{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4RBN452SPARXJBEBUWSONEVVZE","short_pith_number":"pith:4RBN452S","schema_version":"1.0","canonical_sha256":"e442de77527823748481a5a4e692b5c938c1b3a6279f4cec2195ce2d3512fe90","source":{"kind":"arxiv","id":"1506.01901","version":2},"attestation_state":"computed","paper":{"title":"The $\\infty$-Besov Capacity Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Xiao, Mario Milman","submitted_at":"2015-06-05T13:25:29Z","abstract_excerpt":"A theory of $\\infty$-Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the $\\infty$-Besov semi-norms, we obtain new restriction-extension inequalities and we characterize the point-wise multipliers acting on the $\\infty$-Besov spaces."},"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":"1506.01901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-06-05T13:25:29Z","cross_cats_sorted":[],"title_canon_sha256":"fec7ed213819263bce7f6a73e7c736e3a65dcbdb9494e2fff669c7e5a1222863","abstract_canon_sha256":"d8eff87fee739392397c8e42ae020e9905fe9fac100f58823f615e6d84889c57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:36.112806Z","signature_b64":"tXmhQksOEvPsj2z3LuzOBIuvoycC/fpjE57nwp8kYH+M3vw3kSBfqQF/GAY7SrJ/8ETOlY4pqQefsBZgCWgVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e442de77527823748481a5a4e692b5c938c1b3a6279f4cec2195ce2d3512fe90","last_reissued_at":"2026-05-18T00:43:36.112420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:36.112420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $\\infty$-Besov Capacity Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Xiao, Mario Milman","submitted_at":"2015-06-05T13:25:29Z","abstract_excerpt":"A theory of $\\infty$-Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the $\\infty$-Besov semi-norms, we obtain new restriction-extension inequalities and we characterize the point-wise multipliers acting on the $\\infty$-Besov spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01901","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":""},"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":"1506.01901","created_at":"2026-05-18T00:43:36.112479+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.01901v2","created_at":"2026-05-18T00:43:36.112479+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.01901","created_at":"2026-05-18T00:43:36.112479+00:00"},{"alias_kind":"pith_short_12","alias_value":"4RBN452SPARX","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4RBN452SPARXJBEB","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4RBN452S","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE","json":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE.json","graph_json":"https://pith.science/api/pith-number/4RBN452SPARXJBEBUWSONEVVZE/graph.json","events_json":"https://pith.science/api/pith-number/4RBN452SPARXJBEBUWSONEVVZE/events.json","paper":"https://pith.science/paper/4RBN452S"},"agent_actions":{"view_html":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE","download_json":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE.json","view_paper":"https://pith.science/paper/4RBN452S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.01901&json=true","fetch_graph":"https://pith.science/api/pith-number/4RBN452SPARXJBEBUWSONEVVZE/graph.json","fetch_events":"https://pith.science/api/pith-number/4RBN452SPARXJBEBUWSONEVVZE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE/action/storage_attestation","attest_author":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE/action/author_attestation","sign_citation":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE/action/citation_signature","submit_replication":"https://pith.science/pith/4RBN452SPARXJBEBUWSONEVVZE/action/replication_record"}},"created_at":"2026-05-18T00:43:36.112479+00:00","updated_at":"2026-05-18T00:43:36.112479+00:00"}