{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BZFHCBR33EAP44V6DBH6UFCGK7","short_pith_number":"pith:BZFHCBR3","schema_version":"1.0","canonical_sha256":"0e4a71063bd900fe72be184fea144657c7e43027e1dc7250e213b7890660fb17","source":{"kind":"arxiv","id":"1904.06889","version":1},"attestation_state":"computed","paper":{"title":"The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Franziska Flegel, Martin Heida","submitted_at":"2019-04-15T07:44:47Z","abstract_excerpt":"We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional $p$-Laplace operator.\n  Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Laplace operator to the continuous fractional Laplace operator."},"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":"1904.06889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-15T07:44:47Z","cross_cats_sorted":[],"title_canon_sha256":"188719fbb9f66e704cad7bdb78a22e851cececa05cde43ce5bcceaec85a18cad","abstract_canon_sha256":"b9b389cb7521533b78826a2d0618fd065302a7abd73d0ee1d24947e484e9f823"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:35.869601Z","signature_b64":"Jn2M8HfxO6jdO2u+DvpFQCwJOztYJS5srT1AB3ZY3OmiCR3aMm0xS6ykI5gptS1dxXfHFrSrV9w+QgBwXoYyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e4a71063bd900fe72be184fea144657c7e43027e1dc7250e213b7890660fb17","last_reissued_at":"2026-05-17T23:48:35.868865Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:35.868865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Franziska Flegel, Martin Heida","submitted_at":"2019-04-15T07:44:47Z","abstract_excerpt":"We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional $p$-Laplace operator.\n  Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Laplace operator to the continuous fractional Laplace operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06889","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":"1904.06889","created_at":"2026-05-17T23:48:35.868978+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.06889v1","created_at":"2026-05-17T23:48:35.868978+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06889","created_at":"2026-05-17T23:48:35.868978+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZFHCBR33EAP","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZFHCBR33EAP44V6","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZFHCBR3","created_at":"2026-05-18T12:33:12.712433+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/BZFHCBR33EAP44V6DBH6UFCGK7","json":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7.json","graph_json":"https://pith.science/api/pith-number/BZFHCBR33EAP44V6DBH6UFCGK7/graph.json","events_json":"https://pith.science/api/pith-number/BZFHCBR33EAP44V6DBH6UFCGK7/events.json","paper":"https://pith.science/paper/BZFHCBR3"},"agent_actions":{"view_html":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7","download_json":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7.json","view_paper":"https://pith.science/paper/BZFHCBR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.06889&json=true","fetch_graph":"https://pith.science/api/pith-number/BZFHCBR33EAP44V6DBH6UFCGK7/graph.json","fetch_events":"https://pith.science/api/pith-number/BZFHCBR33EAP44V6DBH6UFCGK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/action/storage_attestation","attest_author":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/action/author_attestation","sign_citation":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/action/citation_signature","submit_replication":"https://pith.science/pith/BZFHCBR33EAP44V6DBH6UFCGK7/action/replication_record"}},"created_at":"2026-05-17T23:48:35.868978+00:00","updated_at":"2026-05-17T23:48:35.868978+00:00"}