{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IBZYSZG2ERADT6MPNRCSUPKKYF","short_pith_number":"pith:IBZYSZG2","canonical_record":{"source":{"id":"1904.03319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-05T23:08:21Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"884794ca1e21f0d0eb319d42deaefe25c22fe14a8bc45338e8121debd56b7243","abstract_canon_sha256":"d6f9cf7fcfa5bdecd997a510d47f068de94998469e312b8c092f8bbf18a7ce71"},"schema_version":"1.0"},"canonical_sha256":"40738964da244039f98f6c452a3d4ac148c16bea8cd06588ab46401bb492b9be","source":{"kind":"arxiv","id":"1904.03319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03319","created_at":"2026-05-17T23:49:13Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03319v1","created_at":"2026-05-17T23:49:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03319","created_at":"2026-05-17T23:49:13Z"},{"alias_kind":"pith_short_12","alias_value":"IBZYSZG2ERAD","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IBZYSZG2ERADT6MP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IBZYSZG2","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IBZYSZG2ERADT6MPNRCSUPKKYF","target":"record","payload":{"canonical_record":{"source":{"id":"1904.03319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-05T23:08:21Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"884794ca1e21f0d0eb319d42deaefe25c22fe14a8bc45338e8121debd56b7243","abstract_canon_sha256":"d6f9cf7fcfa5bdecd997a510d47f068de94998469e312b8c092f8bbf18a7ce71"},"schema_version":"1.0"},"canonical_sha256":"40738964da244039f98f6c452a3d4ac148c16bea8cd06588ab46401bb492b9be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:13.840582Z","signature_b64":"o94hQpsYZUrabDn97jP14b+MK3Q5/XDM046XgLV22/c3i8dSqPF28hMLKeifuR4387Uc0vduP1/JFI4LLBtoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40738964da244039f98f6c452a3d4ac148c16bea8cd06588ab46401bb492b9be","last_reissued_at":"2026-05-17T23:49:13.839937Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:13.839937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.03319","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":"2026-05-17T23:49:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJbQsbPcSB8Bh4q1LctYQTVZqKRPgc6RKvatjQXKH5/3xmrSNmZ79xuRCUDqKB9bXKKxSgzO/t0vDsmiU7BDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:18:54.406076Z"},"content_sha256":"88552ebd96af22e2949a88967347e5663107f00b046cc089069c05972622c8a9","schema_version":"1.0","event_id":"sha256:88552ebd96af22e2949a88967347e5663107f00b046cc089069c05972622c8a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IBZYSZG2ERADT6MPNRCSUPKKYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The KPZ Universality Class and Related Topics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Axel Saenz","submitted_at":"2019-04-05T23:08:21Z","abstract_excerpt":"These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions related to random growth processes in $1+1$ dimensions. We describe some of the characteristic properties of the KPZ universality class such as scaling exponents and limiting statistics. In particular, we aim to extract the characteristic properties of the KPZ universality class by understanding the KPZ stochastic partial differential equation by a special disc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03319","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":"2026-05-17T23:49:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xkSGmxoO+F+kT34bFY3DxxCoE6NejmQ7vnOnJCkTxLM39uqEehiK/Vn5x857VBFtYxBzigJjJEt90yFEnp+dCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:18:54.406429Z"},"content_sha256":"26cda2d195bc54433eb50b5061bfd89749c52724669b1e8b091699b9246c1d82","schema_version":"1.0","event_id":"sha256:26cda2d195bc54433eb50b5061bfd89749c52724669b1e8b091699b9246c1d82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBZYSZG2ERADT6MPNRCSUPKKYF/bundle.json","state_url":"https://pith.science/pith/IBZYSZG2ERADT6MPNRCSUPKKYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBZYSZG2ERADT6MPNRCSUPKKYF/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":"2026-06-26T08:18:54Z","links":{"resolver":"https://pith.science/pith/IBZYSZG2ERADT6MPNRCSUPKKYF","bundle":"https://pith.science/pith/IBZYSZG2ERADT6MPNRCSUPKKYF/bundle.json","state":"https://pith.science/pith/IBZYSZG2ERADT6MPNRCSUPKKYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBZYSZG2ERADT6MPNRCSUPKKYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IBZYSZG2ERADT6MPNRCSUPKKYF","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":"d6f9cf7fcfa5bdecd997a510d47f068de94998469e312b8c092f8bbf18a7ce71","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-05T23:08:21Z","title_canon_sha256":"884794ca1e21f0d0eb319d42deaefe25c22fe14a8bc45338e8121debd56b7243"},"schema_version":"1.0","source":{"id":"1904.03319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03319","created_at":"2026-05-17T23:49:13Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03319v1","created_at":"2026-05-17T23:49:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03319","created_at":"2026-05-17T23:49:13Z"},{"alias_kind":"pith_short_12","alias_value":"IBZYSZG2ERAD","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IBZYSZG2ERADT6MP","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IBZYSZG2","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:26cda2d195bc54433eb50b5061bfd89749c52724669b1e8b091699b9246c1d82","target":"graph","created_at":"2026-05-17T23:49:13Z","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":"These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions related to random growth processes in $1+1$ dimensions. We describe some of the characteristic properties of the KPZ universality class such as scaling exponents and limiting statistics. In particular, we aim to extract the characteristic properties of the KPZ universality class by understanding the KPZ stochastic partial differential equation by a special disc","authors_text":"Axel Saenz","cross_cats":["math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-05T23:08:21Z","title":"The KPZ Universality Class and Related Topics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03319","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":"sha256:88552ebd96af22e2949a88967347e5663107f00b046cc089069c05972622c8a9","target":"record","created_at":"2026-05-17T23:49:13Z","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":"d6f9cf7fcfa5bdecd997a510d47f068de94998469e312b8c092f8bbf18a7ce71","cross_cats_sorted":["math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-05T23:08:21Z","title_canon_sha256":"884794ca1e21f0d0eb319d42deaefe25c22fe14a8bc45338e8121debd56b7243"},"schema_version":"1.0","source":{"id":"1904.03319","kind":"arxiv","version":1}},"canonical_sha256":"40738964da244039f98f6c452a3d4ac148c16bea8cd06588ab46401bb492b9be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40738964da244039f98f6c452a3d4ac148c16bea8cd06588ab46401bb492b9be","first_computed_at":"2026-05-17T23:49:13.839937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:13.839937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o94hQpsYZUrabDn97jP14b+MK3Q5/XDM046XgLV22/c3i8dSqPF28hMLKeifuR4387Uc0vduP1/JFI4LLBtoDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:13.840582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88552ebd96af22e2949a88967347e5663107f00b046cc089069c05972622c8a9","sha256:26cda2d195bc54433eb50b5061bfd89749c52724669b1e8b091699b9246c1d82"],"state_sha256":"e5f0961fb5d442f0f05da260d1f4e8883d8d3467f39f2c73cc36fa0add7d56c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYYMDX9D/HylNNGdjPrWppBNyhi8fj4zTFBGl5iAm86aeMy6L01QbDHW0Hoa+Z/h3z0nTONmGzVZ+zMFNrRgAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:18:54.408396Z","bundle_sha256":"f144a0989f4e02f95dfee22e67ad6d17dc719965a347e77c5dd24953063a33c7"}}