{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JQXBLMW72HO4F7HF3JHMSZUZBT","short_pith_number":"pith:JQXBLMW7","canonical_record":{"source":{"id":"1610.09881","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-31T11:53:06Z","cross_cats_sorted":[],"title_canon_sha256":"9517f3f71025dd174bbec19aa257bfb9c3cbdacc8dea1db6a73d407d47e82b3b","abstract_canon_sha256":"454f0065f1e04fee0601a09569c5da486092129379952c3528f9c8eac898c8f4"},"schema_version":"1.0"},"canonical_sha256":"4c2e15b2dfd1ddc2fce5da4ec966990cd624d4e96b3d172fb6c1b0ab0218aa4d","source":{"kind":"arxiv","id":"1610.09881","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09881","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09881v4","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09881","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"JQXBLMW72HO4","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JQXBLMW72HO4F7HF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JQXBLMW7","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JQXBLMW72HO4F7HF3JHMSZUZBT","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09881","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-31T11:53:06Z","cross_cats_sorted":[],"title_canon_sha256":"9517f3f71025dd174bbec19aa257bfb9c3cbdacc8dea1db6a73d407d47e82b3b","abstract_canon_sha256":"454f0065f1e04fee0601a09569c5da486092129379952c3528f9c8eac898c8f4"},"schema_version":"1.0"},"canonical_sha256":"4c2e15b2dfd1ddc2fce5da4ec966990cd624d4e96b3d172fb6c1b0ab0218aa4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:57.049033Z","signature_b64":"bwUuYDWgC9r3xew2+vwVOzQETIXlbDmQ9fmE/Zpm11L/+xyq9eOeZABo2msHad7TCT4sBTBmQ2KTSD9vVerZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c2e15b2dfd1ddc2fce5da4ec966990cd624d4e96b3d172fb6c1b0ab0218aa4d","last_reissued_at":"2026-05-18T00:20:57.048583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:57.048583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09881","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eEB4TTz5orgwddOSQo1Yva1VmJxemzbuOn37dM5b05fNUiQeG7ysxGn61ZFIiwWnDu8o3dZeUSD2fN5pDvObCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:40:59.285459Z"},"content_sha256":"d1c8997a674fd178a653bad78613cad6ce13d922769a8619e9d9eadc0cb970a3","schema_version":"1.0","event_id":"sha256:d1c8997a674fd178a653bad78613cad6ce13d922769a8619e9d9eadc0cb970a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JQXBLMW72HO4F7HF3JHMSZUZBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Juan Luis Vazquez, Matteo Bonforte","submitted_at":"2016-10-31T11:53:06Z","abstract_excerpt":"This paper provides a quantitative study of nonnegative solutions to nonlinear diffusion equations of porous medium-type of the form $\\partial_t u + {\\mathcal L}u^m=0$, $m>1$, where the operator ${\\mathcal L}$ belongs to a general class of linear operators, and the equation is posed in a bounded domain $\\Omega\\subset{\\mathbb R}^N$. As possible operators we include the three most common definitions of the fractional Laplacian in a bounded domain with zero Dirichlet conditions, and also a number of other nonlocal versions. In particular, ${\\mathcal L}$ can be a power of a uniformly elliptic oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09881","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NgCRtqbu3acgPjueKDTTAzPVgW2WXRAs3bcJtdhbfslyaYHP42JN4vftXX5XakyNvTFlwq+73vQxU8CJXz+RBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:40:59.286023Z"},"content_sha256":"b8b24fe22c462504f48016690e715b70939fa6b1c22b5abc4c1ab6ed4cb71b78","schema_version":"1.0","event_id":"sha256:b8b24fe22c462504f48016690e715b70939fa6b1c22b5abc4c1ab6ed4cb71b78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQXBLMW72HO4F7HF3JHMSZUZBT/bundle.json","state_url":"https://pith.science/pith/JQXBLMW72HO4F7HF3JHMSZUZBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQXBLMW72HO4F7HF3JHMSZUZBT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T01:40:59Z","links":{"resolver":"https://pith.science/pith/JQXBLMW72HO4F7HF3JHMSZUZBT","bundle":"https://pith.science/pith/JQXBLMW72HO4F7HF3JHMSZUZBT/bundle.json","state":"https://pith.science/pith/JQXBLMW72HO4F7HF3JHMSZUZBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQXBLMW72HO4F7HF3JHMSZUZBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JQXBLMW72HO4F7HF3JHMSZUZBT","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":"454f0065f1e04fee0601a09569c5da486092129379952c3528f9c8eac898c8f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-31T11:53:06Z","title_canon_sha256":"9517f3f71025dd174bbec19aa257bfb9c3cbdacc8dea1db6a73d407d47e82b3b"},"schema_version":"1.0","source":{"id":"1610.09881","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09881","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09881v4","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09881","created_at":"2026-05-18T00:20:57Z"},{"alias_kind":"pith_short_12","alias_value":"JQXBLMW72HO4","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JQXBLMW72HO4F7HF","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JQXBLMW7","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:b8b24fe22c462504f48016690e715b70939fa6b1c22b5abc4c1ab6ed4cb71b78","target":"graph","created_at":"2026-05-18T00:20:57Z","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":"This paper provides a quantitative study of nonnegative solutions to nonlinear diffusion equations of porous medium-type of the form $\\partial_t u + {\\mathcal L}u^m=0$, $m>1$, where the operator ${\\mathcal L}$ belongs to a general class of linear operators, and the equation is posed in a bounded domain $\\Omega\\subset{\\mathbb R}^N$. As possible operators we include the three most common definitions of the fractional Laplacian in a bounded domain with zero Dirichlet conditions, and also a number of other nonlocal versions. In particular, ${\\mathcal L}$ can be a power of a uniformly elliptic oper","authors_text":"Alessio Figalli, Juan Luis Vazquez, Matteo Bonforte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-31T11:53:06Z","title":"Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09881","kind":"arxiv","version":4},"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:d1c8997a674fd178a653bad78613cad6ce13d922769a8619e9d9eadc0cb970a3","target":"record","created_at":"2026-05-18T00:20:57Z","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":"454f0065f1e04fee0601a09569c5da486092129379952c3528f9c8eac898c8f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-31T11:53:06Z","title_canon_sha256":"9517f3f71025dd174bbec19aa257bfb9c3cbdacc8dea1db6a73d407d47e82b3b"},"schema_version":"1.0","source":{"id":"1610.09881","kind":"arxiv","version":4}},"canonical_sha256":"4c2e15b2dfd1ddc2fce5da4ec966990cd624d4e96b3d172fb6c1b0ab0218aa4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c2e15b2dfd1ddc2fce5da4ec966990cd624d4e96b3d172fb6c1b0ab0218aa4d","first_computed_at":"2026-05-18T00:20:57.048583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:57.048583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bwUuYDWgC9r3xew2+vwVOzQETIXlbDmQ9fmE/Zpm11L/+xyq9eOeZABo2msHad7TCT4sBTBmQ2KTSD9vVerZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:57.049033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09881","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1c8997a674fd178a653bad78613cad6ce13d922769a8619e9d9eadc0cb970a3","sha256:b8b24fe22c462504f48016690e715b70939fa6b1c22b5abc4c1ab6ed4cb71b78"],"state_sha256":"a5a3a1d9259f3fe7b266550710a867863735e71bde7ceb76447ec97feb052db8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5rBEMDQ3VbVB7L1FEuOXqPFGWHu9MRUErxVeLClZJtuKQCr7cSENualHmp+I7YERyE+ZnOvxzsjttromnvmpDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:40:59.288637Z","bundle_sha256":"6baa811fc082fd67ad276c42f8513c7d102b0e5ae77a7c5197bd15c65835a03b"}}