{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:A2NHKKRIROHZQIVV46DLK3CI3Y","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":"81dbdb24a23fc239f908c97ce2b80d50bb6cc6eb2df10ab673f377b50e5372b7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-25T07:13:39Z","title_canon_sha256":"ba22588b956f586ac188d7160d257448891579a2f2ec3dfe52ccf742ea80bc4a"},"schema_version":"1.0","source":{"id":"2606.26681","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26681","created_at":"2026-06-26T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26681v1","created_at":"2026-06-26T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26681","created_at":"2026-06-26T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"A2NHKKRIROHZ","created_at":"2026-06-26T01:15:56Z"},{"alias_kind":"pith_short_16","alias_value":"A2NHKKRIROHZQIVV","created_at":"2026-06-26T01:15:56Z"},{"alias_kind":"pith_short_8","alias_value":"A2NHKKRI","created_at":"2026-06-26T01:15:56Z"}],"graph_snapshots":[{"event_id":"sha256:373d18a07149d8be6dd0d1a71acb9e5f79400fa240554bd2529f4f2f8e5e4727","target":"graph","created_at":"2026-06-26T01:15:56Z","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/2606.26681/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For every $ 0<\\kappa<\\sqrt 5-2$, we prove global existence for the two-dimensional generalized parabolic Anderson model on the whole space $\\mathbb R^2$ with nonlinearity $F\\in C_b^2(\\mathbb R)$, driven by an enhanced noise $(\\eta,\\Psi)$. Here the noise $\\eta$ has polynomially weighted spatial Besov--H\\\"older regularity $-1-\\kappa$, and $\\Psi$ is the corresponding renormalized second-order object. If $F''$ is globally Lipschitz, the solution is unique.\n  The proof combines a weight-compatible annular high-low decomposition with a paracontrolled transport representation. The final remainder is ","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":"2026-06-25T07:13:39Z","title":"Global well-posedness for general parabolic Anderson model on the whole plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26681","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":"sha256:7634b0695305b26bcfb0d6be0914d7d9777882de26de15e190a59d65cb8754f8","target":"record","created_at":"2026-06-26T01:15:56Z","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":"81dbdb24a23fc239f908c97ce2b80d50bb6cc6eb2df10ab673f377b50e5372b7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-25T07:13:39Z","title_canon_sha256":"ba22588b956f586ac188d7160d257448891579a2f2ec3dfe52ccf742ea80bc4a"},"schema_version":"1.0","source":{"id":"2606.26681","kind":"arxiv","version":1}},"canonical_sha256":"069a752a288b8f9822b5e786b56c48de10ca767371c10642505a0b7983b7b33f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"069a752a288b8f9822b5e786b56c48de10ca767371c10642505a0b7983b7b33f","first_computed_at":"2026-06-26T01:15:56.694881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:56.694881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xqACi8sgbOnuIO9Ncgkw/T8JUtyceJI8KwdGQX1kLCVeiDbX5QI8P7OXpUKZ+z440u1hNnPuQb1/ol3HwrmNAA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:56.695278Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26681","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7634b0695305b26bcfb0d6be0914d7d9777882de26de15e190a59d65cb8754f8","sha256:373d18a07149d8be6dd0d1a71acb9e5f79400fa240554bd2529f4f2f8e5e4727"],"state_sha256":"6dd4e30666eeab112b6684c2c7617f97fde37dea45dae5d62129eb0042515c88"}