{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SMSDXVBYMYDOBQ5B5JZURB6CWS","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":"f74d90ab7d41a112f079e3144c4bd4b2784ad94f6d314e20940beaed4d91a762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-27T15:10:31Z","title_canon_sha256":"4e8ff460ac03e8ad7cd221c673a8f64d72c8e970c1873d571e97e4fb5464cea8"},"schema_version":"1.0","source":{"id":"1311.6997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6997","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6997v1","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6997","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"SMSDXVBYMYDO","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SMSDXVBYMYDOBQ5B","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SMSDXVBY","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:24447337f8ca51fa5f43398ba1486f0e5d5734c316d7d87580cf5940771794f8","target":"graph","created_at":"2026-05-18T03:06:04Z","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 investigate quantitative properties of the nonnegative solutions $u(t,x)\\ge 0$ to the nonlinear fractional diffusion equation, $\\partial_t u + {\\mathcal L} (u^m)=0$, posed in a bounded domain, $x\\in\\Omega\\subset {\\mathbb R}^N$ with $m>1$ for $t>0$. As ${\\mathcal L}$ we use one of the most common definitions of the fractional Laplacian $(-\\Delta)^s$, $0<s<1$, in a bounded domain with zero Dirichlet boundary conditions. We consider a general class of very weak solutions of the equation, and obtain a priori estimates in the form of smoothing effects, absolute upper bounds, lower bounds, and Ha","authors_text":"Juan Luis V\\'azquez, Matteo Bonforte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-27T15:10:31Z","title":"A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6997","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":"sha256:5679a907b20373a032eb26740e85210bdf1ea4e0a300f4389d5b3950899feaaf","target":"record","created_at":"2026-05-18T03:06:04Z","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":"f74d90ab7d41a112f079e3144c4bd4b2784ad94f6d314e20940beaed4d91a762","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-27T15:10:31Z","title_canon_sha256":"4e8ff460ac03e8ad7cd221c673a8f64d72c8e970c1873d571e97e4fb5464cea8"},"schema_version":"1.0","source":{"id":"1311.6997","kind":"arxiv","version":1}},"canonical_sha256":"93243bd4386606e0c3a1ea734887c2b485f4af0eebd95f6eba618cc97957d3b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93243bd4386606e0c3a1ea734887c2b485f4af0eebd95f6eba618cc97957d3b0","first_computed_at":"2026-05-18T03:06:04.363746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:04.363746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zr60B3iYYy/Yuw06xmrIHxSrZYrvT4p1juwc4BX6wXFGEh5q1gQzdeiGFmB4FuF6BAcdAqWBg1H2dh4VaOUZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:04.364272Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5679a907b20373a032eb26740e85210bdf1ea4e0a300f4389d5b3950899feaaf","sha256:24447337f8ca51fa5f43398ba1486f0e5d5734c316d7d87580cf5940771794f8"],"state_sha256":"a391430e8176f7973ad2a0605cfb11174570807e29fc8079447fc2d5d9837ed6"}