{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FIYOC7FT46RX3NIBZHM4OFIGU2","short_pith_number":"pith:FIYOC7FT","canonical_record":{"source":{"id":"1311.0155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-01T12:01:28Z","cross_cats_sorted":[],"title_canon_sha256":"21617de63f19eb571337033581eb58d872f22fc6bb2a423baf9a54c019d16b35","abstract_canon_sha256":"bb916a3837055d3df57a2bd494836fe2c6f54a983fffb9e4caeba307b60ed76a"},"schema_version":"1.0"},"canonical_sha256":"2a30e17cb3e7a37db501c9d9c71506a68719e0d3e48d4ff605501b1349d8e713","source":{"kind":"arxiv","id":"1311.0155","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0155","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0155v1","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0155","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"FIYOC7FT46RX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FIYOC7FT46RX3NIB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FIYOC7FT","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FIYOC7FT46RX3NIBZHM4OFIGU2","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-01T12:01:28Z","cross_cats_sorted":[],"title_canon_sha256":"21617de63f19eb571337033581eb58d872f22fc6bb2a423baf9a54c019d16b35","abstract_canon_sha256":"bb916a3837055d3df57a2bd494836fe2c6f54a983fffb9e4caeba307b60ed76a"},"schema_version":"1.0"},"canonical_sha256":"2a30e17cb3e7a37db501c9d9c71506a68719e0d3e48d4ff605501b1349d8e713","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:15.409908Z","signature_b64":"OQOHYyUalm96akNPMwTpneOT7dMqr4jCilpgwYAXz3qQy7WfyaPxf4MoFd6NOigieemOdnZE/kIGsHBg5XYBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a30e17cb3e7a37db501c9d9c71506a68719e0d3e48d4ff605501b1349d8e713","last_reissued_at":"2026-05-18T03:08:15.409500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:15.409500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0155","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zO4zYZwfQ/gNIjK722k9tHzbhDvH/aDdxRDM9jYy1xmYIXBj5hXPAvBROz/ol7NqmzSykP/lEYgAaenvZKXsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:45:19.175057Z"},"content_sha256":"680bc318e16654e3d711d699aa1124ba461478e95527f74d8b21939dfeda5045","schema_version":"1.0","event_id":"sha256:680bc318e16654e3d711d699aa1124ba461478e95527f74d8b21939dfeda5045"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FIYOC7FT46RX3NIBZHM4OFIGU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compactness of higher-order Sobolev embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lenka Slav\\'ikov\\'a","submitted_at":"2013-11-01T12:01:28Z","abstract_excerpt":"We study higher-order compact Sobolev embeddings on a domain $\\Omega \\subseteq \\mathbb R^n$ endowed with a probability measure $\\nu$ and satisfying certain isoperimetric inequality. Given $m\\in \\mathbb N$, we present a condition on a pair of rearrangement-invariant spaces $X(\\Omega,\\nu)$ and $Y(\\Omega,\\nu)$ which suffices to guarantee a compact embedding of the Sobolev space $V^mX(\\Omega,\\nu)$ into $Y(\\Omega,\\nu)$. The condition is given in terms of compactness of certain one-dimensional operator depending on the isoperimetric function of $(\\Omega,\\nu)$. We then apply this result to the charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0155","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vAmIFGMNqe78zmRYMjiX9cUKZBElmx1vf1J1D/AOvuExmixDeeDvzBRcroIUf1dp/NdtyofE4EqEbCqXXKn+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:45:19.175842Z"},"content_sha256":"28ffcf736615b139136391d367479fbd430b16186b9e2660b7c4dcd2c005bf2c","schema_version":"1.0","event_id":"sha256:28ffcf736615b139136391d367479fbd430b16186b9e2660b7c4dcd2c005bf2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FIYOC7FT46RX3NIBZHM4OFIGU2/bundle.json","state_url":"https://pith.science/pith/FIYOC7FT46RX3NIBZHM4OFIGU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FIYOC7FT46RX3NIBZHM4OFIGU2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T09:45:19Z","links":{"resolver":"https://pith.science/pith/FIYOC7FT46RX3NIBZHM4OFIGU2","bundle":"https://pith.science/pith/FIYOC7FT46RX3NIBZHM4OFIGU2/bundle.json","state":"https://pith.science/pith/FIYOC7FT46RX3NIBZHM4OFIGU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FIYOC7FT46RX3NIBZHM4OFIGU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FIYOC7FT46RX3NIBZHM4OFIGU2","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":"bb916a3837055d3df57a2bd494836fe2c6f54a983fffb9e4caeba307b60ed76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-01T12:01:28Z","title_canon_sha256":"21617de63f19eb571337033581eb58d872f22fc6bb2a423baf9a54c019d16b35"},"schema_version":"1.0","source":{"id":"1311.0155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0155","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0155v1","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0155","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"FIYOC7FT46RX","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FIYOC7FT46RX3NIB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FIYOC7FT","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:28ffcf736615b139136391d367479fbd430b16186b9e2660b7c4dcd2c005bf2c","target":"graph","created_at":"2026-05-18T03:08:15Z","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"},"paper":{"abstract_excerpt":"We study higher-order compact Sobolev embeddings on a domain $\\Omega \\subseteq \\mathbb R^n$ endowed with a probability measure $\\nu$ and satisfying certain isoperimetric inequality. Given $m\\in \\mathbb N$, we present a condition on a pair of rearrangement-invariant spaces $X(\\Omega,\\nu)$ and $Y(\\Omega,\\nu)$ which suffices to guarantee a compact embedding of the Sobolev space $V^mX(\\Omega,\\nu)$ into $Y(\\Omega,\\nu)$. The condition is given in terms of compactness of certain one-dimensional operator depending on the isoperimetric function of $(\\Omega,\\nu)$. We then apply this result to the charac","authors_text":"Lenka Slav\\'ikov\\'a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-01T12:01:28Z","title":"Compactness of higher-order Sobolev embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0155","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":"sha256:680bc318e16654e3d711d699aa1124ba461478e95527f74d8b21939dfeda5045","target":"record","created_at":"2026-05-18T03:08:15Z","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":"bb916a3837055d3df57a2bd494836fe2c6f54a983fffb9e4caeba307b60ed76a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-11-01T12:01:28Z","title_canon_sha256":"21617de63f19eb571337033581eb58d872f22fc6bb2a423baf9a54c019d16b35"},"schema_version":"1.0","source":{"id":"1311.0155","kind":"arxiv","version":1}},"canonical_sha256":"2a30e17cb3e7a37db501c9d9c71506a68719e0d3e48d4ff605501b1349d8e713","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a30e17cb3e7a37db501c9d9c71506a68719e0d3e48d4ff605501b1349d8e713","first_computed_at":"2026-05-18T03:08:15.409500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:15.409500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OQOHYyUalm96akNPMwTpneOT7dMqr4jCilpgwYAXz3qQy7WfyaPxf4MoFd6NOigieemOdnZE/kIGsHBg5XYBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:15.409908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:680bc318e16654e3d711d699aa1124ba461478e95527f74d8b21939dfeda5045","sha256:28ffcf736615b139136391d367479fbd430b16186b9e2660b7c4dcd2c005bf2c"],"state_sha256":"fa968871576fdd169739a642d9eae0ba38362e0d2fef9ef01c965d0750a4010e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J5F73ekYTzvQiFxdnY4IpC5/Q15ShtVOqHoAOxmE8LUasxR+yElvTKZ7T32PVKDU+7NF0Qf7pojjXBuwqSCwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:45:19.179616Z","bundle_sha256":"fad7cc1bd1237f1823a831aeacea6d8950363e161a514cde890db47d754eeae4"}}