{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:25N7AEHDOPU5KLDRU3EYA3Q34B","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3b986f3b3172915871965c996a45eb69d9437c6be9c998cafff6849900ac15f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T23:24:59Z","title_canon_sha256":"6e0bf5c2e824eaa4ddfb8da38cba37a25b8f8cd9eb2850e1318f1e27a3d47864"},"schema_version":"1.0","source":{"id":"2608.06646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06646","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06646v1","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06646","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"25N7AEHDOPU5","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_16","alias_value":"25N7AEHDOPU5KLDR","created_at":"2026-08-10T01:11:34Z"},{"alias_kind":"pith_short_8","alias_value":"25N7AEHD","created_at":"2026-08-10T01:11:34Z"}],"graph_snapshots":[{"event_id":"sha256:cc68d165bdc8470bcfe4079d7bcff8f1ee7af8d8d6b575df80301bda01a198c9","target":"graph","created_at":"2026-08-10T01:11:34Z","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/2608.06646/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the three-dimensional stochastic wave equation (SWE) driven by a multiplicative Gaussian noise that is white in time and colored in space: \\[\n  \\frac{\\partial^2 u}{\\partial t^2}\n  = \\Delta u\n  + b\\bigl(u\\bigr)\n  + \\sigma\\bigl(u\\bigr)\\,\\dot{W}, \\] where the drift function $ b $ and diffusion coefficient $\\sigma$ are assumed to be locally Lipschitz and exhibit logarithmic superlinear growth at infinity. We establish the existence and uniqueness of a global mild solution on any fixed time interval $[0,T]$ under suitable assumptions on the spatial covariance function $ f $ of the noise","authors_text":"Jingyu Huang, Wenxuan Tao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T23:24:59Z","title":"Three-dimensional stochastic wave equation with non-Lipschitz coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06646","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:db77073d6fc4ac9cb84b2f652a9d306cbdfa32b94c661873dedf74c6983c2623","target":"record","created_at":"2026-08-10T01:11:34Z","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":"3b986f3b3172915871965c996a45eb69d9437c6be9c998cafff6849900ac15f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-06T23:24:59Z","title_canon_sha256":"6e0bf5c2e824eaa4ddfb8da38cba37a25b8f8cd9eb2850e1318f1e27a3d47864"},"schema_version":"1.0","source":{"id":"2608.06646","kind":"arxiv","version":1}},"canonical_sha256":"d75bf010e373e9d52c71a6c9806e1be04faa7333e44dd903a5013ed6597edc04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d75bf010e373e9d52c71a6c9806e1be04faa7333e44dd903a5013ed6597edc04","first_computed_at":"2026-08-10T01:11:34.600132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-10T01:11:34.600132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qJdwGyWMunb2ICv5u6F4FyqhyWB7amNSn5gXkaaHHkKlQDOV02HHTieSZ40qDkYUmSZo3eft1vHHaQoU/tT1AQ==","signature_status":"signed_v1","signed_at":"2026-08-10T01:11:34.602544Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db77073d6fc4ac9cb84b2f652a9d306cbdfa32b94c661873dedf74c6983c2623","sha256:cc68d165bdc8470bcfe4079d7bcff8f1ee7af8d8d6b575df80301bda01a198c9","sha256:c3b05dd61103a8bc8509767a79ea353b21b459fc544519e4f03c600887899f9e"],"state_sha256":"01bc6af66e0b3f6e554f0bd1edc9ebfaebcb4c80cbf35d30fc86550cd382efe1"}