{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UNIYKQRTYABWNR2BT326C4UNK2","short_pith_number":"pith:UNIYKQRT","schema_version":"1.0","canonical_sha256":"a351854233c00366c7419ef5e1728d56b075fb2b84235d383b9edd415a232a11","source":{"kind":"arxiv","id":"1811.07808","version":3},"attestation_state":"computed","paper":{"title":"Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Herbert Koch, Massimiliano Gubinelli, Tadahiro Oh","submitted_at":"2018-11-19T17:11:19Z","abstract_excerpt":"Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a periodic domain. There are two new ingredients as compared to the parabolic setting. (i) In constructing stochastic objects, we have to carefully exploit dispersion at a multilinear level. (ii) We introduce novel random operators and leverage their regularity to overcome the lack of smoothing of usual paradifferential commutators."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.07808","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T17:11:19Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b99acd2e9f42bfd40076ad3abd345277400c8998c0ee629c377520ca874e62cf","abstract_canon_sha256":"4282d28b1dac6e2e995f0ed3696413ced3ca0844aa4091b0ebc7178b389a5274"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:51:04.733879Z","signature_b64":"xVEmjbL8YyAx5ip53+Wfq303/Ys/jwK9p0aX9owKmaTlCa/GKvgtcRASPH4YQrAJl3Lat8oGQevq5rd23wsIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a351854233c00366c7419ef5e1728d56b075fb2b84235d383b9edd415a232a11","last_reissued_at":"2026-07-05T02:51:04.733450Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:51:04.733450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Herbert Koch, Massimiliano Gubinelli, Tadahiro Oh","submitted_at":"2018-11-19T17:11:19Z","abstract_excerpt":"Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a periodic domain. There are two new ingredients as compared to the parabolic setting. (i) In constructing stochastic objects, we have to carefully exploit dispersion at a multilinear level. (ii) We introduce novel random operators and leverage their regularity to overcome the lack of smoothing of usual paradifferential commutators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07808","kind":"arxiv","version":3},"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/1811.07808/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.07808","created_at":"2026-07-05T02:51:04.733509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.07808v3","created_at":"2026-07-05T02:51:04.733509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07808","created_at":"2026-07-05T02:51:04.733509+00:00"},{"alias_kind":"pith_short_12","alias_value":"UNIYKQRTYABW","created_at":"2026-07-05T02:51:04.733509+00:00"},{"alias_kind":"pith_short_16","alias_value":"UNIYKQRTYABWNR2B","created_at":"2026-07-05T02:51:04.733509+00:00"},{"alias_kind":"pith_short_8","alias_value":"UNIYKQRT","created_at":"2026-07-05T02:51:04.733509+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.03490","citing_title":"Comparing the stochastic nonlinear wave and heat equations: a case study","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2","json":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2.json","graph_json":"https://pith.science/api/pith-number/UNIYKQRTYABWNR2BT326C4UNK2/graph.json","events_json":"https://pith.science/api/pith-number/UNIYKQRTYABWNR2BT326C4UNK2/events.json","paper":"https://pith.science/paper/UNIYKQRT"},"agent_actions":{"view_html":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2","download_json":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2.json","view_paper":"https://pith.science/paper/UNIYKQRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.07808&json=true","fetch_graph":"https://pith.science/api/pith-number/UNIYKQRTYABWNR2BT326C4UNK2/graph.json","fetch_events":"https://pith.science/api/pith-number/UNIYKQRTYABWNR2BT326C4UNK2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2/action/storage_attestation","attest_author":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2/action/author_attestation","sign_citation":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2/action/citation_signature","submit_replication":"https://pith.science/pith/UNIYKQRTYABWNR2BT326C4UNK2/action/replication_record"}},"created_at":"2026-07-05T02:51:04.733509+00:00","updated_at":"2026-07-05T02:51:04.733509+00:00"}