{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:F5EOQVBPXMUQZOBVORY3A3TKAI","short_pith_number":"pith:F5EOQVBP","canonical_record":{"source":{"id":"1908.07754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-21T09:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"1cb6925030ef7b579c467fb8d9ded26f5668129378764f0261e9f9f0e27b60b1","abstract_canon_sha256":"7618d13705c17cb6e45e85a6ee553295f5f1ad1b8f2590aa6b9805680a972eb3"},"schema_version":"1.0"},"canonical_sha256":"2f48e8542fbb290cb8357471b06e6a02299355a3663b85ae307748c885c50644","source":{"kind":"arxiv","id":"1908.07754","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07754","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07754v1","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07754","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"pith_short_12","alias_value":"F5EOQVBPXMUQ","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"pith_short_16","alias_value":"F5EOQVBPXMUQZOBV","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"pith_short_8","alias_value":"F5EOQVBP","created_at":"2026-07-04T23:59:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:F5EOQVBPXMUQZOBVORY3A3TKAI","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-21T09:02:49Z","cross_cats_sorted":[],"title_canon_sha256":"1cb6925030ef7b579c467fb8d9ded26f5668129378764f0261e9f9f0e27b60b1","abstract_canon_sha256":"7618d13705c17cb6e45e85a6ee553295f5f1ad1b8f2590aa6b9805680a972eb3"},"schema_version":"1.0"},"canonical_sha256":"2f48e8542fbb290cb8357471b06e6a02299355a3663b85ae307748c885c50644","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:00.903127Z","signature_b64":"PNZ/ahdVafmqH5FRlVdiS1u1w6bWDMoSjZNhbnv9Gs/+kbVDBMVyUEIi5EOgWoKyke9+X7WpnvCnUV4OCL8TAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f48e8542fbb290cb8357471b06e6a02299355a3663b85ae307748c885c50644","last_reissued_at":"2026-07-04T23:59:00.902738Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:00.902738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07754","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":"2026-07-04T23:59:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f/7UCl3MEjHCU3zFIDGP7Bvk8g+PXGOH+G7F6hrQ10p24eV4nsOATKNoNe9dfBNmAlqPJ5V8LWdyhC+A87CxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:12:30.207051Z"},"content_sha256":"0dacccb0c45d1aa294da039550b6db41144bee16a375b983657c26e1ae7d5198","schema_version":"1.0","event_id":"sha256:0dacccb0c45d1aa294da039550b6db41144bee16a375b983657c26e1ae7d5198"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:F5EOQVBPXMUQZOBVORY3A3TKAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebra of convolution type operators with continuous data on Banach function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Cl\\'audio A. Fernandes, Yuri I. Karlovich","submitted_at":"2019-08-21T09:02:49Z","abstract_excerpt":"We show that if the Hardy-Littlewood maximal operator is bounded on a reflexive Banach function space $X(\\mathbb{R})$ and on its associate space $X'(\\mathbb{R})$, then the space $X(\\mathbb{R})$ has an unconditional wavelet basis. As a consequence of the existence of a Schauder basis in $X(\\mathbb{R})$, we prove that the ideal of compact operators $\\mathcal{K}(X(\\mathbb{R}))$ on the space $X(\\mathbb{R})$ is contained in the Banach algebra generated by all operators of multiplication $aI$ by functions $a\\in C(\\dot{\\mathbb{R}})$, where $\\dot{\\mathbb{R}}=\\mathbb{R}\\cup\\{\\infty\\}$, and by all Fouri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07754","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07754/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:59:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sKji9mbg25kr5iY8J+zCnDJN9bbynEAHEFSreagXaUVmhl5/gNu51oZwYkxcLAOkoQCA97f2rVBYOSXk6uMABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:12:30.207705Z"},"content_sha256":"1c64c8cd023cd42f7b2a1c77f8b86a0847625e50559737fe0f2806a6f70c3228","schema_version":"1.0","event_id":"sha256:1c64c8cd023cd42f7b2a1c77f8b86a0847625e50559737fe0f2806a6f70c3228"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5EOQVBPXMUQZOBVORY3A3TKAI/bundle.json","state_url":"https://pith.science/pith/F5EOQVBPXMUQZOBVORY3A3TKAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5EOQVBPXMUQZOBVORY3A3TKAI/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":"2026-08-16T10:12:30Z","links":{"resolver":"https://pith.science/pith/F5EOQVBPXMUQZOBVORY3A3TKAI","bundle":"https://pith.science/pith/F5EOQVBPXMUQZOBVORY3A3TKAI/bundle.json","state":"https://pith.science/pith/F5EOQVBPXMUQZOBVORY3A3TKAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5EOQVBPXMUQZOBVORY3A3TKAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:F5EOQVBPXMUQZOBVORY3A3TKAI","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":"7618d13705c17cb6e45e85a6ee553295f5f1ad1b8f2590aa6b9805680a972eb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-21T09:02:49Z","title_canon_sha256":"1cb6925030ef7b579c467fb8d9ded26f5668129378764f0261e9f9f0e27b60b1"},"schema_version":"1.0","source":{"id":"1908.07754","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07754","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07754v1","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07754","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"pith_short_12","alias_value":"F5EOQVBPXMUQ","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"pith_short_16","alias_value":"F5EOQVBPXMUQZOBV","created_at":"2026-07-04T23:59:00Z"},{"alias_kind":"pith_short_8","alias_value":"F5EOQVBP","created_at":"2026-07-04T23:59:00Z"}],"graph_snapshots":[{"event_id":"sha256:1c64c8cd023cd42f7b2a1c77f8b86a0847625e50559737fe0f2806a6f70c3228","target":"graph","created_at":"2026-07-04T23:59:00Z","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/1908.07754/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that if the Hardy-Littlewood maximal operator is bounded on a reflexive Banach function space $X(\\mathbb{R})$ and on its associate space $X'(\\mathbb{R})$, then the space $X(\\mathbb{R})$ has an unconditional wavelet basis. As a consequence of the existence of a Schauder basis in $X(\\mathbb{R})$, we prove that the ideal of compact operators $\\mathcal{K}(X(\\mathbb{R}))$ on the space $X(\\mathbb{R})$ is contained in the Banach algebra generated by all operators of multiplication $aI$ by functions $a\\in C(\\dot{\\mathbb{R}})$, where $\\dot{\\mathbb{R}}=\\mathbb{R}\\cup\\{\\infty\\}$, and by all Fouri","authors_text":"Alexei Yu. Karlovich, Cl\\'audio A. Fernandes, Yuri I. Karlovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-21T09:02:49Z","title":"Algebra of convolution type operators with continuous data on Banach function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07754","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":"sha256:0dacccb0c45d1aa294da039550b6db41144bee16a375b983657c26e1ae7d5198","target":"record","created_at":"2026-07-04T23:59:00Z","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":"7618d13705c17cb6e45e85a6ee553295f5f1ad1b8f2590aa6b9805680a972eb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-21T09:02:49Z","title_canon_sha256":"1cb6925030ef7b579c467fb8d9ded26f5668129378764f0261e9f9f0e27b60b1"},"schema_version":"1.0","source":{"id":"1908.07754","kind":"arxiv","version":1}},"canonical_sha256":"2f48e8542fbb290cb8357471b06e6a02299355a3663b85ae307748c885c50644","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f48e8542fbb290cb8357471b06e6a02299355a3663b85ae307748c885c50644","first_computed_at":"2026-07-04T23:59:00.902738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:00.902738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PNZ/ahdVafmqH5FRlVdiS1u1w6bWDMoSjZNhbnv9Gs/+kbVDBMVyUEIi5EOgWoKyke9+X7WpnvCnUV4OCL8TAw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:00.903127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07754","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dacccb0c45d1aa294da039550b6db41144bee16a375b983657c26e1ae7d5198","sha256:1c64c8cd023cd42f7b2a1c77f8b86a0847625e50559737fe0f2806a6f70c3228"],"state_sha256":"50f444d4da782c7d03f48570078c8426b5bf776faafec4a3d850188cd7c46552"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ph7QwhixAP2SykRvHS9hC1MN8DRUCh25cPxpMXjgUiVUvTXTi4DM4QMm85QrtuKQHkmO8Y44AokH8ET75mdVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:12:30.211687Z","bundle_sha256":"9e248b5056752910dbfeb045be903c7450d63bc2351642414bc502a448708854"}}