{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:W5AH7JKKHM2GA2AZC67OFXFZZL","short_pith_number":"pith:W5AH7JKK","canonical_record":{"source":{"id":"1908.09542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-26T09:11:55Z","cross_cats_sorted":[],"title_canon_sha256":"3c27ff0b389247e99a39ed4c35c49499efe09bba9603178fb4d582a1b5993948","abstract_canon_sha256":"d81534bfa7b4bca732608d2a0c16bd6d2d197806f710f7fc328ed26c8395aa7e"},"schema_version":"1.0"},"canonical_sha256":"b7407fa54a3b3460681917bee2dcb9cac6ffac68ff220ed57f10d4e3e1e77f56","source":{"kind":"arxiv","id":"1908.09542","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09542","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09542v1","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09542","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"pith_short_12","alias_value":"W5AH7JKKHM2G","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"pith_short_16","alias_value":"W5AH7JKKHM2GA2AZ","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"pith_short_8","alias_value":"W5AH7JKK","created_at":"2026-07-04T23:59:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:W5AH7JKKHM2GA2AZC67OFXFZZL","target":"record","payload":{"canonical_record":{"source":{"id":"1908.09542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-26T09:11:55Z","cross_cats_sorted":[],"title_canon_sha256":"3c27ff0b389247e99a39ed4c35c49499efe09bba9603178fb4d582a1b5993948","abstract_canon_sha256":"d81534bfa7b4bca732608d2a0c16bd6d2d197806f710f7fc328ed26c8395aa7e"},"schema_version":"1.0"},"canonical_sha256":"b7407fa54a3b3460681917bee2dcb9cac6ffac68ff220ed57f10d4e3e1e77f56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:41.338549Z","signature_b64":"WrGJBGejSOXm6W0lV6Avl4cGOybi9z3Q769ORJc50Wl3luWk4Hga1pJ4xFhNKQMh4pnjzGW/lRqrA+n0Eco6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7407fa54a3b3460681917bee2dcb9cac6ffac68ff220ed57f10d4e3e1e77f56","last_reissued_at":"2026-07-04T23:59:41.338130Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:41.338130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.09542","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":"2026-07-04T23:59:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBZvsHsMG1FNxZLTzdRobO0T8VKAqihMmJiX6KsWLC6+Ew+KndhvToCNpu4J9JBYvBZVORGH9t9WtofxHbUKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T09:59:42.897349Z"},"content_sha256":"ee354614f5ce45287348523516d1dc3ae6e7390a1ef4434385c1ccf38daec81f","schema_version":"1.0","event_id":"sha256:ee354614f5ce45287348523516d1dc3ae6e7390a1ef4434385c1ccf38daec81f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:W5AH7JKKHM2GA2AZC67OFXFZZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The optimal symmetric quasi-Banach range of the discrete Hilbert transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"K.S. Tulenov","submitted_at":"2019-08-26T09:11:55Z","abstract_excerpt":"We identify symmetric quasi-Banach range of the discrete Calder\\'{o}n operator and Hilbert transform acting on a symmetric quasi-Banach sequence space. As an application we present an example of optimal range in the case when the domain of those operators is the weak-$\\ell_{1}$ space of sequences."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09542","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/1908.09542/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":"2026-07-04T23:59:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dLJbqyMZBfAV+ARWK2CYyEXxYeC+X4rhN+Qb62S/sRsFtHSwqgMW8lBZ5/eZ+NOZUA4f1Hm/NWhloqWHCRI4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T09:59:42.898145Z"},"content_sha256":"9d3ea775c7cf7bb112815ba22e7f8957355a32b97a3986715c412a909b8c0d9a","schema_version":"1.0","event_id":"sha256:9d3ea775c7cf7bb112815ba22e7f8957355a32b97a3986715c412a909b8c0d9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W5AH7JKKHM2GA2AZC67OFXFZZL/bundle.json","state_url":"https://pith.science/pith/W5AH7JKKHM2GA2AZC67OFXFZZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W5AH7JKKHM2GA2AZC67OFXFZZL/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":"2026-08-16T09:59:42Z","links":{"resolver":"https://pith.science/pith/W5AH7JKKHM2GA2AZC67OFXFZZL","bundle":"https://pith.science/pith/W5AH7JKKHM2GA2AZC67OFXFZZL/bundle.json","state":"https://pith.science/pith/W5AH7JKKHM2GA2AZC67OFXFZZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W5AH7JKKHM2GA2AZC67OFXFZZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:W5AH7JKKHM2GA2AZC67OFXFZZL","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":"d81534bfa7b4bca732608d2a0c16bd6d2d197806f710f7fc328ed26c8395aa7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-26T09:11:55Z","title_canon_sha256":"3c27ff0b389247e99a39ed4c35c49499efe09bba9603178fb4d582a1b5993948"},"schema_version":"1.0","source":{"id":"1908.09542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.09542","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"arxiv_version","alias_value":"1908.09542v1","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09542","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"pith_short_12","alias_value":"W5AH7JKKHM2G","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"pith_short_16","alias_value":"W5AH7JKKHM2GA2AZ","created_at":"2026-07-04T23:59:41Z"},{"alias_kind":"pith_short_8","alias_value":"W5AH7JKK","created_at":"2026-07-04T23:59:41Z"}],"graph_snapshots":[{"event_id":"sha256:9d3ea775c7cf7bb112815ba22e7f8957355a32b97a3986715c412a909b8c0d9a","target":"graph","created_at":"2026-07-04T23:59:41Z","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/1908.09542/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We identify symmetric quasi-Banach range of the discrete Calder\\'{o}n operator and Hilbert transform acting on a symmetric quasi-Banach sequence space. As an application we present an example of optimal range in the case when the domain of those operators is the weak-$\\ell_{1}$ space of sequences.","authors_text":"K.S. Tulenov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-26T09:11:55Z","title":"The optimal symmetric quasi-Banach range of the discrete Hilbert transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09542","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:ee354614f5ce45287348523516d1dc3ae6e7390a1ef4434385c1ccf38daec81f","target":"record","created_at":"2026-07-04T23:59:41Z","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":"d81534bfa7b4bca732608d2a0c16bd6d2d197806f710f7fc328ed26c8395aa7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-26T09:11:55Z","title_canon_sha256":"3c27ff0b389247e99a39ed4c35c49499efe09bba9603178fb4d582a1b5993948"},"schema_version":"1.0","source":{"id":"1908.09542","kind":"arxiv","version":1}},"canonical_sha256":"b7407fa54a3b3460681917bee2dcb9cac6ffac68ff220ed57f10d4e3e1e77f56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7407fa54a3b3460681917bee2dcb9cac6ffac68ff220ed57f10d4e3e1e77f56","first_computed_at":"2026-07-04T23:59:41.338130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:41.338130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WrGJBGejSOXm6W0lV6Avl4cGOybi9z3Q769ORJc50Wl3luWk4Hga1pJ4xFhNKQMh4pnjzGW/lRqrA+n0Eco6DA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:41.338549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.09542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee354614f5ce45287348523516d1dc3ae6e7390a1ef4434385c1ccf38daec81f","sha256:9d3ea775c7cf7bb112815ba22e7f8957355a32b97a3986715c412a909b8c0d9a"],"state_sha256":"82556ce0116cc3cd4a9052d2728160e1fb469d5fb278fededb0bb8d86519d5ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rrHkedbMnPbL5uP8U4GPmC3fYS2ykFUC7/ZzUfFU5ANdnXxgmvX+hxpRzsQ2G8gwrirdBnvIh5ZquS8SRPlCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T09:59:42.906520Z","bundle_sha256":"69a8e05103e7ca4694d13d4e093ba6b9d55c4f57e366ad7b1370e4295a3d9d90"}}