{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ALVBFF7JDCMZ3BF5RVAYTP5ZEI","short_pith_number":"pith:ALVBFF7J","schema_version":"1.0","canonical_sha256":"02ea1297e918999d84bd8d4189bfb9223a797c2d1eb88dc7df774e13301947d6","source":{"kind":"arxiv","id":"1605.09005","version":1},"attestation_state":"computed","paper":{"title":"On the chain rule formulas for divergences and applications to conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Graziano Crasta, Virginia De Cicco","submitted_at":"2016-05-29T14:01:53Z","abstract_excerpt":"In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function $\\boldsymbol{v}(x)=\\boldsymbol{B}(x,u(x))$, where $\\boldsymbol{B}(\\cdot,t)$ is a divergence--measure vector field and $u$ is a function of bounded variation. As an application, we prove a uniqueness result for scalar conservation laws with discontinuous flux."},"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":"1605.09005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-29T14:01:53Z","cross_cats_sorted":[],"title_canon_sha256":"6534e6e5ee7963df7e11e28de33d1970692f366d2815475561dabf109932eeaf","abstract_canon_sha256":"58867b6b09ca06d250da86f0917cf5bd9c5dec2fc9aa4b8caebb8dc9f81b133f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:21.270006Z","signature_b64":"ixlsZb7gwOEjeQ6kjntTXrOsQMb9ETbF2M9OoW+8d9HIfNT0JWyPfJ6PvoHFHwwcYjy47wkhaZcCYI7qE/NhCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02ea1297e918999d84bd8d4189bfb9223a797c2d1eb88dc7df774e13301947d6","last_reissued_at":"2026-05-17T23:45:21.269343Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:21.269343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the chain rule formulas for divergences and applications to conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Graziano Crasta, Virginia De Cicco","submitted_at":"2016-05-29T14:01:53Z","abstract_excerpt":"In this paper we prove a nonautonomous chain rule formula for the distributional divergence of the composite function $\\boldsymbol{v}(x)=\\boldsymbol{B}(x,u(x))$, where $\\boldsymbol{B}(\\cdot,t)$ is a divergence--measure vector field and $u$ is a function of bounded variation. As an application, we prove a uniqueness result for scalar conservation laws with discontinuous flux."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09005","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":"1605.09005","created_at":"2026-05-17T23:45:21.269457+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.09005v1","created_at":"2026-05-17T23:45:21.269457+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09005","created_at":"2026-05-17T23:45:21.269457+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALVBFF7JDCMZ","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALVBFF7JDCMZ3BF5","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALVBFF7J","created_at":"2026-05-18T12:30:07.202191+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/ALVBFF7JDCMZ3BF5RVAYTP5ZEI","json":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI.json","graph_json":"https://pith.science/api/pith-number/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/graph.json","events_json":"https://pith.science/api/pith-number/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/events.json","paper":"https://pith.science/paper/ALVBFF7J"},"agent_actions":{"view_html":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI","download_json":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI.json","view_paper":"https://pith.science/paper/ALVBFF7J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.09005&json=true","fetch_graph":"https://pith.science/api/pith-number/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/graph.json","fetch_events":"https://pith.science/api/pith-number/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/action/storage_attestation","attest_author":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/action/author_attestation","sign_citation":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/action/citation_signature","submit_replication":"https://pith.science/pith/ALVBFF7JDCMZ3BF5RVAYTP5ZEI/action/replication_record"}},"created_at":"2026-05-17T23:45:21.269457+00:00","updated_at":"2026-05-17T23:45:21.269457+00:00"}