{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3ASLLLHSGTMXBDYVTFEMQQ3GYE","short_pith_number":"pith:3ASLLLHS","canonical_record":{"source":{"id":"1704.03501","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-04-11T19:08:04Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"5da7bfc6cfcbfea3bf1b9b3ff22a5dfe4dbe1f0da7c79c2c12e93ce3a56c12d9","abstract_canon_sha256":"a51428a41c8d6ad6c2ce4110a86a5f73e1020c63c9a830d6e9c38a08ac175efc"},"schema_version":"1.0"},"canonical_sha256":"d824b5acf234d9708f159948c84366c10111bf1aa9a03abfe75c045c8113d0ba","source":{"kind":"arxiv","id":"1704.03501","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03501","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03501v2","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03501","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"3ASLLLHSGTMX","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"pith_short_16","alias_value":"3ASLLLHSGTMXBDYV","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"pith_short_8","alias_value":"3ASLLLHS","created_at":"2026-07-05T04:52:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3ASLLLHSGTMXBDYVTFEMQQ3GYE","target":"record","payload":{"canonical_record":{"source":{"id":"1704.03501","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-04-11T19:08:04Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"5da7bfc6cfcbfea3bf1b9b3ff22a5dfe4dbe1f0da7c79c2c12e93ce3a56c12d9","abstract_canon_sha256":"a51428a41c8d6ad6c2ce4110a86a5f73e1020c63c9a830d6e9c38a08ac175efc"},"schema_version":"1.0"},"canonical_sha256":"d824b5acf234d9708f159948c84366c10111bf1aa9a03abfe75c045c8113d0ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:52:20.976363Z","signature_b64":"2foLTcb97Y+FVmTLiuRTFsfU39zFgkaURI6AiSuk5Dj1zf5M9GnjR9vrjOLE4q4KK/jW7h6nHVmBe/dBIV4LDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d824b5acf234d9708f159948c84366c10111bf1aa9a03abfe75c045c8113d0ba","last_reissued_at":"2026-07-05T04:52:20.975864Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:52:20.975864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.03501","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":"2026-07-05T04:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f550ito8JbbQZE3ATx1GKq8A4BCKTLCRbc7iPShpar4BDIeEkqcagJ0Nwn0/f99X0vPVnqTDHV+wLX13csOTCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:03:25.563846Z"},"content_sha256":"d11211dea9e10fee9860586accc44bac30408db2635b0e64cf074554b356ad8d","schema_version":"1.0","event_id":"sha256:d11211dea9e10fee9860586accc44bac30408db2635b0e64cf074554b356ad8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3ASLLLHSGTMXBDYVTFEMQQ3GYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rules of calculus in the path integral representation of white noise Langevin equations: the Onsager-Machlup approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Leticia F. Cugliandolo, Vivien Lecomte","submitted_at":"2017-04-11T19:08:04Z","abstract_excerpt":"The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known It\\=o prescription ($dB^2=dt$) in a way that defines a modified stochastic calculus to be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03501","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/1704.03501/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":"2026-07-05T04:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rUo/PgA3kwOwJ700fsrdoVNQGk/ZQDALF2jPFTrviJQSETi8GaRMM2gNY1XoLLI9Zq+Iif+4tzms7tHC9SkmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:03:25.564355Z"},"content_sha256":"a7ce078f09a4bdb3280234f4b485069f4ad108aee960b5ad8473b47482c4bb29","schema_version":"1.0","event_id":"sha256:a7ce078f09a4bdb3280234f4b485069f4ad108aee960b5ad8473b47482c4bb29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3ASLLLHSGTMXBDYVTFEMQQ3GYE/bundle.json","state_url":"https://pith.science/pith/3ASLLLHSGTMXBDYVTFEMQQ3GYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3ASLLLHSGTMXBDYVTFEMQQ3GYE/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":"2026-08-17T18:03:25Z","links":{"resolver":"https://pith.science/pith/3ASLLLHSGTMXBDYVTFEMQQ3GYE","bundle":"https://pith.science/pith/3ASLLLHSGTMXBDYVTFEMQQ3GYE/bundle.json","state":"https://pith.science/pith/3ASLLLHSGTMXBDYVTFEMQQ3GYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3ASLLLHSGTMXBDYVTFEMQQ3GYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3ASLLLHSGTMXBDYVTFEMQQ3GYE","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":"a51428a41c8d6ad6c2ce4110a86a5f73e1020c63c9a830d6e9c38a08ac175efc","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-04-11T19:08:04Z","title_canon_sha256":"5da7bfc6cfcbfea3bf1b9b3ff22a5dfe4dbe1f0da7c79c2c12e93ce3a56c12d9"},"schema_version":"1.0","source":{"id":"1704.03501","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.03501","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"1704.03501v2","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03501","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"3ASLLLHSGTMX","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"pith_short_16","alias_value":"3ASLLLHSGTMXBDYV","created_at":"2026-07-05T04:52:20Z"},{"alias_kind":"pith_short_8","alias_value":"3ASLLLHS","created_at":"2026-07-05T04:52:20Z"}],"graph_snapshots":[{"event_id":"sha256:a7ce078f09a4bdb3280234f4b485069f4ad108aee960b5ad8473b47482c4bb29","target":"graph","created_at":"2026-07-05T04:52:20Z","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/1704.03501/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known It\\=o prescription ($dB^2=dt$) in a way that defines a modified stochastic calculus to be","authors_text":"Leticia F. Cugliandolo, Vivien Lecomte","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-04-11T19:08:04Z","title":"Rules of calculus in the path integral representation of white noise Langevin equations: the Onsager-Machlup approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03501","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:d11211dea9e10fee9860586accc44bac30408db2635b0e64cf074554b356ad8d","target":"record","created_at":"2026-07-05T04:52:20Z","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":"a51428a41c8d6ad6c2ce4110a86a5f73e1020c63c9a830d6e9c38a08ac175efc","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-04-11T19:08:04Z","title_canon_sha256":"5da7bfc6cfcbfea3bf1b9b3ff22a5dfe4dbe1f0da7c79c2c12e93ce3a56c12d9"},"schema_version":"1.0","source":{"id":"1704.03501","kind":"arxiv","version":2}},"canonical_sha256":"d824b5acf234d9708f159948c84366c10111bf1aa9a03abfe75c045c8113d0ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d824b5acf234d9708f159948c84366c10111bf1aa9a03abfe75c045c8113d0ba","first_computed_at":"2026-07-05T04:52:20.975864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:52:20.975864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2foLTcb97Y+FVmTLiuRTFsfU39zFgkaURI6AiSuk5Dj1zf5M9GnjR9vrjOLE4q4KK/jW7h6nHVmBe/dBIV4LDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:52:20.976363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.03501","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d11211dea9e10fee9860586accc44bac30408db2635b0e64cf074554b356ad8d","sha256:a7ce078f09a4bdb3280234f4b485069f4ad108aee960b5ad8473b47482c4bb29"],"state_sha256":"5fbf32cd08033693e13c5eb0357bb24ef92dea05ec9eefdebf35744af19e3c0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9z05CWMYIyG5llL/J7Rwqh9LGxFU55qLN1Q6SdzkgIOIsrU7FuIUvYjZymBXGt7sSY08yBpwq/p7sZULacRvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:03:25.567980Z","bundle_sha256":"b6ed5cbf2e8db875e80d45bc84dcbf0abe423444f860b664db81742cfac9ed4a"}}