{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ZKES6SKJWFUKV4QMYWJAQEEDT3","short_pith_number":"pith:ZKES6SKJ","schema_version":"1.0","canonical_sha256":"ca892f4949b168aaf20cc5920810839efdb5f5dd98f0375e955b800d58ce27a5","source":{"kind":"arxiv","id":"1508.07764","version":2},"attestation_state":"computed","paper":{"title":"Energy solutions of KPZ are unique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"M. Gubinelli, N. Perkowski","submitted_at":"2015-08-31T11:04:39Z","abstract_excerpt":"The Kardar-Parisi-Zhang (KPZ) equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well-posedness result for the KPZ equation on the real line by showing that its energy solutions (as introduced by Gon\\c{c}alves and Jara and later refined by Gubinelli and Jara) are unique. Together with various convergence results already present in the literature, this establishes the weak KPZ universality conjecture for a wide class of models. A remarkable consequence is that the energy solution to the KPZ equation is not "},"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":"1508.07764","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-31T11:04:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e67d074f9d7885479806459a580bac741e4d504c37d004a14682842cf84041cd","abstract_canon_sha256":"4b55d79ef0b3c4d84504f0874bc834d585380c2c8b5ede70a73919496d3f1882"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:42.126622Z","signature_b64":"/2TwhGrJQZZ3m6jqW7ZwNne+NluTilDKw/VHmqFLuFrR3epOVKSV4SrUPOZRxkMCGunKqcLw4EIAxJ4kCJbUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca892f4949b168aaf20cc5920810839efdb5f5dd98f0375e955b800d58ce27a5","last_reissued_at":"2026-05-18T01:09:42.126069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:42.126069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy solutions of KPZ are unique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"M. Gubinelli, N. Perkowski","submitted_at":"2015-08-31T11:04:39Z","abstract_excerpt":"The Kardar-Parisi-Zhang (KPZ) equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well-posedness result for the KPZ equation on the real line by showing that its energy solutions (as introduced by Gon\\c{c}alves and Jara and later refined by Gubinelli and Jara) are unique. Together with various convergence results already present in the literature, this establishes the weak KPZ universality conjecture for a wide class of models. A remarkable consequence is that the energy solution to the KPZ equation is not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07764","kind":"arxiv","version":2},"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":"1508.07764","created_at":"2026-05-18T01:09:42.126131+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.07764v2","created_at":"2026-05-18T01:09:42.126131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07764","created_at":"2026-05-18T01:09:42.126131+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKES6SKJWFUK","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKES6SKJWFUKV4QM","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKES6SKJ","created_at":"2026-05-18T12:29:52.810259+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/ZKES6SKJWFUKV4QMYWJAQEEDT3","json":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3.json","graph_json":"https://pith.science/api/pith-number/ZKES6SKJWFUKV4QMYWJAQEEDT3/graph.json","events_json":"https://pith.science/api/pith-number/ZKES6SKJWFUKV4QMYWJAQEEDT3/events.json","paper":"https://pith.science/paper/ZKES6SKJ"},"agent_actions":{"view_html":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3","download_json":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3.json","view_paper":"https://pith.science/paper/ZKES6SKJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.07764&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKES6SKJWFUKV4QMYWJAQEEDT3/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKES6SKJWFUKV4QMYWJAQEEDT3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3/action/storage_attestation","attest_author":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3/action/author_attestation","sign_citation":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3/action/citation_signature","submit_replication":"https://pith.science/pith/ZKES6SKJWFUKV4QMYWJAQEEDT3/action/replication_record"}},"created_at":"2026-05-18T01:09:42.126131+00:00","updated_at":"2026-05-18T01:09:42.126131+00:00"}