-Ampere formulation of the Optimal Transportation Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4873","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":"sha256:28b92eedf1ec4964e3e662c171ffb139ad3969979f8886d3545b518ef6f5aadf","target":"record","created_at":"2026-05-18T03:16:49Z","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":"3fe9f3da1fb6e47cd95a85547217c3487f2f2e420c79221d8f58e8f671aa0b57","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-08-23T22:09:07Z","title_canon_sha256":"e7f8f05b2a8f9102d3be5d8b0bfda138dcdc1a859d831d09f3e29a6f13fbec8d"},"schema_version":"1.0","source":{"id":"1208.4873","kind":"arxiv","version":2}},"canonical_sha256":"fe97278bd13ac5daed711178519594297864c88cb6d92f5d35e46b4e1fa9c27e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe97278bd13ac5daed711178519594297864c88cb6d92f5d35e46b4e1fa9c27e","first_computed_at":"2026-05-18T03:16:49.731232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:49.731232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rZoyeb62CSJTuTc/nV1gS+35e0BYEB/jckgke939HMvNpO0fA2Q6RhBd9tawptu8/8ZmKiHsmYEupgzhFgNZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:49.731978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4873","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28b92eedf1ec4964e3e662c171ffb139ad3969979f8886d3545b518ef6f5aadf","sha256:85eaff1b0531b053e1af4138002a595c7f7fc6d1beffa783f7f68adea7152d2c"],"state_sha256":"70fd4b73cc7aa6ea53ee9570d3e77e629a04b5b633806d487a466dd192d6326f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D64wqZqpmbDgGqIjuwagVv9R/RJi9JGuweP+UPTkKyHrD0MfQbW75lyE6p8r7N2hhGJepu7eUgAMCAAilUcSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:30:41.977716Z","bundle_sha256":"ae84caeb011220b781085156ed712a3ac03bf254aade1a70d6f55ee48e1452b1"}}