{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GTWFMGMBKP3C2Z4XQCYKOISPZQ","short_pith_number":"pith:GTWFMGMB","canonical_record":{"source":{"id":"1202.2226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-10T10:06:16Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5b6db7bb4e111af61c17d54f69e940664ab60a488fbe17bb27d7cfac7e8dbc76","abstract_canon_sha256":"c0efb8621d4f2fcd36419fd1cc7e85f84a925db5b31e16ee95e7bdec7baed7f4"},"schema_version":"1.0"},"canonical_sha256":"34ec56198153f62d679780b0a7224fcc347277637a3c3811e242a4ccaa1264a6","source":{"kind":"arxiv","id":"1202.2226","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2226","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2226v1","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2226","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"GTWFMGMBKP3C","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GTWFMGMBKP3C2Z4X","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GTWFMGMB","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GTWFMGMBKP3C2Z4XQCYKOISPZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1202.2226","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-10T10:06:16Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5b6db7bb4e111af61c17d54f69e940664ab60a488fbe17bb27d7cfac7e8dbc76","abstract_canon_sha256":"c0efb8621d4f2fcd36419fd1cc7e85f84a925db5b31e16ee95e7bdec7baed7f4"},"schema_version":"1.0"},"canonical_sha256":"34ec56198153f62d679780b0a7224fcc347277637a3c3811e242a4ccaa1264a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:36.877938Z","signature_b64":"9+PHoLUQ4TaPvPw3GDBk4PhMkVkM8YTjvvb47Xfvsr+1heFZm1O5uODHpOSWNdkRVu+8GNux+gaawiJKjGVBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34ec56198153f62d679780b0a7224fcc347277637a3c3811e242a4ccaa1264a6","last_reissued_at":"2026-05-18T04:02:36.877453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:36.877453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.2226","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":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"te1+INFfpyht+oqPSa27yxyHuQayPK9TIHDJkvO3HETNiZ4ddlU3eA1WGsZiTkKZzH7iHFRMSolxQDlla0aTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:32:34.453008Z"},"content_sha256":"c915da9290ec27b84ae627c8d5dd632ab7d88fe6cba8bf7c27370a1a54e953c1","schema_version":"1.0","event_id":"sha256:c915da9290ec27b84ae627c8d5dd632ab7d88fe6cba8bf7c27370a1a54e953c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GTWFMGMBKP3C2Z4XQCYKOISPZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Alexei Yu. Karlovich, Ilya M. Spitkovsky","submitted_at":"2012-02-10T10:06:16Z","abstract_excerpt":"Let $p:\\R\\to(1,\\infty)$ be a globally log-H\\\"older continuous variable exponent and $w:\\R\\to[0,\\infty]$ be a weight. We prove that the Cauchy singular integral operator $S$ is bounded on the weighted variable Lebesgue space $L^{p(\\cdot)}(\\R,w)=\\{f:fw\\in L^{p(\\cdot)}(\\R)\\}$ if and only if the weight $w$ satisfies \\[ \\sup_{-\\infty<a<b<\\infty} \\frac{1}{b-a}\\|w\\chi_{(a,b)}\\|_{p(\\cdot)}\\|w^{-1}\\chi_{(a,b)}\\|_{p'(\\cdot)}<\\infty \\quad (1/p(x)+1/p'(x)=1). \\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2226","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":"2026-05-18T04:02:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cv27LV0Q5K+t6shMCWgvxyo0Dc0w6Xll42U/s+E3WytWRpCm0uvwp6q1jF2LitA/N2p0QMiQWpbXB/5YanQ1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:32:34.453351Z"},"content_sha256":"0f4165c24bf44f8ee549ab2aa28e6280cb73592dce12fe912ad446c9bc4b17d9","schema_version":"1.0","event_id":"sha256:0f4165c24bf44f8ee549ab2aa28e6280cb73592dce12fe912ad446c9bc4b17d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTWFMGMBKP3C2Z4XQCYKOISPZQ/bundle.json","state_url":"https://pith.science/pith/GTWFMGMBKP3C2Z4XQCYKOISPZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTWFMGMBKP3C2Z4XQCYKOISPZQ/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":"2026-06-20T06:32:34Z","links":{"resolver":"https://pith.science/pith/GTWFMGMBKP3C2Z4XQCYKOISPZQ","bundle":"https://pith.science/pith/GTWFMGMBKP3C2Z4XQCYKOISPZQ/bundle.json","state":"https://pith.science/pith/GTWFMGMBKP3C2Z4XQCYKOISPZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTWFMGMBKP3C2Z4XQCYKOISPZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GTWFMGMBKP3C2Z4XQCYKOISPZQ","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":"c0efb8621d4f2fcd36419fd1cc7e85f84a925db5b31e16ee95e7bdec7baed7f4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-10T10:06:16Z","title_canon_sha256":"5b6db7bb4e111af61c17d54f69e940664ab60a488fbe17bb27d7cfac7e8dbc76"},"schema_version":"1.0","source":{"id":"1202.2226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2226","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2226v1","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2226","created_at":"2026-05-18T04:02:36Z"},{"alias_kind":"pith_short_12","alias_value":"GTWFMGMBKP3C","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GTWFMGMBKP3C2Z4X","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GTWFMGMB","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:0f4165c24bf44f8ee549ab2aa28e6280cb73592dce12fe912ad446c9bc4b17d9","target":"graph","created_at":"2026-05-18T04:02:36Z","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":"Let $p:\\R\\to(1,\\infty)$ be a globally log-H\\\"older continuous variable exponent and $w:\\R\\to[0,\\infty]$ be a weight. We prove that the Cauchy singular integral operator $S$ is bounded on the weighted variable Lebesgue space $L^{p(\\cdot)}(\\R,w)=\\{f:fw\\in L^{p(\\cdot)}(\\R)\\}$ if and only if the weight $w$ satisfies \\[ \\sup_{-\\infty<a<b<\\infty} \\frac{1}{b-a}\\|w\\chi_{(a,b)}\\|_{p(\\cdot)}\\|w^{-1}\\chi_{(a,b)}\\|_{p'(\\cdot)}<\\infty \\quad (1/p(x)+1/p'(x)=1). \\]","authors_text":"Alexei Yu. Karlovich, Ilya M. Spitkovsky","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-10T10:06:16Z","title":"The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2226","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:c915da9290ec27b84ae627c8d5dd632ab7d88fe6cba8bf7c27370a1a54e953c1","target":"record","created_at":"2026-05-18T04:02:36Z","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":"c0efb8621d4f2fcd36419fd1cc7e85f84a925db5b31e16ee95e7bdec7baed7f4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-10T10:06:16Z","title_canon_sha256":"5b6db7bb4e111af61c17d54f69e940664ab60a488fbe17bb27d7cfac7e8dbc76"},"schema_version":"1.0","source":{"id":"1202.2226","kind":"arxiv","version":1}},"canonical_sha256":"34ec56198153f62d679780b0a7224fcc347277637a3c3811e242a4ccaa1264a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34ec56198153f62d679780b0a7224fcc347277637a3c3811e242a4ccaa1264a6","first_computed_at":"2026-05-18T04:02:36.877453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:36.877453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9+PHoLUQ4TaPvPw3GDBk4PhMkVkM8YTjvvb47Xfvsr+1heFZm1O5uODHpOSWNdkRVu+8GNux+gaawiJKjGVBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:36.877938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c915da9290ec27b84ae627c8d5dd632ab7d88fe6cba8bf7c27370a1a54e953c1","sha256:0f4165c24bf44f8ee549ab2aa28e6280cb73592dce12fe912ad446c9bc4b17d9"],"state_sha256":"a2e0a54924e441923238e4eaf11c6d0bc25de3e8d731be4b184760ace3c5cefb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrdAgzhLRGVAKRet8FXRjNkt8EfRXrYY784Cql0M0MpkS9mwDxJhfAfAMzY1QTsbHscrN9c9IjP/bzVUU3GLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:32:34.455184Z","bundle_sha256":"510d6d31767639fabddb244265b43c4adda94c1802ae1e8593de256a49672751"}}