{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:H4LKNTEX36UXY6L467G4PWMY5N","short_pith_number":"pith:H4LKNTEX","canonical_record":{"source":{"id":"cond-mat/9901010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-01-04T10:18:05Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"6b9f481919431784f616e430d3036f873d228f3a1654ab4bad236ca94273ba7c","abstract_canon_sha256":"60b21cf9e42c61775404bc9f0b2e0ccb6838b11a328ce2fa5df5ef1f481b3bb6"},"schema_version":"1.0"},"canonical_sha256":"3f16a6cc97dfa97c797cf7cdc7d998eb707a1fdc3adcf6bf3848b971d6e5560b","source":{"kind":"arxiv","id":"cond-mat/9901010","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9901010","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9901010v1","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9901010","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"H4LKNTEX36UX","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"H4LKNTEX36UXY6L4","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"H4LKNTEX","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:H4LKNTEX36UXY6L467G4PWMY5N","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9901010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-01-04T10:18:05Z","cross_cats_sorted":["cond-mat.soft"],"title_canon_sha256":"6b9f481919431784f616e430d3036f873d228f3a1654ab4bad236ca94273ba7c","abstract_canon_sha256":"60b21cf9e42c61775404bc9f0b2e0ccb6838b11a328ce2fa5df5ef1f481b3bb6"},"schema_version":"1.0"},"canonical_sha256":"3f16a6cc97dfa97c797cf7cdc7d998eb707a1fdc3adcf6bf3848b971d6e5560b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:01.891305Z","signature_b64":"AK1bu50Jsg911XTGqziuGSgQs0eYjRcW7neh3JmL7iofwSGBwdnAI3UWbX/LY3o2iSIMN3ZBoFstyrupxD1tCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f16a6cc97dfa97c797cf7cdc7d998eb707a1fdc3adcf6bf3848b971d6e5560b","last_reissued_at":"2026-05-18T02:41:01.890713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:01.890713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9901010","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gDDl2sdtS9Gk8NXzfimHoZSndVmlsEFHJqd8x2+nF7J0zO69Mza80UKL6VlwLtHaF2w/Ans+bzD1D/eNMglgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:10:40.331154Z"},"content_sha256":"159f2c42f97eccd7392b9e704f26c6d183548be72cb2abbd7d274cb045e35e70","schema_version":"1.0","event_id":"sha256:159f2c42f97eccd7392b9e704f26c6d183548be72cb2abbd7d274cb045e35e70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:H4LKNTEX36UXY6L467G4PWMY5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Canonical phase space approach to the noisy Burgers equation: Probability distributions","license":"","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aarhus, Astronomy, Copenhagen, Denmark), Hans C. Fogedby (Institute of Physics, NORDITA","submitted_at":"1999-01-04T10:18:05Z","abstract_excerpt":"We present a canonical phase space approach to stochastic systems described by Langevin equations driven by white noise. Mapping the associated Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative weak noise limit we invoke a {\\em principle of least action} for the determination of the probability distributions. We apply the scheme to the noisy Burgers and KPZ equations and discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9901010","kind":"arxiv","version":1},"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":"2026-05-18T02:41:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1sjnZj2QhM5ZDIFgs3eLsqDANiNmw2DKd92OnT6iG00RKLwsjugyO68uflDKEEqj4xVmUAwDH8I5F1FjMpSoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:10:40.331877Z"},"content_sha256":"21bedd5d3c8bcb39c74f692d9a450c88426915d2a5452cf9c872daa4b2f8ebcf","schema_version":"1.0","event_id":"sha256:21bedd5d3c8bcb39c74f692d9a450c88426915d2a5452cf9c872daa4b2f8ebcf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4LKNTEX36UXY6L467G4PWMY5N/bundle.json","state_url":"https://pith.science/pith/H4LKNTEX36UXY6L467G4PWMY5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4LKNTEX36UXY6L467G4PWMY5N/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":"2026-05-25T16:10:40Z","links":{"resolver":"https://pith.science/pith/H4LKNTEX36UXY6L467G4PWMY5N","bundle":"https://pith.science/pith/H4LKNTEX36UXY6L467G4PWMY5N/bundle.json","state":"https://pith.science/pith/H4LKNTEX36UXY6L467G4PWMY5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4LKNTEX36UXY6L467G4PWMY5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:H4LKNTEX36UXY6L467G4PWMY5N","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":"60b21cf9e42c61775404bc9f0b2e0ccb6838b11a328ce2fa5df5ef1f481b3bb6","cross_cats_sorted":["cond-mat.soft"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-01-04T10:18:05Z","title_canon_sha256":"6b9f481919431784f616e430d3036f873d228f3a1654ab4bad236ca94273ba7c"},"schema_version":"1.0","source":{"id":"cond-mat/9901010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9901010","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9901010v1","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9901010","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"H4LKNTEX36UX","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"H4LKNTEX36UXY6L4","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"H4LKNTEX","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:21bedd5d3c8bcb39c74f692d9a450c88426915d2a5452cf9c872daa4b2f8ebcf","target":"graph","created_at":"2026-05-18T02:41:01Z","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 present a canonical phase space approach to stochastic systems described by Langevin equations driven by white noise. Mapping the associated Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative weak noise limit we invoke a {\\em principle of least action} for the determination of the probability distributions. We apply the scheme to the noisy Burgers and KPZ equations and discuss the time-dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short","authors_text":"Aarhus, Astronomy, Copenhagen, Denmark), Hans C. Fogedby (Institute of Physics, NORDITA","cross_cats":["cond-mat.soft"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-01-04T10:18:05Z","title":"Canonical phase space approach to the noisy Burgers equation: Probability distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9901010","kind":"arxiv","version":1},"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":"sha256:159f2c42f97eccd7392b9e704f26c6d183548be72cb2abbd7d274cb045e35e70","target":"record","created_at":"2026-05-18T02:41:01Z","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":"60b21cf9e42c61775404bc9f0b2e0ccb6838b11a328ce2fa5df5ef1f481b3bb6","cross_cats_sorted":["cond-mat.soft"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1999-01-04T10:18:05Z","title_canon_sha256":"6b9f481919431784f616e430d3036f873d228f3a1654ab4bad236ca94273ba7c"},"schema_version":"1.0","source":{"id":"cond-mat/9901010","kind":"arxiv","version":1}},"canonical_sha256":"3f16a6cc97dfa97c797cf7cdc7d998eb707a1fdc3adcf6bf3848b971d6e5560b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f16a6cc97dfa97c797cf7cdc7d998eb707a1fdc3adcf6bf3848b971d6e5560b","first_computed_at":"2026-05-18T02:41:01.890713Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:01.890713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AK1bu50Jsg911XTGqziuGSgQs0eYjRcW7neh3JmL7iofwSGBwdnAI3UWbX/LY3o2iSIMN3ZBoFstyrupxD1tCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:01.891305Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9901010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:159f2c42f97eccd7392b9e704f26c6d183548be72cb2abbd7d274cb045e35e70","sha256:21bedd5d3c8bcb39c74f692d9a450c88426915d2a5452cf9c872daa4b2f8ebcf"],"state_sha256":"9c5d3d69e3ece76a7c236005d3b786ed7e83e6c9ca16ca9bb58ec89ebcc39741"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTADpXlEtccBm1EtllH7uTWftCi3mjsXqu10nHkJkxp1qPCMdqCF/Nd8Kk8RFuKJPMPeeQ1hi4jWXLsT+XahAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:10:40.335735Z","bundle_sha256":"5e978d016d9f7cbf56a0cb8b0a9a4c26adf8b7c86ed950eb1d8cc58da25972d5"}}