{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ENRNDECC6SVUVUVMQL5SHI6PCN","short_pith_number":"pith:ENRNDECC","schema_version":"1.0","canonical_sha256":"2362d19042f4ab4ad2ac82fb23a3cf13789998a67bf184825a34f3abeaae1953","source":{"kind":"arxiv","id":"2410.10013","version":2},"attestation_state":"computed","paper":{"title":"A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Cannone, Silvia Cingolani","submitted_at":"2024-10-13T21:19:28Z","abstract_excerpt":"In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball or the entire space. We also show that the extremal functions satisfy suitable Euler-Lagrange equations. When the domain is the entire space, such equation can be derived by N-Laplacian Schrodinger equation strongly coupled with a higher order fractional Poisson's equation. The results extends [16] to any dimension N bigger than 2."},"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":"2410.10013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-10-13T21:19:28Z","cross_cats_sorted":[],"title_canon_sha256":"fa375bfdadc4bb94707c036b218af903009f38d5404debe8dbcc9329a4737931","abstract_canon_sha256":"6f40f4bc227973bfb2a80b9bb3217f0587599634ce8b060fbb090cd4aaf8c8d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:04:58.150431Z","signature_b64":"FEb7cgHbgPBpBySCVesq6X/VcDuMDZO14bu5pXMjEYm75LksXrx6dstjxRxwwLYNXuOLTR8M5Lr7FvogDE4PCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2362d19042f4ab4ad2ac82fb23a3cf13789998a67bf184825a34f3abeaae1953","last_reissued_at":"2026-07-05T10:04:58.150036Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:04:58.150036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp threshold for Trudinger-Moser type inequalities with logarithmic kernels in dimension N","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Cannone, Silvia Cingolani","submitted_at":"2024-10-13T21:19:28Z","abstract_excerpt":"In the paper we investigate Trudinger-Moser type inequalities in presence of logarithmic kernels in dimension N. A sharp threshold, depending on N, is detected for the existence of estremal functions or blow-up, where the domain is the ball or the entire space. We also show that the extremal functions satisfy suitable Euler-Lagrange equations. When the domain is the entire space, such equation can be derived by N-Laplacian Schrodinger equation strongly coupled with a higher order fractional Poisson's equation. The results extends [16] to any dimension N bigger than 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.10013","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/2410.10013/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":"2410.10013","created_at":"2026-07-05T10:04:58.150091+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.10013v2","created_at":"2026-07-05T10:04:58.150091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.10013","created_at":"2026-07-05T10:04:58.150091+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENRNDECC6SVU","created_at":"2026-07-05T10:04:58.150091+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENRNDECC6SVUVUVM","created_at":"2026-07-05T10:04:58.150091+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENRNDECC","created_at":"2026-07-05T10:04:58.150091+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.20069","citing_title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN","json":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN.json","graph_json":"https://pith.science/api/pith-number/ENRNDECC6SVUVUVMQL5SHI6PCN/graph.json","events_json":"https://pith.science/api/pith-number/ENRNDECC6SVUVUVMQL5SHI6PCN/events.json","paper":"https://pith.science/paper/ENRNDECC"},"agent_actions":{"view_html":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN","download_json":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN.json","view_paper":"https://pith.science/paper/ENRNDECC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.10013&json=true","fetch_graph":"https://pith.science/api/pith-number/ENRNDECC6SVUVUVMQL5SHI6PCN/graph.json","fetch_events":"https://pith.science/api/pith-number/ENRNDECC6SVUVUVMQL5SHI6PCN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN/action/storage_attestation","attest_author":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN/action/author_attestation","sign_citation":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN/action/citation_signature","submit_replication":"https://pith.science/pith/ENRNDECC6SVUVUVMQL5SHI6PCN/action/replication_record"}},"created_at":"2026-07-05T10:04:58.150091+00:00","updated_at":"2026-07-05T10:04:58.150091+00:00"}