{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4MS7KOAH3TO3QXMXZJ2YVV53FJ","short_pith_number":"pith:4MS7KOAH","schema_version":"1.0","canonical_sha256":"e325f53807dcddb85d97ca758ad7bb2a46423822f9fadd174ef0561aee996524","source":{"kind":"arxiv","id":"1805.09475","version":1},"attestation_state":"computed","paper":{"title":"Nodal Sets and Doubling Conditions in Elliptic Homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fanghua Lin, Zhongwei Shen","submitted_at":"2018-05-24T01:27:38Z","abstract_excerpt":"This paper is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators $\\{ \\mathcal{L}_\\e\\}$ in divergence form with rapidly oscillating and periodic coefficients. We show that the $(d-1)$-dimensional Hausdorff measures of the nodal sets of solutions to $\\mathcal{L}_\\e (u_\\e)=0$ in a ball in $\\R^d$ are bounded uniformly in $\\e>0$. The proof relies on a uniform doubling condition and approximation of $u_\\e$ by solutions of the homogenized equation."},"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":"1805.09475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-24T01:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"02e667f3118337796daf317dd198ec8c6e26150327b799156c509a6b3ced0cb2","abstract_canon_sha256":"d3aecbea5742aba8cd9ca6d73e86c4cdf3536e7ff53c5b520e34ef61f6a13dc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:03.806146Z","signature_b64":"gvtxSwfyCgQDd36kpq0UeX0mT54Z/a2P+T1Wx1xJlmausl9pexLpSjsd50Hm+8lBl7trY11YaVZXDDDMrr10Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e325f53807dcddb85d97ca758ad7bb2a46423822f9fadd174ef0561aee996524","last_reissued_at":"2026-05-18T00:15:03.805567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:03.805567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nodal Sets and Doubling Conditions in Elliptic Homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fanghua Lin, Zhongwei Shen","submitted_at":"2018-05-24T01:27:38Z","abstract_excerpt":"This paper is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators $\\{ \\mathcal{L}_\\e\\}$ in divergence form with rapidly oscillating and periodic coefficients. We show that the $(d-1)$-dimensional Hausdorff measures of the nodal sets of solutions to $\\mathcal{L}_\\e (u_\\e)=0$ in a ball in $\\R^d$ are bounded uniformly in $\\e>0$. The proof relies on a uniform doubling condition and approximation of $u_\\e$ by solutions of the homogenized equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09475","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":"1805.09475","created_at":"2026-05-18T00:15:03.805657+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.09475v1","created_at":"2026-05-18T00:15:03.805657+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09475","created_at":"2026-05-18T00:15:03.805657+00:00"},{"alias_kind":"pith_short_12","alias_value":"4MS7KOAH3TO3","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4MS7KOAH3TO3QXMX","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4MS7KOAH","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/4MS7KOAH3TO3QXMXZJ2YVV53FJ","json":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ.json","graph_json":"https://pith.science/api/pith-number/4MS7KOAH3TO3QXMXZJ2YVV53FJ/graph.json","events_json":"https://pith.science/api/pith-number/4MS7KOAH3TO3QXMXZJ2YVV53FJ/events.json","paper":"https://pith.science/paper/4MS7KOAH"},"agent_actions":{"view_html":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ","download_json":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ.json","view_paper":"https://pith.science/paper/4MS7KOAH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.09475&json=true","fetch_graph":"https://pith.science/api/pith-number/4MS7KOAH3TO3QXMXZJ2YVV53FJ/graph.json","fetch_events":"https://pith.science/api/pith-number/4MS7KOAH3TO3QXMXZJ2YVV53FJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ/action/storage_attestation","attest_author":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ/action/author_attestation","sign_citation":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ/action/citation_signature","submit_replication":"https://pith.science/pith/4MS7KOAH3TO3QXMXZJ2YVV53FJ/action/replication_record"}},"created_at":"2026-05-18T00:15:03.805657+00:00","updated_at":"2026-05-18T00:15:03.805657+00:00"}