{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CMWOXCQSHXZA45EJZXNR7TSKTU","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":"b25c2ab928728fc21fe0501e77b8dc8136aaa8505f7bc3ca8a98c1fbee8fb897","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-03-08T11:01:34Z","title_canon_sha256":"a074710eaa287a5efc6746d2f46478143ab21abff574884c098641fa049ebd64"},"schema_version":"1.0","source":{"id":"0803.1235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1235","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1235v1","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1235","created_at":"2026-05-18T02:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"CMWOXCQSHXZA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CMWOXCQSHXZA45EJ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CMWOXCQS","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:08369c899145600dd430c3f8dc38f8032063a4fdc4b950d4e13b87f9daf9fe78","target":"graph","created_at":"2026-05-18T02:42:54Z","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"},"paper":{"abstract_excerpt":"We introduce a new class of distances between nonnegative Radon measures in Euclidean spaces. They are modeled on the dynamical characterization of the Kantorovich-Rubinstein-Wasserstein distances proposed by Benamou-Brenier and provide a wide family interpolating between the Wasserstein and the homogeneous (dual) Sobolev distances.\n  From the point of view of optimal transport theory, these distances minimize a dynamical cost to move a given initial distribution of mass to a final configuration. An important difference with the classical setting in mass transport theory is that the cost not o","authors_text":"Bruno Nazaret, Giuseppe Savare, Jean Dolbeault","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-03-08T11:01:34Z","title":"A new class of transport distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1235","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:a80934076e468d8666d4ada01ef59b5fe5b6f35bfc1908cda51476bff2aea3ac","target":"record","created_at":"2026-05-18T02:42:54Z","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":"b25c2ab928728fc21fe0501e77b8dc8136aaa8505f7bc3ca8a98c1fbee8fb897","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-03-08T11:01:34Z","title_canon_sha256":"a074710eaa287a5efc6746d2f46478143ab21abff574884c098641fa049ebd64"},"schema_version":"1.0","source":{"id":"0803.1235","kind":"arxiv","version":1}},"canonical_sha256":"132ceb8a123df20e7489cddb1fce4a9d04e72b21c3a31e61b788ccfcdcb3448d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"132ceb8a123df20e7489cddb1fce4a9d04e72b21c3a31e61b788ccfcdcb3448d","first_computed_at":"2026-05-18T02:42:54.563443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:54.563443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mtNWZ/2Cjv/9fwVLHyRvmllWT+dwwr1d9zCChTKOWBgt6brjjYomZF72+O/td+77MN1E/Db2YuOg+hKIhRgHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:54.563840Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.1235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a80934076e468d8666d4ada01ef59b5fe5b6f35bfc1908cda51476bff2aea3ac","sha256:08369c899145600dd430c3f8dc38f8032063a4fdc4b950d4e13b87f9daf9fe78"],"state_sha256":"1c5a5bd381e0896b5ad7f2d5dfaad09bd15183a01112c2cea6721881a06b13ee"}