{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:YDBUQNFBBCHAZZZDDBMBNH7NHU","short_pith_number":"pith:YDBUQNFB","schema_version":"1.0","canonical_sha256":"c0c34834a1088e0ce7231858169fed3d15e4357e2acba50dad13a557fc622166","source":{"kind":"arxiv","id":"2506.14258","version":1},"attestation_state":"computed","paper":{"title":"Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eurica Henriques, Igor I. Skrypnik, Mariia O. Savchenko, Simone Ciani","submitted_at":"2025-06-17T07:19:05Z","abstract_excerpt":"We define a suitable class $\\mathcal{PDG}$ of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-type and fully anisotropic operators. Yet we prove that members of $\\mathcal{PDG}$ are locally bounded, under critical, sub-critical and limit growth conditions typical of singular parabolic operators, with quantitative a priori estimates that follow the lines of the pioneering work of Ladyzhenskaya, Solonnikov and Uraltseva \\cite{LadSolUra}. These local bounds are new in the sub-critical cases, even for the classic "},"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":"2506.14258","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-17T07:19:05Z","cross_cats_sorted":[],"title_canon_sha256":"6f9a1e1403d76eaae32f8c296ab806a6eb31ec2b606fb66e888cbb59063398b6","abstract_canon_sha256":"df4327d380609d2c64f1d9b53e24bfad9726f5dd2420ccc00b2ece154db37c59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:52.016994Z","signature_b64":"dnu7vFcQ0d9pOKbDGWTdAVj/6KW0Bm8dNXgGnbIS8GC/VfSGrvOZQJqET2K8lHdV72/Bn0PL81/n2c4qmeReDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0c34834a1088e0ce7231858169fed3d15e4357e2acba50dad13a557fc622166","last_reissued_at":"2026-07-05T11:22:52.016528Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:52.016528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parabolic De Giorgi classes with doubly nonlinear, nonstandard growth: local boundedness under exact integrability assumptions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eurica Henriques, Igor I. Skrypnik, Mariia O. Savchenko, Simone Ciani","submitted_at":"2025-06-17T07:19:05Z","abstract_excerpt":"We define a suitable class $\\mathcal{PDG}$ of functions bearing unbalanced energy estimates, that are embodied by local weak subsolutions to doubly nonlinear, double-phase, Orlicz-type and fully anisotropic operators. Yet we prove that members of $\\mathcal{PDG}$ are locally bounded, under critical, sub-critical and limit growth conditions typical of singular parabolic operators, with quantitative a priori estimates that follow the lines of the pioneering work of Ladyzhenskaya, Solonnikov and Uraltseva \\cite{LadSolUra}. These local bounds are new in the sub-critical cases, even for the classic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14258","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/2506.14258/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":"2506.14258","created_at":"2026-07-05T11:22:52.016595+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.14258v1","created_at":"2026-07-05T11:22:52.016595+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14258","created_at":"2026-07-05T11:22:52.016595+00:00"},{"alias_kind":"pith_short_12","alias_value":"YDBUQNFBBCHA","created_at":"2026-07-05T11:22:52.016595+00:00"},{"alias_kind":"pith_short_16","alias_value":"YDBUQNFBBCHAZZZD","created_at":"2026-07-05T11:22:52.016595+00:00"},{"alias_kind":"pith_short_8","alias_value":"YDBUQNFB","created_at":"2026-07-05T11:22:52.016595+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/YDBUQNFBBCHAZZZDDBMBNH7NHU","json":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU.json","graph_json":"https://pith.science/api/pith-number/YDBUQNFBBCHAZZZDDBMBNH7NHU/graph.json","events_json":"https://pith.science/api/pith-number/YDBUQNFBBCHAZZZDDBMBNH7NHU/events.json","paper":"https://pith.science/paper/YDBUQNFB"},"agent_actions":{"view_html":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU","download_json":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU.json","view_paper":"https://pith.science/paper/YDBUQNFB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.14258&json=true","fetch_graph":"https://pith.science/api/pith-number/YDBUQNFBBCHAZZZDDBMBNH7NHU/graph.json","fetch_events":"https://pith.science/api/pith-number/YDBUQNFBBCHAZZZDDBMBNH7NHU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU/action/storage_attestation","attest_author":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU/action/author_attestation","sign_citation":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU/action/citation_signature","submit_replication":"https://pith.science/pith/YDBUQNFBBCHAZZZDDBMBNH7NHU/action/replication_record"}},"created_at":"2026-07-05T11:22:52.016595+00:00","updated_at":"2026-07-05T11:22:52.016595+00:00"}