{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VVZ4DNIPMGXQ676VBGRMUKVWAH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"edce3479efdd9f3a8fd320184262dd0459d6d4b9f246cbbaecfd31685e680329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-02T09:16:17Z","title_canon_sha256":"d7e6ad49cb6f90ecd1951fd32e2614c732205e20705bc3e1f7f71f8921ac1cec"},"schema_version":"1.0","source":{"id":"1104.0306","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0306","created_at":"2026-05-18T04:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0306v1","created_at":"2026-05-18T04:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0306","created_at":"2026-05-18T04:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"VVZ4DNIPMGXQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VVZ4DNIPMGXQ676V","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VVZ4DNIP","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:346e4e424888dfe7f90017693f678812882328fe85476e27c3a44e12275d22ba","target":"graph","created_at":"2026-05-18T04:25:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion, $$ \\{ll} \\dfrac{\\partial u}{\\partial t} + (-\\Delta)^{\\sigma/2} (|u|^{m-1}u)=0, & \\qquad x\\in\\mathbb{R}^N,\\; t>0,  [8pt] u(x,0) = f(x), & \\qquad x\\in\\mathbb{R}^N.%. $$ We consider data $f\\in L^1(\\mathbb{R}^N)$ and all exponents $0<\\sigma<2$ and $m>0$. Existence and uniqueness of a weak solution is established for $m> m_*=(N-\\sigma)_+ /N$, giving rise to an $L^1$-contraction semigroup. In addition, we obtain the main qualitative properties of these solutions. In the lower range $0<","authors_text":"Ana Rodr\\'iguez, Arturo de Pablo, Fernando Quir\\'os, Juan Luis V\\'azquez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-02T09:16:17Z","title":"A general fractional porous medium equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0306","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7d3de05a0d687a5a6a73f5e4862468c5a990e3bf0852af010b81464eba594678","target":"record","created_at":"2026-05-18T04:25:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"edce3479efdd9f3a8fd320184262dd0459d6d4b9f246cbbaecfd31685e680329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-02T09:16:17Z","title_canon_sha256":"d7e6ad49cb6f90ecd1951fd32e2614c732205e20705bc3e1f7f71f8921ac1cec"},"schema_version":"1.0","source":{"id":"1104.0306","kind":"arxiv","version":1}},"canonical_sha256":"ad73c1b50f61af0f7fd509a2ca2ab601cd1f5fa80f7ecb6382b5fa47ea22b794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad73c1b50f61af0f7fd509a2ca2ab601cd1f5fa80f7ecb6382b5fa47ea22b794","first_computed_at":"2026-05-18T04:25:04.259513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:04.259513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2D3bDONankAyfdfZYfewx9E4xuge4ltkFLjuawLOXwBATSxcFV6RhvwoWr/QiNJxU2P2m9WElXKcKnzvikUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:04.259966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0306","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d3de05a0d687a5a6a73f5e4862468c5a990e3bf0852af010b81464eba594678","sha256:346e4e424888dfe7f90017693f678812882328fe85476e27c3a44e12275d22ba"],"state_sha256":"f31ea999427f0596de877dfd0bd61219e882050df4c90fd6da3eb0b340fd76ef"}