{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:D3ZVNG72YHIJKVXNX5ME4CVU4X","short_pith_number":"pith:D3ZVNG72","schema_version":"1.0","canonical_sha256":"1ef3569bfac1d09556edbf584e0ab4e5d69c376f66772516d74b5c728c4cce97","source":{"kind":"arxiv","id":"math/0504136","version":1},"attestation_state":"computed","paper":{"title":"Contractive metrics for scalar conservation laws","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"F. Bolley, G. Loeper, Y. Brenier","submitted_at":"2005-04-07T12:27:55Z","abstract_excerpt":"We consider nondecreasing entropy solutions to 1-d scalar conservation laws and show that the spatial derivatives of such solutions satisfy a contraction property with respect to the Wasserstein distance of any order. This result extends the L^1-contraction property shown by Kruzkov."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0504136","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2005-04-07T12:27:55Z","cross_cats_sorted":[],"title_canon_sha256":"cf3e975d3fef73077e6ed9a7760cad4c8d1b52c9e47836e877b23055f2bd773a","abstract_canon_sha256":"3a7171a69a5594dea26593a950b86074d163ea86399d21ca2232ffc64ea75465"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:58.392853Z","signature_b64":"qA3FFkaGOiXa34gnxoKCjdPtJ1sFthLyiXScuArfka5eZUo3DLcY2JJ5pAbZCueEHULmDUEyawLGTmj68jBGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ef3569bfac1d09556edbf584e0ab4e5d69c376f66772516d74b5c728c4cce97","last_reissued_at":"2026-05-18T03:12:58.392177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:58.392177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Contractive metrics for scalar conservation laws","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"F. Bolley, G. Loeper, Y. Brenier","submitted_at":"2005-04-07T12:27:55Z","abstract_excerpt":"We consider nondecreasing entropy solutions to 1-d scalar conservation laws and show that the spatial derivatives of such solutions satisfy a contraction property with respect to the Wasserstein distance of any order. This result extends the L^1-contraction property shown by Kruzkov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504136","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0504136","created_at":"2026-05-18T03:12:58.392286+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0504136v1","created_at":"2026-05-18T03:12:58.392286+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504136","created_at":"2026-05-18T03:12:58.392286+00:00"},{"alias_kind":"pith_short_12","alias_value":"D3ZVNG72YHIJ","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"D3ZVNG72YHIJKVXN","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"D3ZVNG72","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X","json":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X.json","graph_json":"https://pith.science/api/pith-number/D3ZVNG72YHIJKVXNX5ME4CVU4X/graph.json","events_json":"https://pith.science/api/pith-number/D3ZVNG72YHIJKVXNX5ME4CVU4X/events.json","paper":"https://pith.science/paper/D3ZVNG72"},"agent_actions":{"view_html":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X","download_json":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X.json","view_paper":"https://pith.science/paper/D3ZVNG72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0504136&json=true","fetch_graph":"https://pith.science/api/pith-number/D3ZVNG72YHIJKVXNX5ME4CVU4X/graph.json","fetch_events":"https://pith.science/api/pith-number/D3ZVNG72YHIJKVXNX5ME4CVU4X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X/action/storage_attestation","attest_author":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X/action/author_attestation","sign_citation":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X/action/citation_signature","submit_replication":"https://pith.science/pith/D3ZVNG72YHIJKVXNX5ME4CVU4X/action/replication_record"}},"created_at":"2026-05-18T03:12:58.392286+00:00","updated_at":"2026-05-18T03:12:58.392286+00:00"}