{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:THOA7SQTO2M57ZYFPWVCU4ADOF","short_pith_number":"pith:THOA7SQT","schema_version":"1.0","canonical_sha256":"99dc0fca137699dfe7057daa2a70037153fb3c733cd52aad1ffc0c403f7b244b","source":{"kind":"arxiv","id":"1701.02656","version":1},"attestation_state":"computed","paper":{"title":"An Anzellotti type pairing for divergence-measure fields and a notion of weakly super-$1$-harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Scheven, Thomas Schmidt","submitted_at":"2017-01-10T16:08:33Z","abstract_excerpt":"We study generalized products of divergence-measure fields and gradient measures of {\\rm BV} functions. These products depend on the choice of a representative of the {\\rm BV} function, and here we single out a specific choice which is suitable in order to define and investigate a notion of weak supersolutions for the $1$-Laplace operator."},"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":"1701.02656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-10T16:08:33Z","cross_cats_sorted":[],"title_canon_sha256":"ddc48443ea0f9f966f8d2445679071a2e5e7655255217daf985608f9f8e77bf0","abstract_canon_sha256":"41aa24c30ac139b5dcec920e646b481aac68a67b1829474a0a6641acf0d57fdb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:03.753703Z","signature_b64":"Bx9p9KwmfQwjkrrS/jsVhaH4ImFEzesN9Jg4nQEKPW3vUGTHk0xvCGaKIRxJVrrqGuyKNYcsO9jecothNtHPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99dc0fca137699dfe7057daa2a70037153fb3c733cd52aad1ffc0c403f7b244b","last_reissued_at":"2026-05-18T00:53:03.753166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:03.753166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Anzellotti type pairing for divergence-measure fields and a notion of weakly super-$1$-harmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Scheven, Thomas Schmidt","submitted_at":"2017-01-10T16:08:33Z","abstract_excerpt":"We study generalized products of divergence-measure fields and gradient measures of {\\rm BV} functions. These products depend on the choice of a representative of the {\\rm BV} function, and here we single out a specific choice which is suitable in order to define and investigate a notion of weak supersolutions for the $1$-Laplace operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02656","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":"1701.02656","created_at":"2026-05-18T00:53:03.753230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02656v1","created_at":"2026-05-18T00:53:03.753230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02656","created_at":"2026-05-18T00:53:03.753230+00:00"},{"alias_kind":"pith_short_12","alias_value":"THOA7SQTO2M5","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"THOA7SQTO2M57ZYF","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"THOA7SQT","created_at":"2026-05-18T12:31:46.661854+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.07043","citing_title":"The Free Boundary in a Higher-Dimensional Long-Range Segregation Model","ref_index":94,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF","json":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF.json","graph_json":"https://pith.science/api/pith-number/THOA7SQTO2M57ZYFPWVCU4ADOF/graph.json","events_json":"https://pith.science/api/pith-number/THOA7SQTO2M57ZYFPWVCU4ADOF/events.json","paper":"https://pith.science/paper/THOA7SQT"},"agent_actions":{"view_html":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF","download_json":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF.json","view_paper":"https://pith.science/paper/THOA7SQT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02656&json=true","fetch_graph":"https://pith.science/api/pith-number/THOA7SQTO2M57ZYFPWVCU4ADOF/graph.json","fetch_events":"https://pith.science/api/pith-number/THOA7SQTO2M57ZYFPWVCU4ADOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF/action/storage_attestation","attest_author":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF/action/author_attestation","sign_citation":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF/action/citation_signature","submit_replication":"https://pith.science/pith/THOA7SQTO2M57ZYFPWVCU4ADOF/action/replication_record"}},"created_at":"2026-05-18T00:53:03.753230+00:00","updated_at":"2026-05-18T00:53:03.753230+00:00"}