{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5YST5U7VVZ37V6AL75MU3YOCEP","short_pith_number":"pith:5YST5U7V","canonical_record":{"source":{"id":"2302.08248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-02-16T11:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"5ba396f784a403acb662862d6bd0309f1f4fa40a1bb4e1a72771ce8079073519","abstract_canon_sha256":"9b2d0c06d65e77c45d46411d3cac56fde3601aa810cf4f602fc3412996b868a6"},"schema_version":"1.0"},"canonical_sha256":"ee253ed3f5ae77faf80bff594de1c223dc3db4b97bb5bf8057df914de596db40","source":{"kind":"arxiv","id":"2302.08248","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08248","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08248v2","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08248","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"pith_short_12","alias_value":"5YST5U7VVZ37","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"pith_short_16","alias_value":"5YST5U7VVZ37V6AL","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"pith_short_8","alias_value":"5YST5U7V","created_at":"2026-07-05T06:59:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5YST5U7VVZ37V6AL75MU3YOCEP","target":"record","payload":{"canonical_record":{"source":{"id":"2302.08248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-02-16T11:57:33Z","cross_cats_sorted":[],"title_canon_sha256":"5ba396f784a403acb662862d6bd0309f1f4fa40a1bb4e1a72771ce8079073519","abstract_canon_sha256":"9b2d0c06d65e77c45d46411d3cac56fde3601aa810cf4f602fc3412996b868a6"},"schema_version":"1.0"},"canonical_sha256":"ee253ed3f5ae77faf80bff594de1c223dc3db4b97bb5bf8057df914de596db40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:59:29.479978Z","signature_b64":"rhB2g2YGRyM3Fny/xh/m67o+ypxiSwwXJIp6nwINImwmTJAWKNnEPgILUOIczizKvpb5t59I3iL2YExGqecZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee253ed3f5ae77faf80bff594de1c223dc3db4b97bb5bf8057df914de596db40","last_reissued_at":"2026-07-05T06:59:29.479596Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:59:29.479596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.08248","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:59:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hiHLEm4KefxqVRVTfZFs9YFOub2AmVh5OssOZ8ub8+Am5xoF3YYxLu9RAfWtosne9cJfiUt4iW4Rqjy37miBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T01:57:55.948354Z"},"content_sha256":"8396043ff775e7948924436771ae9b11603ab2d1831963b32db2c0d2c4064828","schema_version":"1.0","event_id":"sha256:8396043ff775e7948924436771ae9b11603ab2d1831963b32db2c0d2c4064828"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5YST5U7VVZ37V6AL75MU3YOCEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlocal approximation of nonlinear diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Esposito, Jeremy Sheung-Him Wu, Jos\\'e Antonio Carrillo","submitted_at":"2023-02-16T11:57:33Z","abstract_excerpt":"We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential equations. The nonlocal equations are obtained as gradient flows of interaction-like energies approximating the internal energy. We construct weak solutions as the limit of a (sub)sequence of weak measure solutions by using the Jordan-Kinderlehrer-Otto scheme from the context of $2$-Wasserstein gradient flows. Our strategy allows to cover the porous medium equation, for the general slow diffusion case, extending previous results in the literature. As a b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08248","kind":"arxiv","version":2},"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/2302.08248/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":"2026-07-05T06:59:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SAkZ4PZ0yebZxS8G9rtjnmLgSCB4GwXrjcEQ8QHO6+mez6wDgBhipeC8jfpIk18Cm9aQ3HpM3gmrEhcEwWoDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T01:57:55.948856Z"},"content_sha256":"a492ae804575b4f19fba717dd5b242089743ebc8ddfbf33a4e6a94e4effcb613","schema_version":"1.0","event_id":"sha256:a492ae804575b4f19fba717dd5b242089743ebc8ddfbf33a4e6a94e4effcb613"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YST5U7VVZ37V6AL75MU3YOCEP/bundle.json","state_url":"https://pith.science/pith/5YST5U7VVZ37V6AL75MU3YOCEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YST5U7VVZ37V6AL75MU3YOCEP/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":"2026-08-20T01:57:55Z","links":{"resolver":"https://pith.science/pith/5YST5U7VVZ37V6AL75MU3YOCEP","bundle":"https://pith.science/pith/5YST5U7VVZ37V6AL75MU3YOCEP/bundle.json","state":"https://pith.science/pith/5YST5U7VVZ37V6AL75MU3YOCEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YST5U7VVZ37V6AL75MU3YOCEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5YST5U7VVZ37V6AL75MU3YOCEP","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":"9b2d0c06d65e77c45d46411d3cac56fde3601aa810cf4f602fc3412996b868a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-02-16T11:57:33Z","title_canon_sha256":"5ba396f784a403acb662862d6bd0309f1f4fa40a1bb4e1a72771ce8079073519"},"schema_version":"1.0","source":{"id":"2302.08248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08248","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08248v2","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08248","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"pith_short_12","alias_value":"5YST5U7VVZ37","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"pith_short_16","alias_value":"5YST5U7VVZ37V6AL","created_at":"2026-07-05T06:59:29Z"},{"alias_kind":"pith_short_8","alias_value":"5YST5U7V","created_at":"2026-07-05T06:59:29Z"}],"graph_snapshots":[{"event_id":"sha256:a492ae804575b4f19fba717dd5b242089743ebc8ddfbf33a4e6a94e4effcb613","target":"graph","created_at":"2026-07-05T06:59:29Z","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/2302.08248/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a limit from a class of nonlocal partial differential equations. The nonlocal equations are obtained as gradient flows of interaction-like energies approximating the internal energy. We construct weak solutions as the limit of a (sub)sequence of weak measure solutions by using the Jordan-Kinderlehrer-Otto scheme from the context of $2$-Wasserstein gradient flows. Our strategy allows to cover the porous medium equation, for the general slow diffusion case, extending previous results in the literature. As a b","authors_text":"Antonio Esposito, Jeremy Sheung-Him Wu, Jos\\'e Antonio Carrillo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-02-16T11:57:33Z","title":"Nonlocal approximation of nonlinear diffusion equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08248","kind":"arxiv","version":2},"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":"sha256:8396043ff775e7948924436771ae9b11603ab2d1831963b32db2c0d2c4064828","target":"record","created_at":"2026-07-05T06:59:29Z","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":"9b2d0c06d65e77c45d46411d3cac56fde3601aa810cf4f602fc3412996b868a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-02-16T11:57:33Z","title_canon_sha256":"5ba396f784a403acb662862d6bd0309f1f4fa40a1bb4e1a72771ce8079073519"},"schema_version":"1.0","source":{"id":"2302.08248","kind":"arxiv","version":2}},"canonical_sha256":"ee253ed3f5ae77faf80bff594de1c223dc3db4b97bb5bf8057df914de596db40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee253ed3f5ae77faf80bff594de1c223dc3db4b97bb5bf8057df914de596db40","first_computed_at":"2026-07-05T06:59:29.479596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:59:29.479596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rhB2g2YGRyM3Fny/xh/m67o+ypxiSwwXJIp6nwINImwmTJAWKNnEPgILUOIczizKvpb5t59I3iL2YExGqecZCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:59:29.479978Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.08248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8396043ff775e7948924436771ae9b11603ab2d1831963b32db2c0d2c4064828","sha256:a492ae804575b4f19fba717dd5b242089743ebc8ddfbf33a4e6a94e4effcb613"],"state_sha256":"abb0d32de8513e51581e542037ad72946c5a722348e22bc8bd1da334b02840df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQCcZNJM6CjMMqpj/NoFnjBJQHNToVx/0spihF5aKV6M8rMwH8OVj6YckFYs2bbeCrBbha8SDQ3gaMRItLpLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T01:57:55.953392Z","bundle_sha256":"61837f187ada91985b2917c71860b1376d204274e093f5dc947f2dfdd488a85e"}}