{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IHD6YZJLKPR5DPK3R5ODWV3BSF","short_pith_number":"pith:IHD6YZJL","schema_version":"1.0","canonical_sha256":"41c7ec652b53e3d1bd5b8f5c3b576191528cf6fd82da7893ad759aa69e7cb515","source":{"kind":"arxiv","id":"2607.20894","version":1},"attestation_state":"computed","paper":{"title":"On the well-posedness of porous medium equations on general metric measure spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diwen Chang","submitted_at":"2026-07-23T03:32:22Z","abstract_excerpt":"We develop, on general metric measure spaces, a well-posedness theory for the Cauchy problem of the signed porous medium equation and its fast diffusion counterpart \\begin{equation*} \\partial_t u=\\mathcal{L}\\left(|u|^{m-1}u\\right), \\qquad m>0, \\end{equation*} where $\\mathcal{L}$ is the generator of a symmetric Dirichlet form. We prove that, for every initial datum $u_0\\in L^{m+1}(M,\\mu)$, there exists a unique function $u$ that weakly solves the equation in a suitable sense. The proof is based on the Rothe method and the theory of monotone operators and only uses the definition of the Dirichle"},"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":"2607.20894","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-23T03:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"04dd69d7b65e041c0132d77101517cabbb7d57b03563b9cc578d42533eb87b67","abstract_canon_sha256":"fd30e5a3a74cad245ec72d20b6417b39242ffc54fa48a03389a6220bece888a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T00:23:40.367567Z","signature_b64":"pySUOFoHdlwAQS/yWW0dlpoftTqKc9MztsWxEAkGi1yMAIumWcs9El+DVLTZbO9iNRtYDR6Nkf1SKHINqPMPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41c7ec652b53e3d1bd5b8f5c3b576191528cf6fd82da7893ad759aa69e7cb515","last_reissued_at":"2026-07-24T00:23:40.366569Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T00:23:40.366569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the well-posedness of porous medium equations on general metric measure spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diwen Chang","submitted_at":"2026-07-23T03:32:22Z","abstract_excerpt":"We develop, on general metric measure spaces, a well-posedness theory for the Cauchy problem of the signed porous medium equation and its fast diffusion counterpart \\begin{equation*} \\partial_t u=\\mathcal{L}\\left(|u|^{m-1}u\\right), \\qquad m>0, \\end{equation*} where $\\mathcal{L}$ is the generator of a symmetric Dirichlet form. We prove that, for every initial datum $u_0\\in L^{m+1}(M,\\mu)$, there exists a unique function $u$ that weakly solves the equation in a suitable sense. The proof is based on the Rothe method and the theory of monotone operators and only uses the definition of the Dirichle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20894","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.20894/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.20894","created_at":"2026-07-24T00:23:40.367033+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.20894v1","created_at":"2026-07-24T00:23:40.367033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20894","created_at":"2026-07-24T00:23:40.367033+00:00"},{"alias_kind":"pith_short_12","alias_value":"IHD6YZJLKPR5","created_at":"2026-07-24T00:23:40.367033+00:00"},{"alias_kind":"pith_short_16","alias_value":"IHD6YZJLKPR5DPK3","created_at":"2026-07-24T00:23:40.367033+00:00"},{"alias_kind":"pith_short_8","alias_value":"IHD6YZJL","created_at":"2026-07-24T00:23:40.367033+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/IHD6YZJLKPR5DPK3R5ODWV3BSF","json":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF.json","graph_json":"https://pith.science/api/pith-number/IHD6YZJLKPR5DPK3R5ODWV3BSF/graph.json","events_json":"https://pith.science/api/pith-number/IHD6YZJLKPR5DPK3R5ODWV3BSF/events.json","paper":"https://pith.science/paper/IHD6YZJL"},"agent_actions":{"view_html":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF","download_json":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF.json","view_paper":"https://pith.science/paper/IHD6YZJL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.20894&json=true","fetch_graph":"https://pith.science/api/pith-number/IHD6YZJLKPR5DPK3R5ODWV3BSF/graph.json","fetch_events":"https://pith.science/api/pith-number/IHD6YZJLKPR5DPK3R5ODWV3BSF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF/action/storage_attestation","attest_author":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF/action/author_attestation","sign_citation":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF/action/citation_signature","submit_replication":"https://pith.science/pith/IHD6YZJLKPR5DPK3R5ODWV3BSF/action/replication_record"}},"created_at":"2026-07-24T00:23:40.367033+00:00","updated_at":"2026-07-24T00:23:40.367033+00:00"}