{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UTZ5V76QYFVAQ3WRO64XGNCVVL","short_pith_number":"pith:UTZ5V76Q","canonical_record":{"source":{"id":"1608.03317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-11T00:16:13Z","cross_cats_sorted":[],"title_canon_sha256":"c21ff4fd380e2c08eec080b21d4799b993d1eaff061c937d00cc3a0f20a46a62","abstract_canon_sha256":"e3c6b4922082a66529a901611a2c715d259a1052809899791d2fbc186ebbd87d"},"schema_version":"1.0"},"canonical_sha256":"a4f3daffd0c16a086ed177b9733455aaf8dff45f8e4f22897bfdaeb50ceb4d91","source":{"kind":"arxiv","id":"1608.03317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03317","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03317v1","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03317","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"UTZ5V76QYFVA","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UTZ5V76QYFVAQ3WR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UTZ5V76Q","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UTZ5V76QYFVAQ3WRO64XGNCVVL","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-11T00:16:13Z","cross_cats_sorted":[],"title_canon_sha256":"c21ff4fd380e2c08eec080b21d4799b993d1eaff061c937d00cc3a0f20a46a62","abstract_canon_sha256":"e3c6b4922082a66529a901611a2c715d259a1052809899791d2fbc186ebbd87d"},"schema_version":"1.0"},"canonical_sha256":"a4f3daffd0c16a086ed177b9733455aaf8dff45f8e4f22897bfdaeb50ceb4d91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:29.202221Z","signature_b64":"7pmt6RLDQ0YqsMfufSGsomRLj+D9Q9nWSoasKpkgMnfq6yQ/doSch5QSiR0bKgDhFrg7cCxhSKJjS/j7GRH7Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4f3daffd0c16a086ed177b9733455aaf8dff45f8e4f22897bfdaeb50ceb4d91","last_reissued_at":"2026-05-18T01:09:29.201761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:29.201761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03317","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":"2026-05-18T01:09:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+uahgx01a4kbQd0uecfHdPAF/WDqCqavJTYAzOb3ttuV6erKbOucO2p9qOntO9/v4BHbF7m5n477memLVzaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:28:53.691117Z"},"content_sha256":"0dc6474fb0cd94d938c03e449fbf22c73e30b992b152f6e0eea88098999ab124","schema_version":"1.0","event_id":"sha256:0dc6474fb0cd94d938c03e449fbf22c73e30b992b152f6e0eea88098999ab124"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UTZ5V76QYFVAQ3WRO64XGNCVVL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp value for the norm of composition and multiplicative operators between two different Grand Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"E.Ostrovsky, L.Sirota","submitted_at":"2016-08-11T00:16:13Z","abstract_excerpt":"We calculate in this paper the norm of composition, multiplicative and product operator, generated by multiplicative and measurable argument transformation between two different ordinary Lebesgue-Riesz and Grand Lebesgue spaces.\n  We set ourselves the aim to obtain the exact expression for the norm of the considered operators by means of building of appropriate examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03317","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":"2026-05-18T01:09:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jb7zAX1uX7c12zEN5fwJMrx4LezXWGbZ3AlzqZtcIxtSnEs8bneDbeYGCNvp0pirkzVe7MAal/ysm9JfdAyVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:28:53.691491Z"},"content_sha256":"a17cbdac37fc478c0538adcaaca3d92a16612e8e92bffea082114ef387301fec","schema_version":"1.0","event_id":"sha256:a17cbdac37fc478c0538adcaaca3d92a16612e8e92bffea082114ef387301fec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTZ5V76QYFVAQ3WRO64XGNCVVL/bundle.json","state_url":"https://pith.science/pith/UTZ5V76QYFVAQ3WRO64XGNCVVL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTZ5V76QYFVAQ3WRO64XGNCVVL/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":"2026-06-23T04:28:53Z","links":{"resolver":"https://pith.science/pith/UTZ5V76QYFVAQ3WRO64XGNCVVL","bundle":"https://pith.science/pith/UTZ5V76QYFVAQ3WRO64XGNCVVL/bundle.json","state":"https://pith.science/pith/UTZ5V76QYFVAQ3WRO64XGNCVVL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTZ5V76QYFVAQ3WRO64XGNCVVL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UTZ5V76QYFVAQ3WRO64XGNCVVL","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":"e3c6b4922082a66529a901611a2c715d259a1052809899791d2fbc186ebbd87d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-11T00:16:13Z","title_canon_sha256":"c21ff4fd380e2c08eec080b21d4799b993d1eaff061c937d00cc3a0f20a46a62"},"schema_version":"1.0","source":{"id":"1608.03317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03317","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03317v1","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03317","created_at":"2026-05-18T01:09:29Z"},{"alias_kind":"pith_short_12","alias_value":"UTZ5V76QYFVA","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UTZ5V76QYFVAQ3WR","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UTZ5V76Q","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:a17cbdac37fc478c0538adcaaca3d92a16612e8e92bffea082114ef387301fec","target":"graph","created_at":"2026-05-18T01:09:29Z","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 calculate in this paper the norm of composition, multiplicative and product operator, generated by multiplicative and measurable argument transformation between two different ordinary Lebesgue-Riesz and Grand Lebesgue spaces.\n  We set ourselves the aim to obtain the exact expression for the norm of the considered operators by means of building of appropriate examples.","authors_text":"E.Ostrovsky, L.Sirota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-11T00:16:13Z","title":"Sharp value for the norm of composition and multiplicative operators between two different Grand Lebesgue spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03317","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":"sha256:0dc6474fb0cd94d938c03e449fbf22c73e30b992b152f6e0eea88098999ab124","target":"record","created_at":"2026-05-18T01:09:29Z","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":"e3c6b4922082a66529a901611a2c715d259a1052809899791d2fbc186ebbd87d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-11T00:16:13Z","title_canon_sha256":"c21ff4fd380e2c08eec080b21d4799b993d1eaff061c937d00cc3a0f20a46a62"},"schema_version":"1.0","source":{"id":"1608.03317","kind":"arxiv","version":1}},"canonical_sha256":"a4f3daffd0c16a086ed177b9733455aaf8dff45f8e4f22897bfdaeb50ceb4d91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4f3daffd0c16a086ed177b9733455aaf8dff45f8e4f22897bfdaeb50ceb4d91","first_computed_at":"2026-05-18T01:09:29.201761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:29.201761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7pmt6RLDQ0YqsMfufSGsomRLj+D9Q9nWSoasKpkgMnfq6yQ/doSch5QSiR0bKgDhFrg7cCxhSKJjS/j7GRH7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:29.202221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dc6474fb0cd94d938c03e449fbf22c73e30b992b152f6e0eea88098999ab124","sha256:a17cbdac37fc478c0538adcaaca3d92a16612e8e92bffea082114ef387301fec"],"state_sha256":"5b5d65876b17c6697012573ffa677fd2a9487d87a42a67917bde326a02f7b301"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owPzz/vL+xSSK0Z3Qt6WQ/vsqrOWYlsTG4YXE2x0YXGkUk86xMZFcsyw0l9ZiKFRjZWbTc2zr5L5Kgq0M+ZKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:28:53.693408Z","bundle_sha256":"801b15d51177e88152e24db00492d0683774e7d41ebbf8fe1dc8de4a34532e26"}}