{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YTHH6LLYZM3TZRNKLHYXQFMJY4","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":"8614e32eaa00adf8a9339afdd03325bd660409fa69d737984cc47b64b2ee6f26","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-10-11T17:15:00Z","title_canon_sha256":"5020b4e0db59620ede11c5f4f89d3a10d0d0ed0b1a52fcabaf8e8bab719a5f61"},"schema_version":"1.0","source":{"id":"2210.05629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.05629","created_at":"2026-07-05T05:05:18Z"},{"alias_kind":"arxiv_version","alias_value":"2210.05629v1","created_at":"2026-07-05T05:05:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.05629","created_at":"2026-07-05T05:05:18Z"},{"alias_kind":"pith_short_12","alias_value":"YTHH6LLYZM3T","created_at":"2026-07-05T05:05:18Z"},{"alias_kind":"pith_short_16","alias_value":"YTHH6LLYZM3TZRNK","created_at":"2026-07-05T05:05:18Z"},{"alias_kind":"pith_short_8","alias_value":"YTHH6LLY","created_at":"2026-07-05T05:05:18Z"}],"graph_snapshots":[{"event_id":"sha256:385c80d771d833b37f0be7331a35ddd7c56f59609edd91216d29e3e9a700661e","target":"graph","created_at":"2026-07-05T05:05:18Z","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/2210.05629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the variational problem associated with the Freidlin--Wentzell Large Deviation Principle of the Stochastic Heat Equation (SHE). The logarithm of the minimizer of the variational problem gives the most probable shape of the solution of the Kardar--Parisi--Zhang equation conditioned on achieving certain unlikely values. Taking the SHE with the delta initial condition and conditioning the value of its solution at the origin at a later time, under suitable scaling, we prove that the logarithm of the minimizer converges to an explicit function as we tune the value of the conditioning to","authors_text":"Li-Cheng Tsai, Yier Lin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-10-11T17:15:00Z","title":"A lower-tail limit in the weak noise theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.05629","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:e1095809b9e1561efe2041327e5ae086649060cc2b571ac642116f847ce36cd1","target":"record","created_at":"2026-07-05T05:05:18Z","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":"8614e32eaa00adf8a9339afdd03325bd660409fa69d737984cc47b64b2ee6f26","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2022-10-11T17:15:00Z","title_canon_sha256":"5020b4e0db59620ede11c5f4f89d3a10d0d0ed0b1a52fcabaf8e8bab719a5f61"},"schema_version":"1.0","source":{"id":"2210.05629","kind":"arxiv","version":1}},"canonical_sha256":"c4ce7f2d78cb373cc5aa59f1781589c736d1eeb82d79e9b351a5ffa42398c2fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4ce7f2d78cb373cc5aa59f1781589c736d1eeb82d79e9b351a5ffa42398c2fa","first_computed_at":"2026-07-05T05:05:18.635154Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:05:18.635154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3/zSEBDBT99vZMVDx8gqvkyoFoKRN7AR2KqDc6zVF7zH7t2E6bdiOm8zm11Z2hLDNV6j3wzfthZXvecKyXmjBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:05:18.635564Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.05629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1095809b9e1561efe2041327e5ae086649060cc2b571ac642116f847ce36cd1","sha256:385c80d771d833b37f0be7331a35ddd7c56f59609edd91216d29e3e9a700661e"],"state_sha256":"7e5eb2408bafec6ea12329aea2adea7ac310a268e2b5f5546d0287655f5a4699"}