{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:Y3VNTNKWZE7S4XGAOJODKTMX4N","short_pith_number":"pith:Y3VNTNKW","schema_version":"1.0","canonical_sha256":"c6ead9b556c93f2e5cc0725c354d97e3714a1c7ae071262932a4d4274e01f2f0","source":{"kind":"arxiv","id":"2202.01171","version":2},"attestation_state":"computed","paper":{"title":"Low regularity integrators via decorated trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP","math.RA"],"primary_cat":"math.NA","authors_text":"Katharina Schratz, Yvain Bruned, Yvonne Alama Bronsard","submitted_at":"2022-02-02T18:02:49Z","abstract_excerpt":"We introduce a general framework of low regularity integrators which allows us to approximate the time dynamics of a large class of equations, including parabolic and hyperbolic problems, as well as dispersive equations, up to arbitrary high order on general domains. The structure of the local error of the new schemes is driven by nested commutators which in general require (much) lower regularity assumptions than classical methods do. Our main idea lies in embedding the central oscillations of the nonlinear PDE into the numerical discretisation. The latter is achieved by a novel decorated tre"},"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":"2202.01171","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2022-02-02T18:02:49Z","cross_cats_sorted":["cs.NA","math.AP","math.RA"],"title_canon_sha256":"6d5dde7feaa02f7c42510a00074d6b293be0422118226c2e132d228460a09f7c","abstract_canon_sha256":"264d5c05e07d03df45a5fd92a41ed714b2c7e369b1c9e5929b22ae2ea9b9885c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:03:15.618834Z","signature_b64":"Cw9fvr/PG0n8UtwGXwC2o+bkoO/Dh6kSMqANNuQTlED8RmmuSZY9645Fjan1Bs5yJPOIGX8TFiorboxtz3mNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6ead9b556c93f2e5cc0725c354d97e3714a1c7ae071262932a4d4274e01f2f0","last_reissued_at":"2026-07-05T04:03:15.618277Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:03:15.618277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low regularity integrators via decorated trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP","math.RA"],"primary_cat":"math.NA","authors_text":"Katharina Schratz, Yvain Bruned, Yvonne Alama Bronsard","submitted_at":"2022-02-02T18:02:49Z","abstract_excerpt":"We introduce a general framework of low regularity integrators which allows us to approximate the time dynamics of a large class of equations, including parabolic and hyperbolic problems, as well as dispersive equations, up to arbitrary high order on general domains. The structure of the local error of the new schemes is driven by nested commutators which in general require (much) lower regularity assumptions than classical methods do. Our main idea lies in embedding the central oscillations of the nonlinear PDE into the numerical discretisation. The latter is achieved by a novel decorated tre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.01171","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.01171/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":"2202.01171","created_at":"2026-07-05T04:03:15.618347+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.01171v2","created_at":"2026-07-05T04:03:15.618347+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.01171","created_at":"2026-07-05T04:03:15.618347+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y3VNTNKWZE7S","created_at":"2026-07-05T04:03:15.618347+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y3VNTNKWZE7S4XGA","created_at":"2026-07-05T04:03:15.618347+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y3VNTNKW","created_at":"2026-07-05T04:03:15.618347+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2410.22359","citing_title":"Low regularity symplectic schemes for stochastic NLS","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2504.03346","citing_title":"Error estimates of an exponential wave integrator for the nonlinear Schr\\\"odinger equation with singular potential","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03355","citing_title":"Optimal error bounds on the exponential wave integrator for nonlinear Schr\\\"odinger equations with highly singular potential","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03355","citing_title":"Optimal error bounds on the exponential wave integrator for nonlinear Schr\\\"odinger equations with highly singular potential","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N","json":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N.json","graph_json":"https://pith.science/api/pith-number/Y3VNTNKWZE7S4XGAOJODKTMX4N/graph.json","events_json":"https://pith.science/api/pith-number/Y3VNTNKWZE7S4XGAOJODKTMX4N/events.json","paper":"https://pith.science/paper/Y3VNTNKW"},"agent_actions":{"view_html":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N","download_json":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N.json","view_paper":"https://pith.science/paper/Y3VNTNKW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.01171&json=true","fetch_graph":"https://pith.science/api/pith-number/Y3VNTNKWZE7S4XGAOJODKTMX4N/graph.json","fetch_events":"https://pith.science/api/pith-number/Y3VNTNKWZE7S4XGAOJODKTMX4N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N/action/storage_attestation","attest_author":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N/action/author_attestation","sign_citation":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N/action/citation_signature","submit_replication":"https://pith.science/pith/Y3VNTNKWZE7S4XGAOJODKTMX4N/action/replication_record"}},"created_at":"2026-07-05T04:03:15.618347+00:00","updated_at":"2026-07-05T04:03:15.618347+00:00"}