{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MREQRSOID6F7I6OTDAJIVF6SCU","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":"23a2b74308c38bcf087aa3f83e28186c6ddaf14f83db333cdae46bdbcb728cfc","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-12T11:58:08Z","title_canon_sha256":"c0d49b611076b8a053f0eb1e87ceb9265693c85ecee23b4271a4791f3c3075ee"},"schema_version":"1.0","source":{"id":"1702.03517","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03517","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03517v3","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03517","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"pith_short_12","alias_value":"MREQRSOID6F7","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MREQRSOID6F7I6OT","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MREQRSOI","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:88f23d100dbbb4d87bd7d38bc33654779a30d89ba57b2cbcda44fc8f8508aa02","target":"graph","created_at":"2026-05-17T23:47:12Z","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":"We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving complexity. For cost functions equal to a p-norm with p in (1,infinity), we provide mathematical justification, convergence analysis, and algorithmic development. Our testing supports the boundary method with these p-norms, as well as other, more general cost functions.","authors_text":"J.D. Walsh III, Luca Dieci","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-12T11:58:08Z","title":"The boundary method for semi-discrete optimal transport partitions and Wasserstein distance computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03517","kind":"arxiv","version":3},"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:fe807343d74763c7640ec2d66bfa2dac220eaa1050cdb029f13fb047c50b0cab","target":"record","created_at":"2026-05-17T23:47:12Z","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":"23a2b74308c38bcf087aa3f83e28186c6ddaf14f83db333cdae46bdbcb728cfc","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-12T11:58:08Z","title_canon_sha256":"c0d49b611076b8a053f0eb1e87ceb9265693c85ecee23b4271a4791f3c3075ee"},"schema_version":"1.0","source":{"id":"1702.03517","kind":"arxiv","version":3}},"canonical_sha256":"644908c9c81f8bf479d318128a97d21501d7b31a3da00a42595d09b1f32b5dbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"644908c9c81f8bf479d318128a97d21501d7b31a3da00a42595d09b1f32b5dbf","first_computed_at":"2026-05-17T23:47:12.908931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:12.908931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uGc8WkoJDVjo5rUIFmdFApZ45sgeaAsv7ySIIMg9lehijF+yZzeuyhFIkXdYhZVxXD81kDnIEuTARY2hO1FNBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:12.909308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03517","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe807343d74763c7640ec2d66bfa2dac220eaa1050cdb029f13fb047c50b0cab","sha256:88f23d100dbbb4d87bd7d38bc33654779a30d89ba57b2cbcda44fc8f8508aa02"],"state_sha256":"a2a3265d4b8d6b8a74a0e44e3f708b610d18e81ff1d79b2bdaf73fd88bd27514"}