{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:D42JLE6RX4TUCVDWSJAJBE5YUV","short_pith_number":"pith:D42JLE6R","canonical_record":{"source":{"id":"2312.11438","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-18T18:39:51Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"72dd13082c10383a491da04e1052f72417e1dd739f9732af68152504b0148118","abstract_canon_sha256":"69a617fa84fe5313261e21fcc794c9efd86835274d6888f88029bca0b79c135d"},"schema_version":"1.0"},"canonical_sha256":"1f349593d1bf2741547692409093b8a577d1a01e6c07b26a0ce372fb0e90568d","source":{"kind":"arxiv","id":"2312.11438","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.11438","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"2312.11438v2","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11438","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"D42JLE6RX4TU","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"pith_short_16","alias_value":"D42JLE6RX4TUCVDW","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"pith_short_8","alias_value":"D42JLE6R","created_at":"2026-07-05T08:04:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:D42JLE6RX4TUCVDWSJAJBE5YUV","target":"record","payload":{"canonical_record":{"source":{"id":"2312.11438","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-18T18:39:51Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"72dd13082c10383a491da04e1052f72417e1dd739f9732af68152504b0148118","abstract_canon_sha256":"69a617fa84fe5313261e21fcc794c9efd86835274d6888f88029bca0b79c135d"},"schema_version":"1.0"},"canonical_sha256":"1f349593d1bf2741547692409093b8a577d1a01e6c07b26a0ce372fb0e90568d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:16.887801Z","signature_b64":"B0HFDpvc+VbsDqEF+9W699TlotCjDZj4TdoqwiCUFuvQA3M3ZZewiTIfS7kPVpQ33UPqqP26pylfFwYt9Y3pDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f349593d1bf2741547692409093b8a577d1a01e6c07b26a0ce372fb0e90568d","last_reissued_at":"2026-07-05T08:04:16.887349Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:16.887349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.11438","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":"2026-07-05T08:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ZM3+9SKSexfz6i8TYVTxVnhbqncF4hTdARLFg/jekPIqsWryCmvDL/1S3e0oIb6UuO748cSa10PtvzMMzfuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T00:13:45.870495Z"},"content_sha256":"c1aad9a3df95290017d4de4d37d96f736ff406ea62b03546226e538cd3679847","schema_version":"1.0","event_id":"sha256:c1aad9a3df95290017d4de4d37d96f736ff406ea62b03546226e538cd3679847"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:D42JLE6RX4TUCVDWSJAJBE5YUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlocal Approximation of Slow and Fast Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Katy Craig, Matt Jacobs, Olga Turanova","submitted_at":"2023-12-18T18:39:51Z","abstract_excerpt":"Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method in the slow, linear, and fast diffusion regimes. A key ingredient of our approach is a novel technique for using the 2-Wasserstein and dual Sobolev gradient flow structures of the diffusion equations to recover the duality relation characterizing the pressure in the nonlocal-to-local limit. Due to the general class of internal energy densities that our metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11438","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/2312.11438/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":"2026-07-05T08:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c4GIGorTpjExFd36LZzQqJlRyn8SV8AXxNDNlzNUNuIqUNQHYM4aXZq9FlMcnkro8VD+qBp88ZnH4DGizT2LAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T00:13:45.871439Z"},"content_sha256":"826963fe862bfc613d19e290bce32332d1534551f4cf59357a0cdaaeda22126b","schema_version":"1.0","event_id":"sha256:826963fe862bfc613d19e290bce32332d1534551f4cf59357a0cdaaeda22126b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D42JLE6RX4TUCVDWSJAJBE5YUV/bundle.json","state_url":"https://pith.science/pith/D42JLE6RX4TUCVDWSJAJBE5YUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D42JLE6RX4TUCVDWSJAJBE5YUV/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":"2026-08-20T00:13:45Z","links":{"resolver":"https://pith.science/pith/D42JLE6RX4TUCVDWSJAJBE5YUV","bundle":"https://pith.science/pith/D42JLE6RX4TUCVDWSJAJBE5YUV/bundle.json","state":"https://pith.science/pith/D42JLE6RX4TUCVDWSJAJBE5YUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D42JLE6RX4TUCVDWSJAJBE5YUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:D42JLE6RX4TUCVDWSJAJBE5YUV","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":"69a617fa84fe5313261e21fcc794c9efd86835274d6888f88029bca0b79c135d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-18T18:39:51Z","title_canon_sha256":"72dd13082c10383a491da04e1052f72417e1dd739f9732af68152504b0148118"},"schema_version":"1.0","source":{"id":"2312.11438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.11438","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"2312.11438v2","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11438","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"D42JLE6RX4TU","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"pith_short_16","alias_value":"D42JLE6RX4TUCVDW","created_at":"2026-07-05T08:04:16Z"},{"alias_kind":"pith_short_8","alias_value":"D42JLE6R","created_at":"2026-07-05T08:04:16Z"}],"graph_snapshots":[{"event_id":"sha256:826963fe862bfc613d19e290bce32332d1534551f4cf59357a0cdaaeda22126b","target":"graph","created_at":"2026-07-05T08:04:16Z","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/2312.11438/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method in the slow, linear, and fast diffusion regimes. A key ingredient of our approach is a novel technique for using the 2-Wasserstein and dual Sobolev gradient flow structures of the diffusion equations to recover the duality relation characterizing the pressure in the nonlocal-to-local limit. Due to the general class of internal energy densities that our metho","authors_text":"Katy Craig, Matt Jacobs, Olga Turanova","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-18T18:39:51Z","title":"Nonlocal Approximation of Slow and Fast Diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11438","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:c1aad9a3df95290017d4de4d37d96f736ff406ea62b03546226e538cd3679847","target":"record","created_at":"2026-07-05T08:04:16Z","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":"69a617fa84fe5313261e21fcc794c9efd86835274d6888f88029bca0b79c135d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-12-18T18:39:51Z","title_canon_sha256":"72dd13082c10383a491da04e1052f72417e1dd739f9732af68152504b0148118"},"schema_version":"1.0","source":{"id":"2312.11438","kind":"arxiv","version":2}},"canonical_sha256":"1f349593d1bf2741547692409093b8a577d1a01e6c07b26a0ce372fb0e90568d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f349593d1bf2741547692409093b8a577d1a01e6c07b26a0ce372fb0e90568d","first_computed_at":"2026-07-05T08:04:16.887349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:04:16.887349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B0HFDpvc+VbsDqEF+9W699TlotCjDZj4TdoqwiCUFuvQA3M3ZZewiTIfS7kPVpQ33UPqqP26pylfFwYt9Y3pDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:04:16.887801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.11438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1aad9a3df95290017d4de4d37d96f736ff406ea62b03546226e538cd3679847","sha256:826963fe862bfc613d19e290bce32332d1534551f4cf59357a0cdaaeda22126b"],"state_sha256":"22374e5f4f57b62e037e9e40003d2bd1ccb780cf8017d4e8a7416fc47cd421be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XClL0K+3GO9/Y3vP59JExFtHV7ZEmjvfUjQGjovcbngXuBFuz9k07HgOEd6LSMpqmD4wY/wIqrZQXkzU/R1XCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T00:13:45.878334Z","bundle_sha256":"cbdf800f4e4e3732a5b4aa8b9cf281c779ef9689d95bc452ea7221889f759d21"}}