{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XUXDD2LT4EV2X3AKTOS4TVGTIQ","short_pith_number":"pith:XUXDD2LT","schema_version":"1.0","canonical_sha256":"bd2e31e973e12babec0a9ba5c9d4d3443973cf87f941db56648c91e8a38a2b70","source":{"kind":"arxiv","id":"2506.02747","version":1},"attestation_state":"computed","paper":{"title":"A priori error estimates for the $\\theta$-method for the flow of nonsmooth velocity fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Gennaro Ciampa, Gianluca Crippa, Raffaele D'Ambrosio, Stefano Spirito, Tommaso Cortopassi","submitted_at":"2025-06-03T11:11:01Z","abstract_excerpt":"Velocity fields with low regularity (below the Lipschitz threshold) naturally arise in many models from mathematical physics, such as the inhomogeneous incompressible Navier-Stokes equations, and play a fundamental role in the analysis of nonlinear PDEs. The DiPerna-Lions theory ensures existence and uniqueness of the flow associated with a divergence-free velocity field with Sobolev regularity. In this paper, we establish a priori error estimates showing a logarithmic rate of convergence of numerical solutions, constructed via the $\\theta$-method, towards the exact (analytic) flow for a veloc"},"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":"2506.02747","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-03T11:11:01Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"7f5f9c805200f0d68cf8b89ed85740761f366e3613057a58f74e0550bef5d44f","abstract_canon_sha256":"b81861b1b5d9a1120bd993192b18f33ed17c62aa16c7b6afeb1a85a715582882"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:03.113461Z","signature_b64":"xPdVVxb2a7Bwl764gJ1hiVDFLWNT2cGGBFnY6CV+0uI8NcXrojVnAnfMbEzeqibF+a9ZiUmuJusD8gk9MbHMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd2e31e973e12babec0a9ba5c9d4d3443973cf87f941db56648c91e8a38a2b70","last_reissued_at":"2026-07-02T01:18:03.113007Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:03.113007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A priori error estimates for the $\\theta$-method for the flow of nonsmooth velocity fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Gennaro Ciampa, Gianluca Crippa, Raffaele D'Ambrosio, Stefano Spirito, Tommaso Cortopassi","submitted_at":"2025-06-03T11:11:01Z","abstract_excerpt":"Velocity fields with low regularity (below the Lipschitz threshold) naturally arise in many models from mathematical physics, such as the inhomogeneous incompressible Navier-Stokes equations, and play a fundamental role in the analysis of nonlinear PDEs. The DiPerna-Lions theory ensures existence and uniqueness of the flow associated with a divergence-free velocity field with Sobolev regularity. In this paper, we establish a priori error estimates showing a logarithmic rate of convergence of numerical solutions, constructed via the $\\theta$-method, towards the exact (analytic) flow for a veloc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02747","kind":"arxiv","version":1},"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/2506.02747/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":"2506.02747","created_at":"2026-07-02T01:18:03.113077+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.02747v1","created_at":"2026-07-02T01:18:03.113077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02747","created_at":"2026-07-02T01:18:03.113077+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUXDD2LT4EV2","created_at":"2026-07-02T01:18:03.113077+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUXDD2LT4EV2X3AK","created_at":"2026-07-02T01:18:03.113077+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUXDD2LT","created_at":"2026-07-02T01:18:03.113077+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/XUXDD2LT4EV2X3AKTOS4TVGTIQ","json":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ.json","graph_json":"https://pith.science/api/pith-number/XUXDD2LT4EV2X3AKTOS4TVGTIQ/graph.json","events_json":"https://pith.science/api/pith-number/XUXDD2LT4EV2X3AKTOS4TVGTIQ/events.json","paper":"https://pith.science/paper/XUXDD2LT"},"agent_actions":{"view_html":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ","download_json":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ.json","view_paper":"https://pith.science/paper/XUXDD2LT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.02747&json=true","fetch_graph":"https://pith.science/api/pith-number/XUXDD2LT4EV2X3AKTOS4TVGTIQ/graph.json","fetch_events":"https://pith.science/api/pith-number/XUXDD2LT4EV2X3AKTOS4TVGTIQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ/action/storage_attestation","attest_author":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ/action/author_attestation","sign_citation":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ/action/citation_signature","submit_replication":"https://pith.science/pith/XUXDD2LT4EV2X3AKTOS4TVGTIQ/action/replication_record"}},"created_at":"2026-07-02T01:18:03.113077+00:00","updated_at":"2026-07-02T01:18:03.113077+00:00"}