{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CJOZEORICLJR7NRVLDSV5AJFLM","short_pith_number":"pith:CJOZEORI","canonical_record":{"source":{"id":"1211.3386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-14T19:13:24Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5e54c933540d205f121e62a6963ddbfbc0fec6c01fad455ae83c267a672f42dc","abstract_canon_sha256":"4a6ff57b28e950cc364536539af37c23b8d19f5a750eb9cbff8705f24f105478"},"schema_version":"1.0"},"canonical_sha256":"125d923a2812d31fb63558e55e81255b0d3d36c6e1902433d152bd745573b4bd","source":{"kind":"arxiv","id":"1211.3386","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3386","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3386v2","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3386","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"CJOZEORICLJR","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CJOZEORICLJR7NRV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CJOZEORI","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CJOZEORICLJR7NRVLDSV5AJFLM","target":"record","payload":{"canonical_record":{"source":{"id":"1211.3386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-14T19:13:24Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5e54c933540d205f121e62a6963ddbfbc0fec6c01fad455ae83c267a672f42dc","abstract_canon_sha256":"4a6ff57b28e950cc364536539af37c23b8d19f5a750eb9cbff8705f24f105478"},"schema_version":"1.0"},"canonical_sha256":"125d923a2812d31fb63558e55e81255b0d3d36c6e1902433d152bd745573b4bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:11.122857Z","signature_b64":"CWI6V2QqfcVaQO9qb3GeuhehYumKTOVAU3Vbk01TgGngpYTTRqW9pgCjoIEYamrpedrIu9wnDobPDDmX4VkECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"125d923a2812d31fb63558e55e81255b0d3d36c6e1902433d152bd745573b4bd","last_reissued_at":"2026-05-18T03:07:11.122281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:11.122281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.3386","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gldHfQ1fv+IVZvy5ox1RlS0NkZsm9gxQxszamfNIpzPsL/WA1vKbJ8twzB0JRidwGAv2kZ9ZHRy3y6Y47N3hDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:16:30.051864Z"},"content_sha256":"d36c1e263db9f6d624736fc85aeff33725a93c2b8158fc30c088490cafd4336c","schema_version":"1.0","event_id":"sha256:d36c1e263db9f6d624736fc85aeff33725a93c2b8158fc30c088490cafd4336c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CJOZEORICLJR7NRVLDSV5AJFLM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of the restricted type spaces R(X)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Javier Soria, Pedro Tradacete","submitted_at":"2012-11-14T19:13:24Z","abstract_excerpt":"We study functorial properties of the spaces $R(X)$, introduced in [Studia Math. 197 (2010), 69-79] as a central tool in the analysis of the Hardy operator minus the identity on decreasing functions. In particular, we provide conditions on a minimal Lorentz space $\\Lambda_{\\varphi}$ so that the equation $R(X)=\\Lambda_{\\varphi}$ has a solution within the category of rearrangement invariant (r.i.) spaces. Moreover, we show that if $R(X)=\\Lambda_{\\varphi}$, then we can always take $X$ to be the minimal r.i. Banach range space for the Hardy operator defined in $\\Lambda_{\\varphi}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3386","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ZxonDzoFnYc6qngURc1/jshKm2CyuSXxWneB5Df8rwESVjwxcO4KlqtQbKeHYR/oh22JuSRfBt6i1GbCWK2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:16:30.052527Z"},"content_sha256":"162eff5360b0c13857dedf02562132bba95d52c5d6472f49e70fe5e4981b22bd","schema_version":"1.0","event_id":"sha256:162eff5360b0c13857dedf02562132bba95d52c5d6472f49e70fe5e4981b22bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJOZEORICLJR7NRVLDSV5AJFLM/bundle.json","state_url":"https://pith.science/pith/CJOZEORICLJR7NRVLDSV5AJFLM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJOZEORICLJR7NRVLDSV5AJFLM/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":"2026-05-25T21:16:30Z","links":{"resolver":"https://pith.science/pith/CJOZEORICLJR7NRVLDSV5AJFLM","bundle":"https://pith.science/pith/CJOZEORICLJR7NRVLDSV5AJFLM/bundle.json","state":"https://pith.science/pith/CJOZEORICLJR7NRVLDSV5AJFLM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJOZEORICLJR7NRVLDSV5AJFLM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CJOZEORICLJR7NRVLDSV5AJFLM","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":"4a6ff57b28e950cc364536539af37c23b8d19f5a750eb9cbff8705f24f105478","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-14T19:13:24Z","title_canon_sha256":"5e54c933540d205f121e62a6963ddbfbc0fec6c01fad455ae83c267a672f42dc"},"schema_version":"1.0","source":{"id":"1211.3386","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3386","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3386v2","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3386","created_at":"2026-05-18T03:07:11Z"},{"alias_kind":"pith_short_12","alias_value":"CJOZEORICLJR","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CJOZEORICLJR7NRV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CJOZEORI","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:162eff5360b0c13857dedf02562132bba95d52c5d6472f49e70fe5e4981b22bd","target":"graph","created_at":"2026-05-18T03:07:11Z","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 functorial properties of the spaces $R(X)$, introduced in [Studia Math. 197 (2010), 69-79] as a central tool in the analysis of the Hardy operator minus the identity on decreasing functions. In particular, we provide conditions on a minimal Lorentz space $\\Lambda_{\\varphi}$ so that the equation $R(X)=\\Lambda_{\\varphi}$ has a solution within the category of rearrangement invariant (r.i.) spaces. Moreover, we show that if $R(X)=\\Lambda_{\\varphi}$, then we can always take $X$ to be the minimal r.i. Banach range space for the Hardy operator defined in $\\Lambda_{\\varphi}$.","authors_text":"Javier Soria, Pedro Tradacete","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-14T19:13:24Z","title":"Characterization of the restricted type spaces R(X)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3386","kind":"arxiv","version":2},"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:d36c1e263db9f6d624736fc85aeff33725a93c2b8158fc30c088490cafd4336c","target":"record","created_at":"2026-05-18T03:07:11Z","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":"4a6ff57b28e950cc364536539af37c23b8d19f5a750eb9cbff8705f24f105478","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-14T19:13:24Z","title_canon_sha256":"5e54c933540d205f121e62a6963ddbfbc0fec6c01fad455ae83c267a672f42dc"},"schema_version":"1.0","source":{"id":"1211.3386","kind":"arxiv","version":2}},"canonical_sha256":"125d923a2812d31fb63558e55e81255b0d3d36c6e1902433d152bd745573b4bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"125d923a2812d31fb63558e55e81255b0d3d36c6e1902433d152bd745573b4bd","first_computed_at":"2026-05-18T03:07:11.122281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:11.122281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CWI6V2QqfcVaQO9qb3GeuhehYumKTOVAU3Vbk01TgGngpYTTRqW9pgCjoIEYamrpedrIu9wnDobPDDmX4VkECw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:11.122857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3386","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d36c1e263db9f6d624736fc85aeff33725a93c2b8158fc30c088490cafd4336c","sha256:162eff5360b0c13857dedf02562132bba95d52c5d6472f49e70fe5e4981b22bd"],"state_sha256":"c551aa15efa3cc4c682c46a4809d094eabcdfd21c5c226f31c6481fe0b092e22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8sfYL7Xnf3xY0kiTTfkdQdMyc2DhS+6iBh+kcbmuD4mdXJei63m0CEIHhf2e6CzIrmubFgErAbEXfCMHenHdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:16:30.056304Z","bundle_sha256":"bbfe31ecc12c7096b9f6baa04ae1e439e5a3021f15f884f6dbde5d7f713fdc8f"}}