{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2QMFEWHA6ZKDCG6K74G6FZVUGZ","short_pith_number":"pith:2QMFEWHA","schema_version":"1.0","canonical_sha256":"d4185258e0f654311bcaff0de2e6b4367da009138f7ce63be31795f385cfed55","source":{"kind":"arxiv","id":"1805.08262","version":2},"attestation_state":"computed","paper":{"title":"Magnetostatic problems in fractal domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MG","math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Alexander Teplyaev, Maria Rosaria Lancia, Michael Hinz, Paola Vernole, Simone Creo","submitted_at":"2018-05-21T19:13:46Z","abstract_excerpt":"We consider a magnetostatic problem in a 3D \"cylindrical\" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the convergence of the pre-fractal solutions to the limit fractal one. We consider the numerical approximation of the pre-fractal problems via FEM and we prove a priori error estimates. Some numerical simulations are also shown. Our long term motivation includes studying problems that appear in quantum physics in fractal domains."},"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":"1805.08262","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-05-21T19:13:46Z","cross_cats_sorted":["math.AP","math.FA","math.MG","math.MP","math.NA"],"title_canon_sha256":"33c6547ff8717ff373f9a94e53e44b2c1cb71c3c56b68ca905eee8afa036d6b3","abstract_canon_sha256":"7768ef9eb7f94d2d8933cf9f7fc1055dff3f6ee310164b12347e6a39177617c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:22.693390Z","signature_b64":"5idq2niK9ebthnhmDdMoIHob91YiwLRnnMoI3BD+fskr2wD5XUXS70Mzz6wPII4rp7/odk/Z7Rt1AVGGCac6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4185258e0f654311bcaff0de2e6b4367da009138f7ce63be31795f385cfed55","last_reissued_at":"2026-05-17T23:59:22.692976Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:22.692976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Magnetostatic problems in fractal domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MG","math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Alexander Teplyaev, Maria Rosaria Lancia, Michael Hinz, Paola Vernole, Simone Creo","submitted_at":"2018-05-21T19:13:46Z","abstract_excerpt":"We consider a magnetostatic problem in a 3D \"cylindrical\" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the convergence of the pre-fractal solutions to the limit fractal one. We consider the numerical approximation of the pre-fractal problems via FEM and we prove a priori error estimates. Some numerical simulations are also shown. Our long term motivation includes studying problems that appear in quantum physics in fractal domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08262","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":"1805.08262","created_at":"2026-05-17T23:59:22.693036+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.08262v2","created_at":"2026-05-17T23:59:22.693036+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08262","created_at":"2026-05-17T23:59:22.693036+00:00"},{"alias_kind":"pith_short_12","alias_value":"2QMFEWHA6ZKD","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2QMFEWHA6ZKDCG6K","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2QMFEWHA","created_at":"2026-05-18T12:32:02.567920+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/2QMFEWHA6ZKDCG6K74G6FZVUGZ","json":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ.json","graph_json":"https://pith.science/api/pith-number/2QMFEWHA6ZKDCG6K74G6FZVUGZ/graph.json","events_json":"https://pith.science/api/pith-number/2QMFEWHA6ZKDCG6K74G6FZVUGZ/events.json","paper":"https://pith.science/paper/2QMFEWHA"},"agent_actions":{"view_html":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ","download_json":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ.json","view_paper":"https://pith.science/paper/2QMFEWHA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.08262&json=true","fetch_graph":"https://pith.science/api/pith-number/2QMFEWHA6ZKDCG6K74G6FZVUGZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2QMFEWHA6ZKDCG6K74G6FZVUGZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ/action/storage_attestation","attest_author":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ/action/author_attestation","sign_citation":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ/action/citation_signature","submit_replication":"https://pith.science/pith/2QMFEWHA6ZKDCG6K74G6FZVUGZ/action/replication_record"}},"created_at":"2026-05-17T23:59:22.693036+00:00","updated_at":"2026-05-17T23:59:22.693036+00:00"}