{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AW35W5HIKLCB6A57R3G3JEDLJK","short_pith_number":"pith:AW35W5HI","canonical_record":{"source":{"id":"1905.11310","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-27T15:51:15Z","cross_cats_sorted":[],"title_canon_sha256":"87742e4f5fb3bf4407fd6dece4df3ed79efd49f9c7e6cc4a899614be29dc833d","abstract_canon_sha256":"299a895d940c893c2e6d4a87523b2e080319094df4510697f19ad5f4595672aa"},"schema_version":"1.0"},"canonical_sha256":"05b7db74e852c41f03bf8ecdb4906b4a8e4b52a87c2ac6253f9df532e4266e50","source":{"kind":"arxiv","id":"1905.11310","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11310","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11310v2","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11310","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"pith_short_12","alias_value":"AW35W5HIKLCB","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"pith_short_16","alias_value":"AW35W5HIKLCB6A57","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"pith_short_8","alias_value":"AW35W5HI","created_at":"2026-07-05T02:23:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AW35W5HIKLCB6A57R3G3JEDLJK","target":"record","payload":{"canonical_record":{"source":{"id":"1905.11310","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-27T15:51:15Z","cross_cats_sorted":[],"title_canon_sha256":"87742e4f5fb3bf4407fd6dece4df3ed79efd49f9c7e6cc4a899614be29dc833d","abstract_canon_sha256":"299a895d940c893c2e6d4a87523b2e080319094df4510697f19ad5f4595672aa"},"schema_version":"1.0"},"canonical_sha256":"05b7db74e852c41f03bf8ecdb4906b4a8e4b52a87c2ac6253f9df532e4266e50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:23:41.672717Z","signature_b64":"o7JHu9mXcUrPj7/j5Br2TpiL4ZmQeH6TEj5eed1Yli+ORm27KKo+FdmXQ/RWileUTZmQgLixROfRgDvTOeCuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05b7db74e852c41f03bf8ecdb4906b4a8e4b52a87c2ac6253f9df532e4266e50","last_reissued_at":"2026-07-05T02:23:41.672206Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:23:41.672206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.11310","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":"2026-07-05T02:23:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aW4nCBqiAl/Z8/UdS4Ylk/endu0M6Kp0KJuerwJSFbWPgo/eEVSNF7/IZjjqF80cowrV5W/9mhVyRMxWsWVEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:32:54.033053Z"},"content_sha256":"8523a783060d8638f26fca0d1c68a53db9bd3e5b645a06657aaa026e063c2608","schema_version":"1.0","event_id":"sha256:8523a783060d8638f26fca0d1c68a53db9bd3e5b645a06657aaa026e063c2608"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AW35W5HIKLCB6A57R3G3JEDLJK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments of the 2D SHE at criticality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeremy Quastel, Li-Cheng Tsai, Yu Gu","submitted_at":"2019-05-27T15:51:15Z","abstract_excerpt":"We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as the limit of the equation driven by a noise that is mollified in space and white in time. As the mollification radius $ \\varepsilon\\to 0 $, we tune the coupling constant near the critical point, and show that the single time correlation functions converge to a limit written in terms of an explicit non-trivial semigroup. Our approach consists of two steps. First we show the convergence of the resolvent of the (tuned) two-dimensional delta Bose gas, by adapting the framework of Dimock and Rajeev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11310","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.11310/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:23:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9n0dLMwLzhkkO4VcpgXjjEG5BVEQErj99mfvvKyWpMQAWHVaEaVZgQqXauHedFFEAaDD0T1N9pecXfkgCQY3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T18:32:54.033569Z"},"content_sha256":"55791a645001c532edac841a21ef33add516eccee221001d7bb92d4a7a0063c3","schema_version":"1.0","event_id":"sha256:55791a645001c532edac841a21ef33add516eccee221001d7bb92d4a7a0063c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AW35W5HIKLCB6A57R3G3JEDLJK/bundle.json","state_url":"https://pith.science/pith/AW35W5HIKLCB6A57R3G3JEDLJK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AW35W5HIKLCB6A57R3G3JEDLJK/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":"2026-08-16T18:32:54Z","links":{"resolver":"https://pith.science/pith/AW35W5HIKLCB6A57R3G3JEDLJK","bundle":"https://pith.science/pith/AW35W5HIKLCB6A57R3G3JEDLJK/bundle.json","state":"https://pith.science/pith/AW35W5HIKLCB6A57R3G3JEDLJK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AW35W5HIKLCB6A57R3G3JEDLJK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AW35W5HIKLCB6A57R3G3JEDLJK","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":"299a895d940c893c2e6d4a87523b2e080319094df4510697f19ad5f4595672aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-27T15:51:15Z","title_canon_sha256":"87742e4f5fb3bf4407fd6dece4df3ed79efd49f9c7e6cc4a899614be29dc833d"},"schema_version":"1.0","source":{"id":"1905.11310","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.11310","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"arxiv_version","alias_value":"1905.11310v2","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11310","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"pith_short_12","alias_value":"AW35W5HIKLCB","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"pith_short_16","alias_value":"AW35W5HIKLCB6A57","created_at":"2026-07-05T02:23:41Z"},{"alias_kind":"pith_short_8","alias_value":"AW35W5HI","created_at":"2026-07-05T02:23:41Z"}],"graph_snapshots":[{"event_id":"sha256:55791a645001c532edac841a21ef33add516eccee221001d7bb92d4a7a0063c3","target":"graph","created_at":"2026-07-05T02:23:41Z","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/1905.11310/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as the limit of the equation driven by a noise that is mollified in space and white in time. As the mollification radius $ \\varepsilon\\to 0 $, we tune the coupling constant near the critical point, and show that the single time correlation functions converge to a limit written in terms of an explicit non-trivial semigroup. Our approach consists of two steps. First we show the convergence of the resolvent of the (tuned) two-dimensional delta Bose gas, by adapting the framework of Dimock and Rajeev","authors_text":"Jeremy Quastel, Li-Cheng Tsai, Yu Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-27T15:51:15Z","title":"Moments of the 2D SHE at criticality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11310","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":"sha256:8523a783060d8638f26fca0d1c68a53db9bd3e5b645a06657aaa026e063c2608","target":"record","created_at":"2026-07-05T02:23:41Z","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":"299a895d940c893c2e6d4a87523b2e080319094df4510697f19ad5f4595672aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-05-27T15:51:15Z","title_canon_sha256":"87742e4f5fb3bf4407fd6dece4df3ed79efd49f9c7e6cc4a899614be29dc833d"},"schema_version":"1.0","source":{"id":"1905.11310","kind":"arxiv","version":2}},"canonical_sha256":"05b7db74e852c41f03bf8ecdb4906b4a8e4b52a87c2ac6253f9df532e4266e50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05b7db74e852c41f03bf8ecdb4906b4a8e4b52a87c2ac6253f9df532e4266e50","first_computed_at":"2026-07-05T02:23:41.672206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:23:41.672206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o7JHu9mXcUrPj7/j5Br2TpiL4ZmQeH6TEj5eed1Yli+ORm27KKo+FdmXQ/RWileUTZmQgLixROfRgDvTOeCuBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:23:41.672717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.11310","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8523a783060d8638f26fca0d1c68a53db9bd3e5b645a06657aaa026e063c2608","sha256:55791a645001c532edac841a21ef33add516eccee221001d7bb92d4a7a0063c3"],"state_sha256":"52797b70635c1d173454c4c1340fe2fb1240a8d25fd2723dffd92e80d8aae812"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLt92d2UAivqsxR/R6+R8P9h8spHFeWFJr7sJ9bm6hfry5g/TOvEW5wLE8hwPNPYMAxGt4CEJmoHQtw3C0NbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T18:32:54.039296Z","bundle_sha256":"13ae87074bdd152b868a0db42aabed2a53861bc21176b5963aa3a5c1fb321493"}}