{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:X2RHJGESQVWEV7YOB35MPXSSF3","short_pith_number":"pith:X2RHJGES","canonical_record":{"source":{"id":"2007.15267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-30T07:13:24Z","cross_cats_sorted":[],"title_canon_sha256":"73916ec72cc6eff17e80e8ab3cbf89768f0e70ac7a50cec25a8ed4c709ee5675","abstract_canon_sha256":"07bed527ece46721b561c86ec6e919b2b8aa994b1af81bb3dea10410461d90c5"},"schema_version":"1.0"},"canonical_sha256":"bea2749892856c4aff0e0efac7de522ed446699a2d46a9d2aac31f96b418ba6d","source":{"kind":"arxiv","id":"2007.15267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.15267","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"2007.15267v1","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.15267","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"X2RHJGESQVWE","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"pith_short_16","alias_value":"X2RHJGESQVWEV7YO","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"pith_short_8","alias_value":"X2RHJGES","created_at":"2026-07-05T01:23:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:X2RHJGESQVWEV7YOB35MPXSSF3","target":"record","payload":{"canonical_record":{"source":{"id":"2007.15267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-30T07:13:24Z","cross_cats_sorted":[],"title_canon_sha256":"73916ec72cc6eff17e80e8ab3cbf89768f0e70ac7a50cec25a8ed4c709ee5675","abstract_canon_sha256":"07bed527ece46721b561c86ec6e919b2b8aa994b1af81bb3dea10410461d90c5"},"schema_version":"1.0"},"canonical_sha256":"bea2749892856c4aff0e0efac7de522ed446699a2d46a9d2aac31f96b418ba6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:23:29.091939Z","signature_b64":"2ppL3kZ8ddLuEWhNwCSuoffTNWrc3vmL2jasLiNhEpgFTjgu6BQCDz+5kvKKligYxrox4rK1CyvrWGiF41A0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bea2749892856c4aff0e0efac7de522ed446699a2d46a9d2aac31f96b418ba6d","last_reissued_at":"2026-07-05T01:23:29.091572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:23:29.091572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.15267","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":"2026-07-05T01:23:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQ8C01rJHQaTfM4o8lSsBJItmSjYem/X9ovx5cDr9tUjkJ1G8ApMdLwg6YD4flekiIZmK/ArtMs2n8uwys4mDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T16:51:03.808605Z"},"content_sha256":"47e78fce222cd46bafbc1a804e8539e2cadfdc634571b2dacc1ea71bc3d77193","schema_version":"1.0","event_id":"sha256:47e78fce222cd46bafbc1a804e8539e2cadfdc634571b2dacc1ea71bc3d77193"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:X2RHJGESQVWEV7YOB35MPXSSF3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Aronson-B\\'enilan Estimate in Lebesgue Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Beno\\^it Perthame, Giulia Bevilacqua, Markus Schmidtchen","submitted_at":"2020-07-30T07:13:24Z","abstract_excerpt":"In a celebrated three-pages long paper in 1979, Aronson and B\\'enilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since its publication, the theory of porous medium flow has expanded relentlessly with applications including thermodynamics, gas flow, ground water flow as well as ecological population dynamics. The purpose of this paper is to clarify the use of recent extensions of the Aronson and B\\'enilan estimate in Lp spaces, of some modifications and improvements, as well as to show certain limitations of their strategy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.15267","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/2007.15267/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":"2026-07-05T01:23:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nOkbxx5xF5kqPofWE057flB5eSQjGr4P+QNlahcG3+Gx4ePBBDi0YUd49dIKEwkwvfmRGeKGcngexQ/WKTjrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T16:51:03.808980Z"},"content_sha256":"4dad6f5561f675eab6bf199ee4bae9b0f4ff052e27fb3eea575629f77125649d","schema_version":"1.0","event_id":"sha256:4dad6f5561f675eab6bf199ee4bae9b0f4ff052e27fb3eea575629f77125649d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2RHJGESQVWEV7YOB35MPXSSF3/bundle.json","state_url":"https://pith.science/pith/X2RHJGESQVWEV7YOB35MPXSSF3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2RHJGESQVWEV7YOB35MPXSSF3/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":"2026-07-12T16:51:03Z","links":{"resolver":"https://pith.science/pith/X2RHJGESQVWEV7YOB35MPXSSF3","bundle":"https://pith.science/pith/X2RHJGESQVWEV7YOB35MPXSSF3/bundle.json","state":"https://pith.science/pith/X2RHJGESQVWEV7YOB35MPXSSF3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2RHJGESQVWEV7YOB35MPXSSF3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:X2RHJGESQVWEV7YOB35MPXSSF3","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":"07bed527ece46721b561c86ec6e919b2b8aa994b1af81bb3dea10410461d90c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-30T07:13:24Z","title_canon_sha256":"73916ec72cc6eff17e80e8ab3cbf89768f0e70ac7a50cec25a8ed4c709ee5675"},"schema_version":"1.0","source":{"id":"2007.15267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.15267","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"2007.15267v1","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.15267","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"X2RHJGESQVWE","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"pith_short_16","alias_value":"X2RHJGESQVWEV7YO","created_at":"2026-07-05T01:23:29Z"},{"alias_kind":"pith_short_8","alias_value":"X2RHJGES","created_at":"2026-07-05T01:23:29Z"}],"graph_snapshots":[{"event_id":"sha256:4dad6f5561f675eab6bf199ee4bae9b0f4ff052e27fb3eea575629f77125649d","target":"graph","created_at":"2026-07-05T01:23:29Z","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/2007.15267/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a celebrated three-pages long paper in 1979, Aronson and B\\'enilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since its publication, the theory of porous medium flow has expanded relentlessly with applications including thermodynamics, gas flow, ground water flow as well as ecological population dynamics. The purpose of this paper is to clarify the use of recent extensions of the Aronson and B\\'enilan estimate in Lp spaces, of some modifications and improvements, as well as to show certain limitations of their strategy.","authors_text":"Beno\\^it Perthame, Giulia Bevilacqua, Markus Schmidtchen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-30T07:13:24Z","title":"The Aronson-B\\'enilan Estimate in Lebesgue Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.15267","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":"sha256:47e78fce222cd46bafbc1a804e8539e2cadfdc634571b2dacc1ea71bc3d77193","target":"record","created_at":"2026-07-05T01:23:29Z","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":"07bed527ece46721b561c86ec6e919b2b8aa994b1af81bb3dea10410461d90c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-07-30T07:13:24Z","title_canon_sha256":"73916ec72cc6eff17e80e8ab3cbf89768f0e70ac7a50cec25a8ed4c709ee5675"},"schema_version":"1.0","source":{"id":"2007.15267","kind":"arxiv","version":1}},"canonical_sha256":"bea2749892856c4aff0e0efac7de522ed446699a2d46a9d2aac31f96b418ba6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bea2749892856c4aff0e0efac7de522ed446699a2d46a9d2aac31f96b418ba6d","first_computed_at":"2026-07-05T01:23:29.091572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:23:29.091572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ppL3kZ8ddLuEWhNwCSuoffTNWrc3vmL2jasLiNhEpgFTjgu6BQCDz+5kvKKligYxrox4rK1CyvrWGiF41A0Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:23:29.091939Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.15267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e78fce222cd46bafbc1a804e8539e2cadfdc634571b2dacc1ea71bc3d77193","sha256:4dad6f5561f675eab6bf199ee4bae9b0f4ff052e27fb3eea575629f77125649d"],"state_sha256":"0c7a2859c1adcc2f0a436a885c4f8209d811cd51d16338b0a5d990da08344cd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qO6t1IfUwvmAQ1zqfa3QATk0i9Pr7h9vJ4vSXyTk/lngbsxpPTbjYqktyr33TgsNLAOP5tpncbCqGVJqpogAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T16:51:03.811101Z","bundle_sha256":"3875fd965c276336373940ab587e880396464236a5d8f7b1c645505265ce96a2"}}