{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BBNNPNLDGPUBSHDSS7KHKP7K4Z","short_pith_number":"pith:BBNNPNLD","schema_version":"1.0","canonical_sha256":"085ad7b56333e8191c7297d4753feae67f739dd52f191c1e802c1fdbf7bd2e3e","source":{"kind":"arxiv","id":"1209.0820","version":3},"attestation_state":"computed","paper":{"title":"Renormalized-Generalized Solutions for the KPZ Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.FA","authors_text":"C. Olivera, P. Catuogno","submitted_at":"2012-09-04T22:21:56Z","abstract_excerpt":"This work introduces a new notion of solution for the KPZ equation, in particular, our approach encompasses the Cole-Hopf solution. We set in the context of the distribution theory the proposed results by Bertini and Giacomin from the mid 90's.\n  This new approach provides a pathwise notion of solution as well as a structured approximation theory. The developments are based on  regularization arguments from the theory of distributions."},"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":"1209.0820","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-04T22:21:56Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"935caeee2a2f9100655f4b63fa40ac35677f7cb491f8b19692af17e69edac081","abstract_canon_sha256":"1b374099520d508f91e7220af95f9896689f558bf143efc782bd469eceb55783"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:13.334121Z","signature_b64":"GdqrmOyK6wUGS9gxz6PsjUb6CuLc/UCpMk9ncByTtBx+2yMuubXJei2LeFXY5DN/zFx8HAB05KaN/bYSP3L1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"085ad7b56333e8191c7297d4753feae67f739dd52f191c1e802c1fdbf7bd2e3e","last_reissued_at":"2026-05-18T02:47:13.333613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:13.333613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renormalized-Generalized Solutions for the KPZ Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.FA","authors_text":"C. Olivera, P. Catuogno","submitted_at":"2012-09-04T22:21:56Z","abstract_excerpt":"This work introduces a new notion of solution for the KPZ equation, in particular, our approach encompasses the Cole-Hopf solution. We set in the context of the distribution theory the proposed results by Bertini and Giacomin from the mid 90's.\n  This new approach provides a pathwise notion of solution as well as a structured approximation theory. The developments are based on  regularization arguments from the theory of distributions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0820","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":""},"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":"1209.0820","created_at":"2026-05-18T02:47:13.333693+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.0820v3","created_at":"2026-05-18T02:47:13.333693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0820","created_at":"2026-05-18T02:47:13.333693+00:00"},{"alias_kind":"pith_short_12","alias_value":"BBNNPNLDGPUB","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BBNNPNLDGPUBSHDS","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BBNNPNLD","created_at":"2026-05-18T12:26:58.693483+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z","json":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z.json","graph_json":"https://pith.science/api/pith-number/BBNNPNLDGPUBSHDSS7KHKP7K4Z/graph.json","events_json":"https://pith.science/api/pith-number/BBNNPNLDGPUBSHDSS7KHKP7K4Z/events.json","paper":"https://pith.science/paper/BBNNPNLD"},"agent_actions":{"view_html":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z","download_json":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z.json","view_paper":"https://pith.science/paper/BBNNPNLD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.0820&json=true","fetch_graph":"https://pith.science/api/pith-number/BBNNPNLDGPUBSHDSS7KHKP7K4Z/graph.json","fetch_events":"https://pith.science/api/pith-number/BBNNPNLDGPUBSHDSS7KHKP7K4Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z/action/storage_attestation","attest_author":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z/action/author_attestation","sign_citation":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z/action/citation_signature","submit_replication":"https://pith.science/pith/BBNNPNLDGPUBSHDSS7KHKP7K4Z/action/replication_record"}},"created_at":"2026-05-18T02:47:13.333693+00:00","updated_at":"2026-05-18T02:47:13.333693+00:00"}