{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TME3C2V7JGDGM6RRAO7HGEQ4OR","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":"6cd5b741b069d1a56b936c6a7ccc2ee22b2ed994949309ad4426e78c0791902d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-07-28T02:54:42Z","title_canon_sha256":"bff5d199b61bc5f8d8407eed923d3af575fb5a0d6477d93efc16b474705248c5"},"schema_version":"1.0","source":{"id":"2507.20487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.20487","created_at":"2026-07-05T11:44:20Z"},{"alias_kind":"arxiv_version","alias_value":"2507.20487v1","created_at":"2026-07-05T11:44:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20487","created_at":"2026-07-05T11:44:20Z"},{"alias_kind":"pith_short_12","alias_value":"TME3C2V7JGDG","created_at":"2026-07-05T11:44:20Z"},{"alias_kind":"pith_short_16","alias_value":"TME3C2V7JGDGM6RR","created_at":"2026-07-05T11:44:20Z"},{"alias_kind":"pith_short_8","alias_value":"TME3C2V7","created_at":"2026-07-05T11:44:20Z"}],"graph_snapshots":[{"event_id":"sha256:b297778c2d31c054e87ca97ec86fd415601117855449660a41d77808537ad074","target":"graph","created_at":"2026-07-05T11:44:20Z","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/2507.20487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The parabolic Airy process is the Airy$_2$ process minus a parabola, initially defined by its finite-dimensional distributions, which are given by a Fredholm determinant formula with the extended Airy kernel. This process is also the one-time spatial marginal of the KPZ fixed point with the narrow wedge initial condition. There are two formulas for the space-time multipoint distribution of the KPZ fixed point with the narrow wedge initial condition obtained by arXiv:1906.01053 and arXiv:1907.09876. Especially, the equal-time case of arXiv:1907.09876 gives a different formula of the multipoint ","authors_text":"Aaron Ortiz, Zhipeng Liu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-07-28T02:54:42Z","title":"On the multipoint distribution formulas of the parabolic Airy process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20487","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":"sha256:040ae139b8f7b6aafa44fcfade8be3cdbc307b0a0ce2f3eb6ddfe450098df621","target":"record","created_at":"2026-07-05T11:44:20Z","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":"6cd5b741b069d1a56b936c6a7ccc2ee22b2ed994949309ad4426e78c0791902d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-07-28T02:54:42Z","title_canon_sha256":"bff5d199b61bc5f8d8407eed923d3af575fb5a0d6477d93efc16b474705248c5"},"schema_version":"1.0","source":{"id":"2507.20487","kind":"arxiv","version":1}},"canonical_sha256":"9b09b16abf4986667a3103be73121c744ffd38e3f4689293d3871f8c998c8f3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b09b16abf4986667a3103be73121c744ffd38e3f4689293d3871f8c998c8f3c","first_computed_at":"2026-07-05T11:44:20.067121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:20.067121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDH4HFEn8IcxJftMDAlXYyzHKri/QnF5KVY7bV2GBVFryJ6xnxliQmwqHKSDKvL3Lm++ZVswh8ApFVQ1PXrIDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:20.067583Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.20487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:040ae139b8f7b6aafa44fcfade8be3cdbc307b0a0ce2f3eb6ddfe450098df621","sha256:b297778c2d31c054e87ca97ec86fd415601117855449660a41d77808537ad074"],"state_sha256":"7fa3e491aebd2734fd234aa8a64363f0f86da57ee2f7af4f5b586c70e6564932"}