{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TVKOY6MJVPVHZBU3OPJ757ZPR5","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":"c64aa875e48058c3bc1a0a301f81e0d695977eea3cc3c2e7e241cada87873817","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T16:49:31Z","title_canon_sha256":"ec67c6ef3fca42b8fe895470b29d5caf59d565a867b1147f049c6c5d63685654"},"schema_version":"1.0","source":{"id":"2403.10458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.10458","created_at":"2026-07-05T10:48:15Z"},{"alias_kind":"arxiv_version","alias_value":"2403.10458v2","created_at":"2026-07-05T10:48:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.10458","created_at":"2026-07-05T10:48:15Z"},{"alias_kind":"pith_short_12","alias_value":"TVKOY6MJVPVH","created_at":"2026-07-05T10:48:15Z"},{"alias_kind":"pith_short_16","alias_value":"TVKOY6MJVPVHZBU3","created_at":"2026-07-05T10:48:15Z"},{"alias_kind":"pith_short_8","alias_value":"TVKOY6MJ","created_at":"2026-07-05T10:48:15Z"}],"graph_snapshots":[{"event_id":"sha256:00e4b270a4ae0175c9447e210a00aa5e731c71f27d3943f2d8c9ffb7750efd47","target":"graph","created_at":"2026-07-05T10:48:15Z","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/2403.10458/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads $$ \\int_{\\mathbb{S}^1}\\arctan\\left(\\frac{\\partial_x u}{u}\\right)\\partial_xu \\,dx\\geq \\arctan\\left(\\|u(t)\\|_{\\dot{W}^{1,1}(\\mathbb{S}^1)}\\right)\\|u(t)\\|_{\\dot{W}^{1,1}(\\mathbb{S}^1)}. $$ Then, these inequalities are used in the study of the nonlinear \\emph{arctan}-fast diffusion equation $$ \\partial_t u-\\partial_x\\arctan\\left(\\frac{\\partial_x u}{u}\\right)=0. $$ For this highly nonlinear PDE we establish a number of wel","authors_text":"Alejandro Ortega, Martina Magliocca, Rafael Granero-Belinch\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T16:49:31Z","title":"New functional inequalities with applications to the arctan-fast diffusion equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.10458","kind":"arxiv","version":2},"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":"sha256:4c5fde24a36312df37dde14706fd8427a185baa14b1b5c3338a7319724ac14fc","target":"record","created_at":"2026-07-05T10:48:15Z","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":"c64aa875e48058c3bc1a0a301f81e0d695977eea3cc3c2e7e241cada87873817","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-03-15T16:49:31Z","title_canon_sha256":"ec67c6ef3fca42b8fe895470b29d5caf59d565a867b1147f049c6c5d63685654"},"schema_version":"1.0","source":{"id":"2403.10458","kind":"arxiv","version":2}},"canonical_sha256":"9d54ec7989abea7c869b73d3feff2f8f74097920d3f160a87127925d6a0a5488","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d54ec7989abea7c869b73d3feff2f8f74097920d3f160a87127925d6a0a5488","first_computed_at":"2026-07-05T10:48:15.008601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:48:15.008601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TZwWXjLiaL82JIqn7NK+9FKBrvAiIyMSOm37w8hTJaw57NydaOyVLDq1SiIZyyFIjIl9C4c6JigwejbqAxALDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:48:15.009052Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.10458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c5fde24a36312df37dde14706fd8427a185baa14b1b5c3338a7319724ac14fc","sha256:00e4b270a4ae0175c9447e210a00aa5e731c71f27d3943f2d8c9ffb7750efd47"],"state_sha256":"8409fd5fe7705659591f1d3152637c1bde7faf930c214a4d43ba2635c5b841e5"}