{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5TTAFZA7JPTOYHKF6YF64QZEC7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf103be72ef5c50fe25fec303170e92e66c2b6456f5924e48e630609b6e64286","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-26T21:51:32Z","title_canon_sha256":"1b81b42d6737288cc3b7aa9373ece949fe45718f4991b38fcfa383e7c3a6b8db"},"schema_version":"1.0","source":{"id":"2507.20069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.20069","created_at":"2026-07-05T11:44:12Z"},{"alias_kind":"arxiv_version","alias_value":"2507.20069v1","created_at":"2026-07-05T11:44:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20069","created_at":"2026-07-05T11:44:12Z"},{"alias_kind":"pith_short_12","alias_value":"5TTAFZA7JPTO","created_at":"2026-07-05T11:44:12Z"},{"alias_kind":"pith_short_16","alias_value":"5TTAFZA7JPTOYHKF","created_at":"2026-07-05T11:44:12Z"},{"alias_kind":"pith_short_8","alias_value":"5TTAFZA7","created_at":"2026-07-05T11:44:12Z"}],"graph_snapshots":[{"event_id":"sha256:4e6b48e4efd1ef30a314f5fcd2e12bc2dc93ea5d78e5bdbc6234015d0b5ac1b2","target":"graph","created_at":"2026-07-05T11:44:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.20069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the following fractional Trudinger-Moser type inequality with logarithmic convolution potential $$ \\sup_{u\\in W^{\\frac{1}{2},2}_0(I),\\|u\\|_{W_0^{\\frac{1}{2},2}}\\leq1}\\int_{I} \\int_{I} \\log \\frac{1}{|x-y|} G(u(x))G(u(y)) \\, dx \\, dy<+\\infty,$$ where $G(s)\\leq C\\frac{e^{\\pi s^{2}}}{(1 + |s|)^{\\gamma}}~ \\forall s\\in\\mathbb{R}$ with some constant $C>0,\\gamma\\geq1$, the domain $I\\subset\\mathbb{R}$ is a bounded interval. This type of inequality in the entire space $\\mathbb{R}$ is also considered. Moreover, we study the existence of corresponding extremal functions.\n  In addition, by the","authors_text":"Huxiao Luo, Shiying Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-26T21:51:32Z","title":"Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20069","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:49f44ab89f1449bc2fa7a31e9f8482c525bbe339ab9ada8c3d2a422969f0c0b6","target":"record","created_at":"2026-07-05T11:44:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf103be72ef5c50fe25fec303170e92e66c2b6456f5924e48e630609b6e64286","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-26T21:51:32Z","title_canon_sha256":"1b81b42d6737288cc3b7aa9373ece949fe45718f4991b38fcfa383e7c3a6b8db"},"schema_version":"1.0","source":{"id":"2507.20069","kind":"arxiv","version":1}},"canonical_sha256":"ece602e41f4be6ec1d45f60bee432417ee027e55200968f9946099355608be9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ece602e41f4be6ec1d45f60bee432417ee027e55200968f9946099355608be9d","first_computed_at":"2026-07-05T11:44:12.781279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:12.781279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dpQMnIwLSFEaZDZzJYxDJx4Q9xOHkH4/UfxaedbekCCS0qJB+icYAi39nj1V0i2UICOzH/oqtMlhY2gc9cCMBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:12.781744Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.20069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49f44ab89f1449bc2fa7a31e9f8482c525bbe339ab9ada8c3d2a422969f0c0b6","sha256:4e6b48e4efd1ef30a314f5fcd2e12bc2dc93ea5d78e5bdbc6234015d0b5ac1b2"],"state_sha256":"2f44bdb63fd094d0682ed37b840bd0b4a281f0978343d7b803261b954e9ee6c8"}