{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EOGMAO7D6SEM7422KIM4QHAZEO","short_pith_number":"pith:EOGMAO7D","canonical_record":{"source":{"id":"1312.7232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-27T10:04:53Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"323a16531903a4f739a2f61a7635d452ead3017a1571ecacf1e236466f69e3e0","abstract_canon_sha256":"e16f435d1c22730811ecbcb9eeb6f01ff8028d2966947b520e86b5af5d9f5ca7"},"schema_version":"1.0"},"canonical_sha256":"238cc03be3f488cff35a5219c81c192398b7f85d95ab199ef87d812e3ed9d4d5","source":{"kind":"arxiv","id":"1312.7232","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7232","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7232v1","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7232","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"pith_short_12","alias_value":"EOGMAO7D6SEM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EOGMAO7D6SEM7422","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EOGMAO7D","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EOGMAO7D6SEM7422KIM4QHAZEO","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-27T10:04:53Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"323a16531903a4f739a2f61a7635d452ead3017a1571ecacf1e236466f69e3e0","abstract_canon_sha256":"e16f435d1c22730811ecbcb9eeb6f01ff8028d2966947b520e86b5af5d9f5ca7"},"schema_version":"1.0"},"canonical_sha256":"238cc03be3f488cff35a5219c81c192398b7f85d95ab199ef87d812e3ed9d4d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:43.328178Z","signature_b64":"6y6/V7gYuslHicCWkA8XzNchyIICSjMDPSgm/Hu3/zZYAddUCcHOPXZcQiCyIZ06yuAgjxpjNqY0byKEq886Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"238cc03be3f488cff35a5219c81c192398b7f85d95ab199ef87d812e3ed9d4d5","last_reissued_at":"2026-05-18T01:55:43.327561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:43.327561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7232","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":"2026-05-18T01:55:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FMXN2rKSkCNLoE9I01K2l6yKWIvDhjP4IEeoRd1OBZFsF8XSi2Vj0xI1jcRxAOUsFHjxw52KuQFTZXzx1TDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:07:38.453117Z"},"content_sha256":"4bdef4d69f3f458bc78722882d0db3bcea550ae0f087d039ad2c699df529f3eb","schema_version":"1.0","event_id":"sha256:4bdef4d69f3f458bc78722882d0db3bcea550ae0f087d039ad2c699df529f3eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EOGMAO7D6SEM7422KIM4QHAZEO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal multiplier operators in $L^{p(\\cdot)}(\\mathbb{R}^{n})$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Amiran Gogatishvili, Tengiz Kopaliani","submitted_at":"2013-12-27T10:04:53Z","abstract_excerpt":"In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7232","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":"2026-05-18T01:55:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxMDDo8qiny4s7RnE+DKiIixjG3ZRGma840LiQJoRNQ+5CggxPzloy3M5aBpck10TApigIe70bO/la9sDd0zAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T16:07:38.453470Z"},"content_sha256":"96dcc097653239556488e7fe52fae8cc4de018bb52c7da7444a34007bf0ac813","schema_version":"1.0","event_id":"sha256:96dcc097653239556488e7fe52fae8cc4de018bb52c7da7444a34007bf0ac813"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EOGMAO7D6SEM7422KIM4QHAZEO/bundle.json","state_url":"https://pith.science/pith/EOGMAO7D6SEM7422KIM4QHAZEO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EOGMAO7D6SEM7422KIM4QHAZEO/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":"2026-06-27T16:07:38Z","links":{"resolver":"https://pith.science/pith/EOGMAO7D6SEM7422KIM4QHAZEO","bundle":"https://pith.science/pith/EOGMAO7D6SEM7422KIM4QHAZEO/bundle.json","state":"https://pith.science/pith/EOGMAO7D6SEM7422KIM4QHAZEO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EOGMAO7D6SEM7422KIM4QHAZEO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EOGMAO7D6SEM7422KIM4QHAZEO","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":"e16f435d1c22730811ecbcb9eeb6f01ff8028d2966947b520e86b5af5d9f5ca7","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-27T10:04:53Z","title_canon_sha256":"323a16531903a4f739a2f61a7635d452ead3017a1571ecacf1e236466f69e3e0"},"schema_version":"1.0","source":{"id":"1312.7232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7232","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7232v1","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7232","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"pith_short_12","alias_value":"EOGMAO7D6SEM","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EOGMAO7D6SEM7422","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EOGMAO7D","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:96dcc097653239556488e7fe52fae8cc4de018bb52c7da7444a34007bf0ac813","target":"graph","created_at":"2026-05-18T01:55:43Z","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":"In this paper we study some estimates of norms in variable exponent Lebesgue spaces for maximal multiplier operators.We will consider the case when multiplier is the Fourier transform of a compactly supported Borel measure","authors_text":"Amiran Gogatishvili, Tengiz Kopaliani","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-27T10:04:53Z","title":"Maximal multiplier operators in $L^{p(\\cdot)}(\\mathbb{R}^{n})$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7232","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":"sha256:4bdef4d69f3f458bc78722882d0db3bcea550ae0f087d039ad2c699df529f3eb","target":"record","created_at":"2026-05-18T01:55:43Z","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":"e16f435d1c22730811ecbcb9eeb6f01ff8028d2966947b520e86b5af5d9f5ca7","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-27T10:04:53Z","title_canon_sha256":"323a16531903a4f739a2f61a7635d452ead3017a1571ecacf1e236466f69e3e0"},"schema_version":"1.0","source":{"id":"1312.7232","kind":"arxiv","version":1}},"canonical_sha256":"238cc03be3f488cff35a5219c81c192398b7f85d95ab199ef87d812e3ed9d4d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"238cc03be3f488cff35a5219c81c192398b7f85d95ab199ef87d812e3ed9d4d5","first_computed_at":"2026-05-18T01:55:43.327561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:43.327561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6y6/V7gYuslHicCWkA8XzNchyIICSjMDPSgm/Hu3/zZYAddUCcHOPXZcQiCyIZ06yuAgjxpjNqY0byKEq886Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:43.328178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bdef4d69f3f458bc78722882d0db3bcea550ae0f087d039ad2c699df529f3eb","sha256:96dcc097653239556488e7fe52fae8cc4de018bb52c7da7444a34007bf0ac813"],"state_sha256":"bc9d192e2063989078cb73ca46afaad13de8a5519048f58437f467a1b8122e8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rEvWLn4sgaXXpALPlUKZlfs/3iQpIfC88Jqstoop9oe4A9bVgQMvklwdgYPtBBdXBxa3nKCTE+0xIDdhcFdyAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T16:07:38.455323Z","bundle_sha256":"97b142a47a697528ed961c5d816b7ed6af0bc47a7d8c6c3f1cf557dde22947ef"}}