{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GUGSJR6PBCT2XQGW6SEN6LVGAK","short_pith_number":"pith:GUGSJR6P","schema_version":"1.0","canonical_sha256":"350d24c7cf08a7abc0d6f488df2ea602acbc21ad1bb5ccfd87b396f234bc8b29","source":{"kind":"arxiv","id":"1503.07928","version":2},"attestation_state":"computed","paper":{"title":"A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Colin Klaus, Emmanuele DiBenedetto, Ugo Gianazza","submitted_at":"2015-03-26T23:44:20Z","abstract_excerpt":"For proper minimizers of parabolic variational integrals with linear growth with respect to $|Du|$, we establish a necessary and sufficient condition for $u$ to be continuous at a point $(x_o,t_o)$, in terms of a sufficient fast decay of the total variation of $u$ about $(x_o,t_o)$ (see (1.4) below). These minimizers arise also as {proper} solutions to the parabolic $1$-laplacian equation. Hence, the continuity condition continues to hold for such solutions (\\S\\ 3)."},"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":"1503.07928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-26T23:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"c2b0886aa9fb341722dbdb6eb6ef67e67dcfad6c13b5d108886c310660ad2c76","abstract_canon_sha256":"92525fc4a1e07ce35c967429c52f44086be185023e2e24362843b12b80940c6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:31.006415Z","signature_b64":"WQ6vAlRRmanQkUfRBKwxbK+flK1WlYgzpctHQAZZWgqJMGWyvuj9gcl7Sz6i5FyypQnnUlrIsG9X/739wInTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"350d24c7cf08a7abc0d6f488df2ea602acbc21ad1bb5ccfd87b396f234bc8b29","last_reissued_at":"2026-05-18T00:10:31.005890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:31.005890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Necessary and Sufficient Condition for the Continuity of Local Minima of Parabolic Variational Integrals with Linear Growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Colin Klaus, Emmanuele DiBenedetto, Ugo Gianazza","submitted_at":"2015-03-26T23:44:20Z","abstract_excerpt":"For proper minimizers of parabolic variational integrals with linear growth with respect to $|Du|$, we establish a necessary and sufficient condition for $u$ to be continuous at a point $(x_o,t_o)$, in terms of a sufficient fast decay of the total variation of $u$ about $(x_o,t_o)$ (see (1.4) below). These minimizers arise also as {proper} solutions to the parabolic $1$-laplacian equation. Hence, the continuity condition continues to hold for such solutions (\\S\\ 3)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07928","kind":"arxiv","version":2},"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":"1503.07928","created_at":"2026-05-18T00:10:31.005973+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.07928v2","created_at":"2026-05-18T00:10:31.005973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07928","created_at":"2026-05-18T00:10:31.005973+00:00"},{"alias_kind":"pith_short_12","alias_value":"GUGSJR6PBCT2","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GUGSJR6PBCT2XQGW","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GUGSJR6P","created_at":"2026-05-18T12:29:22.688609+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/GUGSJR6PBCT2XQGW6SEN6LVGAK","json":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK.json","graph_json":"https://pith.science/api/pith-number/GUGSJR6PBCT2XQGW6SEN6LVGAK/graph.json","events_json":"https://pith.science/api/pith-number/GUGSJR6PBCT2XQGW6SEN6LVGAK/events.json","paper":"https://pith.science/paper/GUGSJR6P"},"agent_actions":{"view_html":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK","download_json":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK.json","view_paper":"https://pith.science/paper/GUGSJR6P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.07928&json=true","fetch_graph":"https://pith.science/api/pith-number/GUGSJR6PBCT2XQGW6SEN6LVGAK/graph.json","fetch_events":"https://pith.science/api/pith-number/GUGSJR6PBCT2XQGW6SEN6LVGAK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK/action/storage_attestation","attest_author":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK/action/author_attestation","sign_citation":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK/action/citation_signature","submit_replication":"https://pith.science/pith/GUGSJR6PBCT2XQGW6SEN6LVGAK/action/replication_record"}},"created_at":"2026-05-18T00:10:31.005973+00:00","updated_at":"2026-05-18T00:10:31.005973+00:00"}