{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YT6JSX2DO5HGFVUMKNZNVSQXBI","short_pith_number":"pith:YT6JSX2D","schema_version":"1.0","canonical_sha256":"c4fc995f43774e62d68c5372daca170a3f8fef518b64f27e80fe8aa8f6010904","source":{"kind":"arxiv","id":"1302.1650","version":1},"attestation_state":"computed","paper":{"title":"Fractional BV spaces and first applications to scalar conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christian Bourdarias (LAMA), Marguerite Gisclon (LAMA), St\\'ephane Junca (JAD)","submitted_at":"2013-02-07T07:10:03Z","abstract_excerpt":"The aim of this paper is to obtain new fine properties of entropy solutions of nonlinear scalar conservation laws. For this purpose, we study some \"fractional $BV$ spaces\" denoted $BV^s$, for $0 < s \\leq 1$, introduced by Love and Young in 1937. The $BV^s(\\R)$ spaces are very closed to the critical Sobolev space $W^{s,1/s}(\\R)$. We investigate these spaces in relation with one-dimensional scalar conservation laws. $BV^s$ spaces allow to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions with $BV^s"},"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":"1302.1650","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-07T07:10:03Z","cross_cats_sorted":[],"title_canon_sha256":"613cf24d3e5fa75fb428a800870d6a2130e61ab9ba219201ff975141143f3f4a","abstract_canon_sha256":"4a659d40146d6530a9f53d21da318f25dbc4c74455a7826f1a0a4e6c211de2c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:15.173127Z","signature_b64":"qStfauNIeyDkox0HsNr4W71cHaueVmEtH2Uaw1IWOqOPJ57LYJsa6AkTkdbHztQMEd/BC6F6XFWyRcEv0EW2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4fc995f43774e62d68c5372daca170a3f8fef518b64f27e80fe8aa8f6010904","last_reissued_at":"2026-05-18T03:34:15.172476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:15.172476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional BV spaces and first applications to scalar conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christian Bourdarias (LAMA), Marguerite Gisclon (LAMA), St\\'ephane Junca (JAD)","submitted_at":"2013-02-07T07:10:03Z","abstract_excerpt":"The aim of this paper is to obtain new fine properties of entropy solutions of nonlinear scalar conservation laws. For this purpose, we study some \"fractional $BV$ spaces\" denoted $BV^s$, for $0 < s \\leq 1$, introduced by Love and Young in 1937. The $BV^s(\\R)$ spaces are very closed to the critical Sobolev space $W^{s,1/s}(\\R)$. We investigate these spaces in relation with one-dimensional scalar conservation laws. $BV^s$ spaces allow to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions with $BV^s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1650","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":"1302.1650","created_at":"2026-05-18T03:34:15.172598+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.1650v1","created_at":"2026-05-18T03:34:15.172598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1650","created_at":"2026-05-18T03:34:15.172598+00:00"},{"alias_kind":"pith_short_12","alias_value":"YT6JSX2DO5HG","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YT6JSX2DO5HGFVUM","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YT6JSX2D","created_at":"2026-05-18T12:28:09.283467+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/YT6JSX2DO5HGFVUMKNZNVSQXBI","json":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI.json","graph_json":"https://pith.science/api/pith-number/YT6JSX2DO5HGFVUMKNZNVSQXBI/graph.json","events_json":"https://pith.science/api/pith-number/YT6JSX2DO5HGFVUMKNZNVSQXBI/events.json","paper":"https://pith.science/paper/YT6JSX2D"},"agent_actions":{"view_html":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI","download_json":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI.json","view_paper":"https://pith.science/paper/YT6JSX2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.1650&json=true","fetch_graph":"https://pith.science/api/pith-number/YT6JSX2DO5HGFVUMKNZNVSQXBI/graph.json","fetch_events":"https://pith.science/api/pith-number/YT6JSX2DO5HGFVUMKNZNVSQXBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI/action/storage_attestation","attest_author":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI/action/author_attestation","sign_citation":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI/action/citation_signature","submit_replication":"https://pith.science/pith/YT6JSX2DO5HGFVUMKNZNVSQXBI/action/replication_record"}},"created_at":"2026-05-18T03:34:15.172598+00:00","updated_at":"2026-05-18T03:34:15.172598+00:00"}