{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5RNGFVQ3S6E3VBNULPPPXABF3B","short_pith_number":"pith:5RNGFVQ3","schema_version":"1.0","canonical_sha256":"ec5a62d61b9789ba85b45bdefb8025d85db6d7c6cbc6fb7852c3d37b8c2fdbf9","source":{"kind":"arxiv","id":"1510.03544","version":1},"attestation_state":"computed","paper":{"title":"Removable singularities for div v = f in weighted Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Emmanuel Russ (IF), Heli Tuominen, Laurent Moonens (LM-Orsay)","submitted_at":"2015-10-13T06:10:57Z","abstract_excerpt":"Let $w\\in L^1\\_{loc}(\\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\\R^n$ which are removable for the distributional divergence in $L^{\\infty}\\_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p\\_{1/w}$, $1\\textless{}p\\textless{}+\\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author."},"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":"1510.03544","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-13T06:10:57Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"26cfa19225c09e056193a2a4d8dbe849066ab54680f6646c029327add8921f26","abstract_canon_sha256":"092db079685d2c8bcae12f1c01aa8a4f335fb84bf801cea2b6cfa23def4d0708"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:16.885298Z","signature_b64":"epPirQ+cBwYRJ3L+U/BTYW6kUb5zellXNCxwZXTwV6pQiG8zPEQa4U1nJV1AZ1B6iidWxH3fT5mxtJ8oEkw2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec5a62d61b9789ba85b45bdefb8025d85db6d7c6cbc6fb7852c3d37b8c2fdbf9","last_reissued_at":"2026-05-18T01:30:16.884646Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:16.884646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Removable singularities for div v = f in weighted Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Emmanuel Russ (IF), Heli Tuominen, Laurent Moonens (LM-Orsay)","submitted_at":"2015-10-13T06:10:57Z","abstract_excerpt":"Let $w\\in L^1\\_{loc}(\\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\\R^n$ which are removable for the distributional divergence in $L^{\\infty}\\_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p\\_{1/w}$, $1\\textless{}p\\textless{}+\\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03544","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":"1510.03544","created_at":"2026-05-18T01:30:16.884751+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03544v1","created_at":"2026-05-18T01:30:16.884751+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03544","created_at":"2026-05-18T01:30:16.884751+00:00"},{"alias_kind":"pith_short_12","alias_value":"5RNGFVQ3S6E3","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"5RNGFVQ3S6E3VBNU","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"5RNGFVQ3","created_at":"2026-05-18T12:29:07.941421+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/5RNGFVQ3S6E3VBNULPPPXABF3B","json":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B.json","graph_json":"https://pith.science/api/pith-number/5RNGFVQ3S6E3VBNULPPPXABF3B/graph.json","events_json":"https://pith.science/api/pith-number/5RNGFVQ3S6E3VBNULPPPXABF3B/events.json","paper":"https://pith.science/paper/5RNGFVQ3"},"agent_actions":{"view_html":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B","download_json":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B.json","view_paper":"https://pith.science/paper/5RNGFVQ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03544&json=true","fetch_graph":"https://pith.science/api/pith-number/5RNGFVQ3S6E3VBNULPPPXABF3B/graph.json","fetch_events":"https://pith.science/api/pith-number/5RNGFVQ3S6E3VBNULPPPXABF3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B/action/storage_attestation","attest_author":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B/action/author_attestation","sign_citation":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B/action/citation_signature","submit_replication":"https://pith.science/pith/5RNGFVQ3S6E3VBNULPPPXABF3B/action/replication_record"}},"created_at":"2026-05-18T01:30:16.884751+00:00","updated_at":"2026-05-18T01:30:16.884751+00:00"}