{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:J4MF2LDKVM36O2IWNSZDFEMOXF","short_pith_number":"pith:J4MF2LDK","canonical_record":{"source":{"id":"1002.1879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-02-09T15:48:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"41deb72e77f97baa1b05c765cf61a7ace206904a5344580db4e25ab63828db74","abstract_canon_sha256":"85abe223e84cc5e62276245b9763efd2d93e46e3b8466f25f57f91c71eff44b5"},"schema_version":"1.0"},"canonical_sha256":"4f185d2c6aab37e769166cb232918eb94afc40cc48fb1dbb842d7aa3e92905bb","source":{"kind":"arxiv","id":"1002.1879","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1879","created_at":"2026-05-18T02:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1879v2","created_at":"2026-05-18T02:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1879","created_at":"2026-05-18T02:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"J4MF2LDKVM36","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J4MF2LDKVM36O2IW","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J4MF2LDK","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:J4MF2LDKVM36O2IWNSZDFEMOXF","target":"record","payload":{"canonical_record":{"source":{"id":"1002.1879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-02-09T15:48:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"41deb72e77f97baa1b05c765cf61a7ace206904a5344580db4e25ab63828db74","abstract_canon_sha256":"85abe223e84cc5e62276245b9763efd2d93e46e3b8466f25f57f91c71eff44b5"},"schema_version":"1.0"},"canonical_sha256":"4f185d2c6aab37e769166cb232918eb94afc40cc48fb1dbb842d7aa3e92905bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:09:10.776883Z","signature_b64":"qoc2a3FR988DiP//hKKZWy36TSrmM5uQ3sBD5d/9FzQUKg7OwbumUxZr9pSlR5pFVdkHQuTEoq2z8PCFKPNEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f185d2c6aab37e769166cb232918eb94afc40cc48fb1dbb842d7aa3e92905bb","last_reissued_at":"2026-05-18T02:09:10.776038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:09:10.776038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.1879","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":"2026-05-18T02:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+d8ICX1aSfP5DrZRRj3Ur3O9AnzS4/AKOnyDV/72lKMnFw5p2HUJ8y4vD5dqvj31G993NAX36KyD8JLCjpXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:46:11.399998Z"},"content_sha256":"43c78e2a9bdf7ec8d984d483363deea6638a589ad479d075b850601c4cfdfd47","schema_version":"1.0","event_id":"sha256:43c78e2a9bdf7ec8d984d483363deea6638a589ad479d075b850601c4cfdfd47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:J4MF2LDKVM36O2IWNSZDFEMOXF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact height distributions for the KPZ equation with narrow wedge initial condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Herbert Spohn, Tomohiro Sasamoto","submitted_at":"2010-02-09T15:48:24Z","abstract_excerpt":"We consider the KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=- |x|/\\delta$, $\\delta\\ll 1$. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution $h(x,t)$ valid for any $x$ and $t>0$. The corresponding distribution function converges in the long time limit, $t\\to\\infty$, to the Tracy-Widom distribution. The first order correction is a shift of order $t^{-1/3}$. We provide numerical computations based on the exact formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1879","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":""},"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":"2026-05-18T02:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hC/S2rY7cC8oP0hWVGGJPC+7jaA7Z+8LP1iftC/0FAyVI9E3R+ATckGUmzWpTti9l9nhoaTEq11+bs0f95CeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T01:46:11.400720Z"},"content_sha256":"0751e8cae18af850831b0d2864ef9c67bbafa26ec7a1f2f9267e08183af538a5","schema_version":"1.0","event_id":"sha256:0751e8cae18af850831b0d2864ef9c67bbafa26ec7a1f2f9267e08183af538a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/bundle.json","state_url":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/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":"2026-05-30T01:46:11Z","links":{"resolver":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF","bundle":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/bundle.json","state":"https://pith.science/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4MF2LDKVM36O2IWNSZDFEMOXF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:J4MF2LDKVM36O2IWNSZDFEMOXF","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":"85abe223e84cc5e62276245b9763efd2d93e46e3b8466f25f57f91c71eff44b5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-02-09T15:48:24Z","title_canon_sha256":"41deb72e77f97baa1b05c765cf61a7ace206904a5344580db4e25ab63828db74"},"schema_version":"1.0","source":{"id":"1002.1879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.1879","created_at":"2026-05-18T02:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"1002.1879v2","created_at":"2026-05-18T02:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.1879","created_at":"2026-05-18T02:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"J4MF2LDKVM36","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J4MF2LDKVM36O2IW","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J4MF2LDK","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:0751e8cae18af850831b0d2864ef9c67bbafa26ec7a1f2f9267e08183af538a5","target":"graph","created_at":"2026-05-18T02:09:10Z","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 KPZ equation in one space dimension with narrow wedge initial condition, $h(x,t=0)=- |x|/\\delta$, $\\delta\\ll 1$. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution $h(x,t)$ valid for any $x$ and $t>0$. The corresponding distribution function converges in the long time limit, $t\\to\\infty$, to the Tracy-Widom distribution. The first order correction is a shift of order $t^{-1/3}$. We provide numerical computations based on the exact formula.","authors_text":"Herbert Spohn, Tomohiro Sasamoto","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-02-09T15:48:24Z","title":"Exact height distributions for the KPZ equation with narrow wedge initial condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1879","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":"sha256:43c78e2a9bdf7ec8d984d483363deea6638a589ad479d075b850601c4cfdfd47","target":"record","created_at":"2026-05-18T02:09:10Z","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":"85abe223e84cc5e62276245b9763efd2d93e46e3b8466f25f57f91c71eff44b5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-02-09T15:48:24Z","title_canon_sha256":"41deb72e77f97baa1b05c765cf61a7ace206904a5344580db4e25ab63828db74"},"schema_version":"1.0","source":{"id":"1002.1879","kind":"arxiv","version":2}},"canonical_sha256":"4f185d2c6aab37e769166cb232918eb94afc40cc48fb1dbb842d7aa3e92905bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f185d2c6aab37e769166cb232918eb94afc40cc48fb1dbb842d7aa3e92905bb","first_computed_at":"2026-05-18T02:09:10.776038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:10.776038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qoc2a3FR988DiP//hKKZWy36TSrmM5uQ3sBD5d/9FzQUKg7OwbumUxZr9pSlR5pFVdkHQuTEoq2z8PCFKPNEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:10.776883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.1879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43c78e2a9bdf7ec8d984d483363deea6638a589ad479d075b850601c4cfdfd47","sha256:0751e8cae18af850831b0d2864ef9c67bbafa26ec7a1f2f9267e08183af538a5"],"state_sha256":"6578cc224bb6523c85c8499415082ad590fd809a832c1b24f598c0e229f86192"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USVK/RT69/0q+lbrAlq9EzLLS7pCVmj0QuKdCOOdouEupd9EMed6VzWOURPNpd4IOsulOSDuwbH3s57eyE2wAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T01:46:11.404415Z","bundle_sha256":"7e9eb7ae472aff6a16f2c63fc5aafaff1f43e524b6c4368f98f17a5bbf954712"}}