{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3YPEE4AKJDPUFJLNTWXEFKZLHS","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":"8e33d55b3181e93aa0f64861b69610812787e6ec4d824eda7efed7c0ffb6157b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-19T15:55:47Z","title_canon_sha256":"cb973153ab17e0ced05bd8bd2896c7017b65969005838fbd4c4439ab0d834db6"},"schema_version":"1.0","source":{"id":"1905.07759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07759","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07759v1","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07759","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"3YPEE4AKJDPU","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"3YPEE4AKJDPUFJLN","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"3YPEE4AK","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:51c032f6867bf398653b69a13a4a0e67b05e7d27ba99b7f39bc2bb5223bdd088","target":"graph","created_at":"2026-05-17T23:45:48Z","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"},"paper":{"abstract_excerpt":"In this paper, we consider a maximizing problem associated with the Sobolev type embedding on the space of bounded variation. We show that, although the maximizing problem suffers from both of the non-compactness of vanishing and concentrating phenomena, there exists a maximizer for some range of the exponents. Furthermore, we show that any maximizer must be given by a characteristic function on a ball.","authors_text":"Hidemitsu Wadade, Michinori Ishiwata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-19T15:55:47Z","title":"On an effect of inhomogeneous constraints for a maximizing problem of the Sobolev embedding associated with the space of bounded variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07759","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:b7172fe998f842e59691bb0795c749c19b2a042ff6dc8ba88342ef659022883f","target":"record","created_at":"2026-05-17T23:45:48Z","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":"8e33d55b3181e93aa0f64861b69610812787e6ec4d824eda7efed7c0ffb6157b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-19T15:55:47Z","title_canon_sha256":"cb973153ab17e0ced05bd8bd2896c7017b65969005838fbd4c4439ab0d834db6"},"schema_version":"1.0","source":{"id":"1905.07759","kind":"arxiv","version":1}},"canonical_sha256":"de1e42700a48df42a56d9dae42ab2b3ca0839caa3cc0a3e6327c0fef3383d622","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de1e42700a48df42a56d9dae42ab2b3ca0839caa3cc0a3e6327c0fef3383d622","first_computed_at":"2026-05-17T23:45:48.565024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:48.565024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+D7BmA/gpVHN9yP7whT+9XnUF86yW+0xNhykKlf2QlC2mxkpkWZI1mp3qN1tq559OUz/tqb3iaJY8ROACFDwAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:48.565565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7172fe998f842e59691bb0795c749c19b2a042ff6dc8ba88342ef659022883f","sha256:51c032f6867bf398653b69a13a4a0e67b05e7d27ba99b7f39bc2bb5223bdd088"],"state_sha256":"fa9d1924ad14eef22750af49d78c232929bdd4bf841a7c70b470403d21247945"}