{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:MWRA5TWPKYE7QIEAVXIHCG2YHY","short_pith_number":"pith:MWRA5TWP","canonical_record":{"source":{"id":"2102.05213","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-02-10T01:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"26034d3c184b7a3e270abe958e433ee72252248399d962e1e869bf379be801ec","abstract_canon_sha256":"8ed2155bac98c52944f8457f5e54a874fb753af64f128d88678c26912d13659c"},"schema_version":"1.0"},"canonical_sha256":"65a20ececf5609f82080add0711b583e02e3e1f3ddb5014264b0d9604d9e2088","source":{"kind":"arxiv","id":"2102.05213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05213","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05213v1","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05213","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"MWRA5TWPKYE7","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"pith_short_16","alias_value":"MWRA5TWPKYE7QIEA","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"pith_short_8","alias_value":"MWRA5TWP","created_at":"2026-07-05T02:14:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:MWRA5TWPKYE7QIEAVXIHCG2YHY","target":"record","payload":{"canonical_record":{"source":{"id":"2102.05213","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-02-10T01:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"26034d3c184b7a3e270abe958e433ee72252248399d962e1e869bf379be801ec","abstract_canon_sha256":"8ed2155bac98c52944f8457f5e54a874fb753af64f128d88678c26912d13659c"},"schema_version":"1.0"},"canonical_sha256":"65a20ececf5609f82080add0711b583e02e3e1f3ddb5014264b0d9604d9e2088","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:16.255330Z","signature_b64":"3w0AqlhPsdhkDgDGnlRr90ho3uZd79MvkipgAnC9x/Zase0iLfiVY3THeQaG1Glp/bt9eVfjG9GkLWRbb5UpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65a20ececf5609f82080add0711b583e02e3e1f3ddb5014264b0d9604d9e2088","last_reissued_at":"2026-07-05T02:14:16.254860Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:16.254860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.05213","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"48rAeTcJnaHGV7WDkr22Ay0FGdqgXuhTzqS3N8hZrorzkQ37PXECyTq5H7MLzOo4ID2P7Pm9J5+Q9lmMWXx1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:25:11.604273Z"},"content_sha256":"86e20643050eb0ec04551473ea156248d878fcf9551a4b4af4d50da00edf9147","schema_version":"1.0","event_id":"sha256:86e20643050eb0ec04551473ea156248d878fcf9551a4b4af4d50da00edf9147"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:MWRA5TWPKYE7QIEAVXIHCG2YHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small scale formations in the incompressible porous media equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Kiselev, Yao Yao","submitted_at":"2021-02-10T01:36:23Z","abstract_excerpt":"We construct examples of solutions to the incompressible porous media (IPM) equation that must exhibit infinite in time growth of derivatives provided they remain smooth. As an application, this allows us to obtain nonlinear instability for a class of stratified steady states of IPM."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05213","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/2102.05213/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cSUTeDOoizh71Ki25GhiqOqEc3sXNN8yLciD9dlgAGn4i2MTRxZVi8vMVjRBWafRvnU5GpsnVuV0gRumt0bfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:25:11.604918Z"},"content_sha256":"30eed5a33fdaf78fbc1d18bc69d853cddd1047d9f90edfc344476286b584bea4","schema_version":"1.0","event_id":"sha256:30eed5a33fdaf78fbc1d18bc69d853cddd1047d9f90edfc344476286b584bea4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWRA5TWPKYE7QIEAVXIHCG2YHY/bundle.json","state_url":"https://pith.science/pith/MWRA5TWPKYE7QIEAVXIHCG2YHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWRA5TWPKYE7QIEAVXIHCG2YHY/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":"2026-08-12T12:25:11Z","links":{"resolver":"https://pith.science/pith/MWRA5TWPKYE7QIEAVXIHCG2YHY","bundle":"https://pith.science/pith/MWRA5TWPKYE7QIEAVXIHCG2YHY/bundle.json","state":"https://pith.science/pith/MWRA5TWPKYE7QIEAVXIHCG2YHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWRA5TWPKYE7QIEAVXIHCG2YHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:MWRA5TWPKYE7QIEAVXIHCG2YHY","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":"8ed2155bac98c52944f8457f5e54a874fb753af64f128d88678c26912d13659c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-02-10T01:36:23Z","title_canon_sha256":"26034d3c184b7a3e270abe958e433ee72252248399d962e1e869bf379be801ec"},"schema_version":"1.0","source":{"id":"2102.05213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05213","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05213v1","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05213","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"MWRA5TWPKYE7","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"pith_short_16","alias_value":"MWRA5TWPKYE7QIEA","created_at":"2026-07-05T02:14:16Z"},{"alias_kind":"pith_short_8","alias_value":"MWRA5TWP","created_at":"2026-07-05T02:14:16Z"}],"graph_snapshots":[{"event_id":"sha256:30eed5a33fdaf78fbc1d18bc69d853cddd1047d9f90edfc344476286b584bea4","target":"graph","created_at":"2026-07-05T02:14:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.05213/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct examples of solutions to the incompressible porous media (IPM) equation that must exhibit infinite in time growth of derivatives provided they remain smooth. As an application, this allows us to obtain nonlinear instability for a class of stratified steady states of IPM.","authors_text":"Alexander Kiselev, Yao Yao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-02-10T01:36:23Z","title":"Small scale formations in the incompressible porous media equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05213","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":"sha256:86e20643050eb0ec04551473ea156248d878fcf9551a4b4af4d50da00edf9147","target":"record","created_at":"2026-07-05T02:14:16Z","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":"8ed2155bac98c52944f8457f5e54a874fb753af64f128d88678c26912d13659c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-02-10T01:36:23Z","title_canon_sha256":"26034d3c184b7a3e270abe958e433ee72252248399d962e1e869bf379be801ec"},"schema_version":"1.0","source":{"id":"2102.05213","kind":"arxiv","version":1}},"canonical_sha256":"65a20ececf5609f82080add0711b583e02e3e1f3ddb5014264b0d9604d9e2088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65a20ececf5609f82080add0711b583e02e3e1f3ddb5014264b0d9604d9e2088","first_computed_at":"2026-07-05T02:14:16.254860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:16.254860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3w0AqlhPsdhkDgDGnlRr90ho3uZd79MvkipgAnC9x/Zase0iLfiVY3THeQaG1Glp/bt9eVfjG9GkLWRbb5UpAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:16.255330Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.05213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86e20643050eb0ec04551473ea156248d878fcf9551a4b4af4d50da00edf9147","sha256:30eed5a33fdaf78fbc1d18bc69d853cddd1047d9f90edfc344476286b584bea4"],"state_sha256":"d5fd8805329307f9f5176638a39ae65b0abc56ef81f92fb4c15bbe0f090dee76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2NVlyBoBqCwhUoSXOEsFn/DRPguWXCUYCL+A2OAvkG1Tp2YyB0Zh9AmaXmx0mdwzeDhVwSz4qOlfOaxPWxoCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T12:25:11.612751Z","bundle_sha256":"00aa53be9635f83f3a130b4d5b3ef4fd1eb2b07cdafc75099b35f124c223b8d8"}}