{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OTRTU23HET5BSCOHRFK6S7QQHC","short_pith_number":"pith:OTRTU23H","canonical_record":{"source":{"id":"1906.08471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-20T07:26:11Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"2887790be512c74e865b900cee99e6caff4fe4bef3754f96ed19b5f4151f468e","abstract_canon_sha256":"f64a6dcc6bf91c07859c863be4a5c0795741bb421672512be982c84a8df47346"},"schema_version":"1.0"},"canonical_sha256":"74e33a6b6724fa1909c78955e97e1038a4bec27c305d7175600385b5d0818135","source":{"kind":"arxiv","id":"1906.08471","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08471","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08471v2","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08471","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"OTRTU23HET5B","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OTRTU23HET5BSCOH","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OTRTU23H","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OTRTU23HET5BSCOHRFK6S7QQHC","target":"record","payload":{"canonical_record":{"source":{"id":"1906.08471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-20T07:26:11Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"2887790be512c74e865b900cee99e6caff4fe4bef3754f96ed19b5f4151f468e","abstract_canon_sha256":"f64a6dcc6bf91c07859c863be4a5c0795741bb421672512be982c84a8df47346"},"schema_version":"1.0"},"canonical_sha256":"74e33a6b6724fa1909c78955e97e1038a4bec27c305d7175600385b5d0818135","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:41.739720Z","signature_b64":"5lpziN3L0WoY6ujeKV3hB3TBkCV8Mfhltrj7CXik3hbjbarBeuzKGiKVsyZo3i75c+NOhxf07kMdxr2Je3peCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74e33a6b6724fa1909c78955e97e1038a4bec27c305d7175600385b5d0818135","last_reissued_at":"2026-05-17T23:41:41.739197Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:41.739197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.08471","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":"2026-05-17T23:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l2iPHNjKC4W7BQpImQYBGQO1q31QA26rqdKR8W7yujKR4ug2xaNQ1B6fZYxMb2HGOlkdvrEbOQy0DvmxZ1nKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:43:13.761589Z"},"content_sha256":"cd0e114b972b1dd1894dd8ead4172bc387fb8a856cb5b9cad53c086b0b381cab","schema_version":"1.0","event_id":"sha256:cd0e114b972b1dd1894dd8ead4172bc387fb8a856cb5b9cad53c086b0b381cab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OTRTU23HET5BSCOHRFK6S7QQHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"math.PR","authors_text":"Jean-Christophe Mourrat","submitted_at":"2019-06-20T07:26:11Z","abstract_excerpt":"Parisi's formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We show that this quantity can be recast as the solution of a Hamilton-Jacobi equation in the Wasserstein space of probability measures on the positive half-line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08471","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":"2026-05-17T23:41:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YBIfibpwek4Mmechb1Q9FTHfsL07VjFiDbHIXQa2t8TfOqjkUlS7E07o1aeZDUfg07cwsQPOS7BfZyGyMIT+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:43:13.761936Z"},"content_sha256":"f98d77b328637cec28f01f626bd2441d84f93d44acc3dda423c3b3f1815566bb","schema_version":"1.0","event_id":"sha256:f98d77b328637cec28f01f626bd2441d84f93d44acc3dda423c3b3f1815566bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OTRTU23HET5BSCOHRFK6S7QQHC/bundle.json","state_url":"https://pith.science/pith/OTRTU23HET5BSCOHRFK6S7QQHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OTRTU23HET5BSCOHRFK6S7QQHC/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":"2026-05-28T02:43:13Z","links":{"resolver":"https://pith.science/pith/OTRTU23HET5BSCOHRFK6S7QQHC","bundle":"https://pith.science/pith/OTRTU23HET5BSCOHRFK6S7QQHC/bundle.json","state":"https://pith.science/pith/OTRTU23HET5BSCOHRFK6S7QQHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OTRTU23HET5BSCOHRFK6S7QQHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OTRTU23HET5BSCOHRFK6S7QQHC","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":"f64a6dcc6bf91c07859c863be4a5c0795741bb421672512be982c84a8df47346","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-20T07:26:11Z","title_canon_sha256":"2887790be512c74e865b900cee99e6caff4fe4bef3754f96ed19b5f4151f468e"},"schema_version":"1.0","source":{"id":"1906.08471","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08471","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08471v2","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08471","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"OTRTU23HET5B","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OTRTU23HET5BSCOH","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OTRTU23H","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:f98d77b328637cec28f01f626bd2441d84f93d44acc3dda423c3b3f1815566bb","target":"graph","created_at":"2026-05-17T23:41:41Z","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":"Parisi's formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We show that this quantity can be recast as the solution of a Hamilton-Jacobi equation in the Wasserstein space of probability measures on the positive half-line.","authors_text":"Jean-Christophe Mourrat","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-20T07:26:11Z","title":"Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08471","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:cd0e114b972b1dd1894dd8ead4172bc387fb8a856cb5b9cad53c086b0b381cab","target":"record","created_at":"2026-05-17T23:41:41Z","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":"f64a6dcc6bf91c07859c863be4a5c0795741bb421672512be982c84a8df47346","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-20T07:26:11Z","title_canon_sha256":"2887790be512c74e865b900cee99e6caff4fe4bef3754f96ed19b5f4151f468e"},"schema_version":"1.0","source":{"id":"1906.08471","kind":"arxiv","version":2}},"canonical_sha256":"74e33a6b6724fa1909c78955e97e1038a4bec27c305d7175600385b5d0818135","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74e33a6b6724fa1909c78955e97e1038a4bec27c305d7175600385b5d0818135","first_computed_at":"2026-05-17T23:41:41.739197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:41.739197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5lpziN3L0WoY6ujeKV3hB3TBkCV8Mfhltrj7CXik3hbjbarBeuzKGiKVsyZo3i75c+NOhxf07kMdxr2Je3peCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:41.739720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08471","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd0e114b972b1dd1894dd8ead4172bc387fb8a856cb5b9cad53c086b0b381cab","sha256:f98d77b328637cec28f01f626bd2441d84f93d44acc3dda423c3b3f1815566bb"],"state_sha256":"5687394ba36e3b6650a1df3f5eeeecc8e7c181ab380eeb7f310111777c288194"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5OEUR+e4+n7lUQPe10FFP7CMvAUnR93Rl18nCWWPUmpxIeVDtmIAGKeKWsJI2q1unda7WdiaqVs+ghW/d7xCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:43:13.763890Z","bundle_sha256":"d77a5dfcf8dc463d12da3cf7886dac96fce7a8dad07abe5135b8db268cf25056"}}