{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6CN3PFIFZDP6GJZCVQCDZB7CQU","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":"2679c087a453a522df5245b7861143a95adc474be8ee7e4fa90de99e186280dc","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-29T13:20:07Z","title_canon_sha256":"f6937d2fddb477c45afed3c6051049cf3105b7e47bd7188aad24db21d7cec350"},"schema_version":"1.0","source":{"id":"2402.19137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.19137","created_at":"2026-07-05T07:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"2402.19137v1","created_at":"2026-07-05T07:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.19137","created_at":"2026-07-05T07:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"6CN3PFIFZDP6","created_at":"2026-07-05T07:50:41Z"},{"alias_kind":"pith_short_16","alias_value":"6CN3PFIFZDP6GJZC","created_at":"2026-07-05T07:50:41Z"},{"alias_kind":"pith_short_8","alias_value":"6CN3PFIF","created_at":"2026-07-05T07:50:41Z"}],"graph_snapshots":[{"event_id":"sha256:665aa1c4237c04b891f068adae56c5f7979967b1c97c32a6ffdb8d95e395d955","target":"graph","created_at":"2026-07-05T07:50:41Z","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/2402.19137/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on $\\mathbb{R}^+\\times \\mathbb{T}^2$ within the framework of paracontrolled calculus \\cite{GIP15}. The model is given by the equation:\n  \\begin{equation*}\n  (\\partial_t-\\Delta) u=F(u)\\eta\n  \\end{equation*}\n  where $\\eta\\in C^{-1-\\kappa}$ with $1/6>\\kappa>0$, and $F\\in C_b^2(\\mathbb{R})$. Assume that $\\eta\\in C^{-1-\\kappa}$ and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work\n  \\cite{CFW24} by A.Chandra, G.L. Feltes and H.Weber to repre","authors_text":"Hao Shen, Rongchan Zhu, Xiangchan Zhu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-29T13:20:07Z","title":"Global well-posedness for 2D generalized Parabolic Anderson Model via paracontrolled calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.19137","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":"sha256:1c1608a27faa7c57cfdd1892af1c29b5bb8c18a34aff61f2013194a2a733b0f3","target":"record","created_at":"2026-07-05T07:50:41Z","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":"2679c087a453a522df5245b7861143a95adc474be8ee7e4fa90de99e186280dc","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-02-29T13:20:07Z","title_canon_sha256":"f6937d2fddb477c45afed3c6051049cf3105b7e47bd7188aad24db21d7cec350"},"schema_version":"1.0","source":{"id":"2402.19137","kind":"arxiv","version":1}},"canonical_sha256":"f09bb79505c8dfe32722ac043c87e2853efb7a93abe647cc1b2a119b899a4b7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f09bb79505c8dfe32722ac043c87e2853efb7a93abe647cc1b2a119b899a4b7f","first_computed_at":"2026-07-05T07:50:41.536620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:50:41.536620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CHYo4xX093SXSrGp7gCBKV2umw6ZUsf/b9H49rWjmH0qztPWitTeOPJR6CdqBVR/PNpMuKQhjchGxwxTy35iAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:50:41.537046Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.19137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c1608a27faa7c57cfdd1892af1c29b5bb8c18a34aff61f2013194a2a733b0f3","sha256:665aa1c4237c04b891f068adae56c5f7979967b1c97c32a6ffdb8d95e395d955"],"state_sha256":"a58529a10967e5bc9f8aac609eebfd0a4769ea3167c5e9a29f19aa48e44f94b3"}