{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2KHYHH23O7AUNJ3GQVDPP5RI3F","short_pith_number":"pith:2KHYHH23","schema_version":"1.0","canonical_sha256":"d28f839f5b77c146a7668546f7f628d97cb8afdbbcb739c7279b7d85b9c2ca54","source":{"kind":"arxiv","id":"1812.04281","version":1},"attestation_state":"computed","paper":{"title":"Detailed proof of classical Gagliardo-Nirenberg interpolation inequality with historical remarks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alberto Fiorenza, Filip Soudsk\\'y, Maria Rosaria Formica, Tom\\'a\\v{s} Roskovec","submitted_at":"2018-12-11T09:16:16Z","abstract_excerpt":"A carefully written Nirenberg's proof of the well known Gagliardo-Nirenberg interpolation inequality for intermediate derivatives in $\\mathbb{R}^n$ seems, surprisingly, to be missing in literature. In our paper we shall first introduce this fundamental result and provide information about it's historical background. Afterwards we present a complete, student-friendly proof. In our proof we use the architecture of Nirenberg's proof, the proof is, however, much more detailed, containing also some differences. The reader can find a short comparison of differences and similarities in the final chap"},"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":"1812.04281","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-12-11T09:16:16Z","cross_cats_sorted":[],"title_canon_sha256":"6bd379e1ff42de8817660534ad87b56bc8a775006fa15d9808fca865b4070146","abstract_canon_sha256":"1af5b99358c40af554a0f181f32963b717214c5699363892e32e4c5c875d28c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:32.745774Z","signature_b64":"c4++zY8ocn/gUyx3cACK6SsI2z/2qlvhnIOxuVb7SA9K0TApaDyHmYqPEsOpZz+DkT4FvGyr1+Y6cvqz4XmADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d28f839f5b77c146a7668546f7f628d97cb8afdbbcb739c7279b7d85b9c2ca54","last_reissued_at":"2026-05-17T23:58:32.745068Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:32.745068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Detailed proof of classical Gagliardo-Nirenberg interpolation inequality with historical remarks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alberto Fiorenza, Filip Soudsk\\'y, Maria Rosaria Formica, Tom\\'a\\v{s} Roskovec","submitted_at":"2018-12-11T09:16:16Z","abstract_excerpt":"A carefully written Nirenberg's proof of the well known Gagliardo-Nirenberg interpolation inequality for intermediate derivatives in $\\mathbb{R}^n$ seems, surprisingly, to be missing in literature. In our paper we shall first introduce this fundamental result and provide information about it's historical background. Afterwards we present a complete, student-friendly proof. In our proof we use the architecture of Nirenberg's proof, the proof is, however, much more detailed, containing also some differences. The reader can find a short comparison of differences and similarities in the final chap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04281","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":""},"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":"1812.04281","created_at":"2026-05-17T23:58:32.745178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.04281v1","created_at":"2026-05-17T23:58:32.745178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04281","created_at":"2026-05-17T23:58:32.745178+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KHYHH23O7AU","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KHYHH23O7AUNJ3G","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KHYHH23","created_at":"2026-05-18T12:32:02.567920+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/2KHYHH23O7AUNJ3GQVDPP5RI3F","json":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F.json","graph_json":"https://pith.science/api/pith-number/2KHYHH23O7AUNJ3GQVDPP5RI3F/graph.json","events_json":"https://pith.science/api/pith-number/2KHYHH23O7AUNJ3GQVDPP5RI3F/events.json","paper":"https://pith.science/paper/2KHYHH23"},"agent_actions":{"view_html":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F","download_json":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F.json","view_paper":"https://pith.science/paper/2KHYHH23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.04281&json=true","fetch_graph":"https://pith.science/api/pith-number/2KHYHH23O7AUNJ3GQVDPP5RI3F/graph.json","fetch_events":"https://pith.science/api/pith-number/2KHYHH23O7AUNJ3GQVDPP5RI3F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F/action/storage_attestation","attest_author":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F/action/author_attestation","sign_citation":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F/action/citation_signature","submit_replication":"https://pith.science/pith/2KHYHH23O7AUNJ3GQVDPP5RI3F/action/replication_record"}},"created_at":"2026-05-17T23:58:32.745178+00:00","updated_at":"2026-05-17T23:58:32.745178+00:00"}