{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LLKYIW6ERZNELP6RKQG4S3LQ24","short_pith_number":"pith:LLKYIW6E","schema_version":"1.0","canonical_sha256":"5ad5845bc48e5a45bfd1540dc96d70d70e15657161f3966dce603578b520c648","source":{"kind":"arxiv","id":"1812.08058","version":1},"attestation_state":"computed","paper":{"title":"Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"{\\L}ukasz P{\\l}ociniczak","submitted_at":"2018-12-19T16:21:27Z","abstract_excerpt":"In this short note we consider a nonlinear and spatially nonlocal PDE modelling moisture evolution in a porous medium. We then show that it naturally arises as a description of superdiffusive jump phenomenon occurring in the medium. We provide a deterministic derivation which allows us to naturally incorporate the nonlinear effects. This reasoning shows that in our setting the so-called nonlocal pressure form of the porous medium equation is preferred as a description of the evolution. In that case the governing nonlocal operator is the fractional gradient rather than the fractional Laplacian."},"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":"1812.08058","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2018-12-19T16:21:27Z","cross_cats_sorted":[],"title_canon_sha256":"7226d729d6c0d9b1edb8acd55d23308c1ce4060df77517d92dc5c862189e49e0","abstract_canon_sha256":"5487a362b71c3720efa133bb859fd35076c4dfeab658cc5bacb6a3975d34404b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:07.554683Z","signature_b64":"x7OOJH5KSDET9KN+jxQ9YT0HYIdY1iPjosglWN+Udl0WWw+k9y9Mg/c6CA8kbjlAgpEpuqRpe7vp+w9WEu74CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ad5845bc48e5a45bfd1540dc96d70d70e15657161f3966dce603578b520c648","last_reissued_at":"2026-05-17T23:48:07.554132Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:07.554132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"{\\L}ukasz P{\\l}ociniczak","submitted_at":"2018-12-19T16:21:27Z","abstract_excerpt":"In this short note we consider a nonlinear and spatially nonlocal PDE modelling moisture evolution in a porous medium. We then show that it naturally arises as a description of superdiffusive jump phenomenon occurring in the medium. We provide a deterministic derivation which allows us to naturally incorporate the nonlinear effects. This reasoning shows that in our setting the so-called nonlocal pressure form of the porous medium equation is preferred as a description of the evolution. In that case the governing nonlocal operator is the fractional gradient rather than the fractional Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08058","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":"1812.08058","created_at":"2026-05-17T23:48:07.554223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.08058v1","created_at":"2026-05-17T23:48:07.554223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.08058","created_at":"2026-05-17T23:48:07.554223+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLKYIW6ERZNE","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLKYIW6ERZNELP6R","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLKYIW6E","created_at":"2026-05-18T12:32:37.024351+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/LLKYIW6ERZNELP6RKQG4S3LQ24","json":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24.json","graph_json":"https://pith.science/api/pith-number/LLKYIW6ERZNELP6RKQG4S3LQ24/graph.json","events_json":"https://pith.science/api/pith-number/LLKYIW6ERZNELP6RKQG4S3LQ24/events.json","paper":"https://pith.science/paper/LLKYIW6E"},"agent_actions":{"view_html":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24","download_json":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24.json","view_paper":"https://pith.science/paper/LLKYIW6E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.08058&json=true","fetch_graph":"https://pith.science/api/pith-number/LLKYIW6ERZNELP6RKQG4S3LQ24/graph.json","fetch_events":"https://pith.science/api/pith-number/LLKYIW6ERZNELP6RKQG4S3LQ24/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24/action/storage_attestation","attest_author":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24/action/author_attestation","sign_citation":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24/action/citation_signature","submit_replication":"https://pith.science/pith/LLKYIW6ERZNELP6RKQG4S3LQ24/action/replication_record"}},"created_at":"2026-05-17T23:48:07.554223+00:00","updated_at":"2026-05-17T23:48:07.554223+00:00"}