{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4KXMX5GSXEFSW7BBPW3Z4BVNIF","short_pith_number":"pith:4KXMX5GS","schema_version":"1.0","canonical_sha256":"e2aecbf4d2b90b2b7c217db79e06ad41651f3f103c03499ed387198d2841602f","source":{"kind":"arxiv","id":"1809.01248","version":3},"attestation_state":"computed","paper":{"title":"Cauchy Fluxes and Gauss-Green Formulas for Divergence-Measure Fields over General Open Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Giovanni E. Comi, Gui-Qiang G. Chen, Monica Torres","submitted_at":"2018-09-04T21:30:25Z","abstract_excerpt":"We establish the interior and exterior Gauss-Green formulas for divergence-measure fields in $L^p$ over general open sets, motivated by the rigorous mathematical formulation of the physical principle of balance law via the Cauchy flux in the axiomatic foundation, for continuum mechanics allowing discontinuities and singularities. The method, based on a distance function, allows to give a representation of the interior (resp. exterior) normal trace of the field on the boundary of any given open set as the limit of classical normal traces over the boundaries of interior (resp. exterior) smooth a"},"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":"1809.01248","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-04T21:30:25Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"c85d9e67b474f7d5377d372ac42fdc6d6a223f4c06fef8fcc999c68dd05bc331","abstract_canon_sha256":"7c5f2c8d8db732df7f7e227e63f1f5071e61102151fcaae5187cfd45431fe694"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:03.829093Z","signature_b64":"/0r5lfbZFrznBZKFpD0XpjlkG3IADmiBG42QEo7w4kAi9bRjDhpW0UkPZ8O0Txsp77wEVnTJPN3c72Ok0HmkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2aecbf4d2b90b2b7c217db79e06ad41651f3f103c03499ed387198d2841602f","last_reissued_at":"2026-05-17T23:56:03.828565Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:03.828565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cauchy Fluxes and Gauss-Green Formulas for Divergence-Measure Fields over General Open Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Giovanni E. Comi, Gui-Qiang G. Chen, Monica Torres","submitted_at":"2018-09-04T21:30:25Z","abstract_excerpt":"We establish the interior and exterior Gauss-Green formulas for divergence-measure fields in $L^p$ over general open sets, motivated by the rigorous mathematical formulation of the physical principle of balance law via the Cauchy flux in the axiomatic foundation, for continuum mechanics allowing discontinuities and singularities. The method, based on a distance function, allows to give a representation of the interior (resp. exterior) normal trace of the field on the boundary of any given open set as the limit of classical normal traces over the boundaries of interior (resp. exterior) smooth a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01248","kind":"arxiv","version":3},"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":"1809.01248","created_at":"2026-05-17T23:56:03.828639+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01248v3","created_at":"2026-05-17T23:56:03.828639+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01248","created_at":"2026-05-17T23:56:03.828639+00:00"},{"alias_kind":"pith_short_12","alias_value":"4KXMX5GSXEFS","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4KXMX5GSXEFSW7BB","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4KXMX5GS","created_at":"2026-05-18T12:32:05.422762+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/4KXMX5GSXEFSW7BBPW3Z4BVNIF","json":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF.json","graph_json":"https://pith.science/api/pith-number/4KXMX5GSXEFSW7BBPW3Z4BVNIF/graph.json","events_json":"https://pith.science/api/pith-number/4KXMX5GSXEFSW7BBPW3Z4BVNIF/events.json","paper":"https://pith.science/paper/4KXMX5GS"},"agent_actions":{"view_html":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF","download_json":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF.json","view_paper":"https://pith.science/paper/4KXMX5GS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01248&json=true","fetch_graph":"https://pith.science/api/pith-number/4KXMX5GSXEFSW7BBPW3Z4BVNIF/graph.json","fetch_events":"https://pith.science/api/pith-number/4KXMX5GSXEFSW7BBPW3Z4BVNIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF/action/storage_attestation","attest_author":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF/action/author_attestation","sign_citation":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF/action/citation_signature","submit_replication":"https://pith.science/pith/4KXMX5GSXEFSW7BBPW3Z4BVNIF/action/replication_record"}},"created_at":"2026-05-17T23:56:03.828639+00:00","updated_at":"2026-05-17T23:56:03.828639+00:00"}