{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2ZU77CFJA23BATHF4ZMDKL4QNF","short_pith_number":"pith:2ZU77CFJ","canonical_record":{"source":{"id":"1006.1338","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-07T19:16:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"364daee8c698064066ae6b0bda06060a2dc68c728f7b2b8238f302b07831e45f","abstract_canon_sha256":"c5265e63a9d8320d74f20491339e6f31cc398822f9209e06007d6da22a7e08ab"},"schema_version":"1.0"},"canonical_sha256":"d669ff88a906b6104ce5e658352f9069439e48187567442da016523bebe1b168","source":{"kind":"arxiv","id":"1006.1338","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1338","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1338v4","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1338","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"2ZU77CFJA23B","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2ZU77CFJA23BATHF","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2ZU77CFJ","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2ZU77CFJA23BATHF4ZMDKL4QNF","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1338","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-07T19:16:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"364daee8c698064066ae6b0bda06060a2dc68c728f7b2b8238f302b07831e45f","abstract_canon_sha256":"c5265e63a9d8320d74f20491339e6f31cc398822f9209e06007d6da22a7e08ab"},"schema_version":"1.0"},"canonical_sha256":"d669ff88a906b6104ce5e658352f9069439e48187567442da016523bebe1b168","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:04.484079Z","signature_b64":"pb+szcRmBKz9gCNN5loLdAFSvrNR82pVtZOuR2YmbjXRHyVAviIaUJ8mwE4D+sUtfy631i2r2ENWgyrm5w+GAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d669ff88a906b6104ce5e658352f9069439e48187567442da016523bebe1b168","last_reissued_at":"2026-05-18T03:25:04.483580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:04.483580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1338","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WHMZcr5G7FOc3x7aevtg+ECD8viHVEiNFJ+bdkg61x4hLHA3VaUtL9eK+VzF/WEfTCeUYJdelN4ZS0I4SftLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T16:37:35.844125Z"},"content_sha256":"fce3670f10b75eb0c043cfe9ab8a39018ecb224f92345f4d77885cc3b4ce5cef","schema_version":"1.0","event_id":"sha256:fce3670f10b75eb0c043cfe9ab8a39018ecb224f92345f4d77885cc3b4ce5cef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2ZU77CFJA23BATHF4ZMDKL4QNF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Crossover distributions at the edge of the rarefaction fan","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ivan Corwin, Jeremy Quastel","submitted_at":"2010-06-07T19:16:40Z","abstract_excerpt":"We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with $\\rho_-<\\rho_+$ so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf--Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point distribution functions have been computed in [Comm. Pure Appl. Math. 64 (2011) 466-537] and [Nuclear Phys"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1338","kind":"arxiv","version":4},"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":"2026-05-18T03:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42miPGf+8yjuVnZ7vlkLaJprratv7OrcFuxH5rweHuf+hz9Sxu1Nq/YC9GReQy+sEGHIohqT3g8jY91b3wK7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T16:37:35.844496Z"},"content_sha256":"0108de611c918dd4c8f19735dd75d23df4f07f01b665d65f15ea35b9418fb3a4","schema_version":"1.0","event_id":"sha256:0108de611c918dd4c8f19735dd75d23df4f07f01b665d65f15ea35b9418fb3a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZU77CFJA23BATHF4ZMDKL4QNF/bundle.json","state_url":"https://pith.science/pith/2ZU77CFJA23BATHF4ZMDKL4QNF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZU77CFJA23BATHF4ZMDKL4QNF/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":"2026-05-20T16:37:35Z","links":{"resolver":"https://pith.science/pith/2ZU77CFJA23BATHF4ZMDKL4QNF","bundle":"https://pith.science/pith/2ZU77CFJA23BATHF4ZMDKL4QNF/bundle.json","state":"https://pith.science/pith/2ZU77CFJA23BATHF4ZMDKL4QNF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZU77CFJA23BATHF4ZMDKL4QNF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2ZU77CFJA23BATHF4ZMDKL4QNF","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":"c5265e63a9d8320d74f20491339e6f31cc398822f9209e06007d6da22a7e08ab","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-07T19:16:40Z","title_canon_sha256":"364daee8c698064066ae6b0bda06060a2dc68c728f7b2b8238f302b07831e45f"},"schema_version":"1.0","source":{"id":"1006.1338","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1338","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1338v4","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1338","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"2ZU77CFJA23B","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2ZU77CFJA23BATHF","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2ZU77CFJ","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:0108de611c918dd4c8f19735dd75d23df4f07f01b665d65f15ea35b9418fb3a4","target":"graph","created_at":"2026-05-18T03:25:04Z","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 consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with $\\rho_-<\\rho_+$ so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf--Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point distribution functions have been computed in [Comm. Pure Appl. Math. 64 (2011) 466-537] and [Nuclear Phys","authors_text":"Ivan Corwin, Jeremy Quastel","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-07T19:16:40Z","title":"Crossover distributions at the edge of the rarefaction fan"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1338","kind":"arxiv","version":4},"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:fce3670f10b75eb0c043cfe9ab8a39018ecb224f92345f4d77885cc3b4ce5cef","target":"record","created_at":"2026-05-18T03:25:04Z","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":"c5265e63a9d8320d74f20491339e6f31cc398822f9209e06007d6da22a7e08ab","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-07T19:16:40Z","title_canon_sha256":"364daee8c698064066ae6b0bda06060a2dc68c728f7b2b8238f302b07831e45f"},"schema_version":"1.0","source":{"id":"1006.1338","kind":"arxiv","version":4}},"canonical_sha256":"d669ff88a906b6104ce5e658352f9069439e48187567442da016523bebe1b168","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d669ff88a906b6104ce5e658352f9069439e48187567442da016523bebe1b168","first_computed_at":"2026-05-18T03:25:04.483580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:04.483580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pb+szcRmBKz9gCNN5loLdAFSvrNR82pVtZOuR2YmbjXRHyVAviIaUJ8mwE4D+sUtfy631i2r2ENWgyrm5w+GAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:04.484079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1338","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fce3670f10b75eb0c043cfe9ab8a39018ecb224f92345f4d77885cc3b4ce5cef","sha256:0108de611c918dd4c8f19735dd75d23df4f07f01b665d65f15ea35b9418fb3a4"],"state_sha256":"b64c608cec9c62f2bdcb50c5f8b887a341f9fa7c69f623584985dab79cd7e289"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElcLo8pmP3T+H+o0+OxE/rBsIAPcQ2URsBZVdmx1+/rGCwy4p8GEVUM8U1icJrkb1Rtv+6d1Xo34dl4QFu1qCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T16:37:35.846474Z","bundle_sha256":"bd8c998b4916ab677b8de2b7b647abb0a4e54f97e4fcda4f478f2a13a6f26d6e"}}