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The vector ${\\vec f}(x)$ is assumed to be $C^\\alpha$ in case $s=0$, and $C^{1,\\alpha}$ (or higher) in case $s>0$.\n  Using geometric methods, we prove almos"},"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":"1705.10910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-31T01:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"acb5e9bab66c10a7b93bad6e3245ad36c472c9bf40cf10f82d727f9f21e6f1b9","abstract_canon_sha256":"c232baeb9e29ffadb4396c445cbbe45ea6c74c1becd26e2b15069f3fae590844"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:19.884174Z","signature_b64":"BDD6k+X7lJ5yabKSOunYuo/2z3tOPIOPBWF7MKJDgAHnB7qdsn1kOYYibpoSghfS4K4szFEHJWj8qkVm0uFSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05805088b10e08aa87afdaffaaa3d33e664a8a00368fac18038b6fc5b8329c7a","last_reissued_at":"2026-05-18T00:43:19.883631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:19.883631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nodal Sets for \"Broken\" Quasilinear PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Henrik Shahgholian, Ki-Ahm Lee, Sunghan Kim","submitted_at":"2017-05-31T01:43:37Z","abstract_excerpt":"We study the local behavior of the nodal sets of the solutions to elliptic quasilinear equations with nonlinear conductivity part, \\begin{equation*} \\operatorname{div}(A_s(x,u)\\nabla u)=\\operatorname{div}{\\vec f}(x), \\end{equation*} where $A_s(x,u)$ has \"broken\" derivatives of order $s\\geq 0$, such as \\begin{equation*} A_s(x,u) = a(x) + b(x)(u^+)^s, \\end{equation*} with $(u^+)^0$ being understood as the characteristic function on $\\{u>0\\}$. The vector ${\\vec f}(x)$ is assumed to be $C^\\alpha$ in case $s=0$, and $C^{1,\\alpha}$ (or higher) in case $s>0$.\n  Using geometric methods, we prove almos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10910","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":"1705.10910","created_at":"2026-05-18T00:43:19.883716+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.10910v1","created_at":"2026-05-18T00:43:19.883716+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10910","created_at":"2026-05-18T00:43:19.883716+00:00"},{"alias_kind":"pith_short_12","alias_value":"AWAFBCFRBYEK","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"AWAFBCFRBYEKVB5P","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"AWAFBCFR","created_at":"2026-05-18T12:31:08.081275+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/AWAFBCFRBYEKVB5P3L72VI6THZ","json":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ.json","graph_json":"https://pith.science/api/pith-number/AWAFBCFRBYEKVB5P3L72VI6THZ/graph.json","events_json":"https://pith.science/api/pith-number/AWAFBCFRBYEKVB5P3L72VI6THZ/events.json","paper":"https://pith.science/paper/AWAFBCFR"},"agent_actions":{"view_html":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ","download_json":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ.json","view_paper":"https://pith.science/paper/AWAFBCFR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.10910&json=true","fetch_graph":"https://pith.science/api/pith-number/AWAFBCFRBYEKVB5P3L72VI6THZ/graph.json","fetch_events":"https://pith.science/api/pith-number/AWAFBCFRBYEKVB5P3L72VI6THZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ/action/storage_attestation","attest_author":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ/action/author_attestation","sign_citation":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ/action/citation_signature","submit_replication":"https://pith.science/pith/AWAFBCFRBYEKVB5P3L72VI6THZ/action/replication_record"}},"created_at":"2026-05-18T00:43:19.883716+00:00","updated_at":"2026-05-18T00:43:19.883716+00:00"}