{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XNIZNVKWTTWKWQ22RWQCBRYHJV","short_pith_number":"pith:XNIZNVKW","canonical_record":{"source":{"id":"1505.05712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-21T13:03:34Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f978818f286990a48f53e3f41be6389e1b94efbb804bf535aa7b508ca00dea7a","abstract_canon_sha256":"74081a14588ede2497928c6e8ecc77ef166a9c17462331906376142ccc26bf80"},"schema_version":"1.0"},"canonical_sha256":"bb5196d5569cecab435a8da020c7074d743093727cc473e043b7073959aebcca","source":{"kind":"arxiv","id":"1505.05712","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05712","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05712v2","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05712","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"XNIZNVKWTTWK","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XNIZNVKWTTWKWQ22","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XNIZNVKW","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XNIZNVKWTTWKWQ22RWQCBRYHJV","target":"record","payload":{"canonical_record":{"source":{"id":"1505.05712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-21T13:03:34Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f978818f286990a48f53e3f41be6389e1b94efbb804bf535aa7b508ca00dea7a","abstract_canon_sha256":"74081a14588ede2497928c6e8ecc77ef166a9c17462331906376142ccc26bf80"},"schema_version":"1.0"},"canonical_sha256":"bb5196d5569cecab435a8da020c7074d743093727cc473e043b7073959aebcca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:12.271457Z","signature_b64":"IJO9YEhuxlrvAp4unowWNDHKBDAzXx+oVhVpxRZUV5W4AtE9xt5xGJTl6AZxp0ff9MhY66vUbhbtgdLCV1KMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb5196d5569cecab435a8da020c7074d743093727cc473e043b7073959aebcca","last_reissued_at":"2026-05-18T01:23:12.270737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:12.270737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.05712","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":"2026-05-18T01:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bGgYVfeGstSyZrH/sJ7g4MqIxIlsPR/OyKoNsk8zsGFpirDotxAltNDGk4nixY2xmVgm0v5whbJi9QjejsnBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:40:18.935953Z"},"content_sha256":"1de5318242c0d1ce68db059ff2ecc091952a8c92bd5a81fa325fc0ba004d8bb3","schema_version":"1.0","event_id":"sha256:1de5318242c0d1ce68db059ff2ecc091952a8c92bd5a81fa325fc0ba004d8bb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XNIZNVKWTTWKWQ22RWQCBRYHJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From large deviations to Wasserstein gradient flows in multiple dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Jan Maas, Matthias Erbar, Michiel Renger","submitted_at":"2015-05-21T13:03:34Z","abstract_excerpt":"We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\\Gamma$-convergence) to the Jordan--Kinderlehrer--Otto functional arising in the Wasserstein gradient flow structure of the Fokker--Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper bound remained open, since the proof in \\cite{DLR2013} re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05712","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":""},"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":"2026-05-18T01:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjKcDBFKrnTvbcj3DyWnyYMPQp+B4D6mgqj9axL3hHz5nJsBQYVjlrMMSOM67npDqdJUSkAhsf/YEjkwmNORDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:40:18.936434Z"},"content_sha256":"f095b1954aafac4db01d3d29946ab368ec5d448c4a4374ad960d7f8c9206e669","schema_version":"1.0","event_id":"sha256:f095b1954aafac4db01d3d29946ab368ec5d448c4a4374ad960d7f8c9206e669"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNIZNVKWTTWKWQ22RWQCBRYHJV/bundle.json","state_url":"https://pith.science/pith/XNIZNVKWTTWKWQ22RWQCBRYHJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNIZNVKWTTWKWQ22RWQCBRYHJV/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":"2026-06-24T23:40:18Z","links":{"resolver":"https://pith.science/pith/XNIZNVKWTTWKWQ22RWQCBRYHJV","bundle":"https://pith.science/pith/XNIZNVKWTTWKWQ22RWQCBRYHJV/bundle.json","state":"https://pith.science/pith/XNIZNVKWTTWKWQ22RWQCBRYHJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNIZNVKWTTWKWQ22RWQCBRYHJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XNIZNVKWTTWKWQ22RWQCBRYHJV","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":"74081a14588ede2497928c6e8ecc77ef166a9c17462331906376142ccc26bf80","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-21T13:03:34Z","title_canon_sha256":"f978818f286990a48f53e3f41be6389e1b94efbb804bf535aa7b508ca00dea7a"},"schema_version":"1.0","source":{"id":"1505.05712","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.05712","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1505.05712v2","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.05712","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"XNIZNVKWTTWK","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XNIZNVKWTTWKWQ22","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XNIZNVKW","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:f095b1954aafac4db01d3d29946ab368ec5d448c4a4374ad960d7f8c9206e669","target":"graph","created_at":"2026-05-18T01:23:12Z","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":"We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically equivalent (in the sense of $\\Gamma$-convergence) to the Jordan--Kinderlehrer--Otto functional arising in the Wasserstein gradient flow structure of the Fokker--Planck equation. In higher dimensions, part of this statement (the lower bound) has been recently proved by Duong, Laschos and Renger, but the upper bound remained open, since the proof in \\cite{DLR2013} re","authors_text":"Jan Maas, Matthias Erbar, Michiel Renger","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-21T13:03:34Z","title":"From large deviations to Wasserstein gradient flows in multiple dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05712","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":"sha256:1de5318242c0d1ce68db059ff2ecc091952a8c92bd5a81fa325fc0ba004d8bb3","target":"record","created_at":"2026-05-18T01:23:12Z","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":"74081a14588ede2497928c6e8ecc77ef166a9c17462331906376142ccc26bf80","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-21T13:03:34Z","title_canon_sha256":"f978818f286990a48f53e3f41be6389e1b94efbb804bf535aa7b508ca00dea7a"},"schema_version":"1.0","source":{"id":"1505.05712","kind":"arxiv","version":2}},"canonical_sha256":"bb5196d5569cecab435a8da020c7074d743093727cc473e043b7073959aebcca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb5196d5569cecab435a8da020c7074d743093727cc473e043b7073959aebcca","first_computed_at":"2026-05-18T01:23:12.270737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:12.270737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJO9YEhuxlrvAp4unowWNDHKBDAzXx+oVhVpxRZUV5W4AtE9xt5xGJTl6AZxp0ff9MhY66vUbhbtgdLCV1KMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:12.271457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.05712","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de5318242c0d1ce68db059ff2ecc091952a8c92bd5a81fa325fc0ba004d8bb3","sha256:f095b1954aafac4db01d3d29946ab368ec5d448c4a4374ad960d7f8c9206e669"],"state_sha256":"3a03388e33934ca7e49f472a1b81e44ce5c51d5a27d3fe43f549f8b52ef0a8fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HWTod5Oi1gzwy+tiboZsgxNvoFwaiD5VvOkxyFoN3kPPG8hJslnLAEYK1+aZpUXACb8g7P1jC4OKcKwCJOAaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:40:18.939085Z","bundle_sha256":"902e181f0a5dbea3c422bca9e488ac5bc545071f36d121971f13f436da5f91bd"}}