{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MS5FSVUM3YRQJABWWKZZ5NPWOB","short_pith_number":"pith:MS5FSVUM","canonical_record":{"source":{"id":"1402.0829","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2014-02-04T18:51:36Z","cross_cats_sorted":[],"title_canon_sha256":"928a92e0561c5f1546ff4f122636434f5109436a79c96751b92105d2376999ad","abstract_canon_sha256":"bc337fecd932defd36cf048d90f2a29bb9b80ff439d3d4c610e4173ed8dc82ec"},"schema_version":"1.0"},"canonical_sha256":"64ba59568cde23048036b2b39eb5f6706fba847f275cce214afa634f31b6a738","source":{"kind":"arxiv","id":"1402.0829","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0829","created_at":"2026-05-18T03:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0829v1","created_at":"2026-05-18T03:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0829","created_at":"2026-05-18T03:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"MS5FSVUM3YRQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MS5FSVUM3YRQJABW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MS5FSVUM","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MS5FSVUM3YRQJABWWKZZ5NPWOB","target":"record","payload":{"canonical_record":{"source":{"id":"1402.0829","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2014-02-04T18:51:36Z","cross_cats_sorted":[],"title_canon_sha256":"928a92e0561c5f1546ff4f122636434f5109436a79c96751b92105d2376999ad","abstract_canon_sha256":"bc337fecd932defd36cf048d90f2a29bb9b80ff439d3d4c610e4173ed8dc82ec"},"schema_version":"1.0"},"canonical_sha256":"64ba59568cde23048036b2b39eb5f6706fba847f275cce214afa634f31b6a738","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:11.893130Z","signature_b64":"hEGaQyfTFusBCUeZQAdXSwuAGamukiiWYvb2Pe9C4LsuYRIJmsuJhPXLdWasGIfSj4MVgymINOJbNFDgmgRFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64ba59568cde23048036b2b39eb5f6706fba847f275cce214afa634f31b6a738","last_reissued_at":"2026-05-18T03:00:11.892327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:11.892327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.0829","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":"2026-05-18T03:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kQpLmY+hyM//uJUT4ous3j0wz9jr59Cby4Y2+xtmJ0Nn7yiH4MnknRfqy3zY1CN+m79EzUB4k6tZdPx2JKAHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:55:04.061848Z"},"content_sha256":"ab053f2706e867307b754bc73a80b734ba34cc1762bff8132da7e6ed9caa35ef","schema_version":"1.0","event_id":"sha256:ab053f2706e867307b754bc73a80b734ba34cc1762bff8132da7e6ed9caa35ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MS5FSVUM3YRQJABWWKZZ5NPWOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp Estimates for Norms of Functions from Conjugate Classes in Metrics C and L","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Vladislav Babenko","submitted_at":"2014-02-04T18:51:36Z","abstract_excerpt":"Sharp estimates for C - and L - norms of functions that are conjugate with functions from the classes W^rH_\\omega of periodic functions having prescribed concave majorant of moduli of continuity, as well as sharp estimates for the differences of such functions are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0829","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":"2026-05-18T03:00:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qbNsVHG6Elr+xpn8WtNvDDIm49gB2z0+D+h0aSC9TzgAW8Cq2NpfcxubNDceknbkyxdGT5QIbWxpFKTjTrERCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:55:04.062670Z"},"content_sha256":"def5152f7ecf65cc3ee83e9ca764878171fdac48c0290249e1e3fce8db7e2091","schema_version":"1.0","event_id":"sha256:def5152f7ecf65cc3ee83e9ca764878171fdac48c0290249e1e3fce8db7e2091"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MS5FSVUM3YRQJABWWKZZ5NPWOB/bundle.json","state_url":"https://pith.science/pith/MS5FSVUM3YRQJABWWKZZ5NPWOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MS5FSVUM3YRQJABWWKZZ5NPWOB/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":"2026-05-30T20:55:04Z","links":{"resolver":"https://pith.science/pith/MS5FSVUM3YRQJABWWKZZ5NPWOB","bundle":"https://pith.science/pith/MS5FSVUM3YRQJABWWKZZ5NPWOB/bundle.json","state":"https://pith.science/pith/MS5FSVUM3YRQJABWWKZZ5NPWOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MS5FSVUM3YRQJABWWKZZ5NPWOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MS5FSVUM3YRQJABWWKZZ5NPWOB","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":"bc337fecd932defd36cf048d90f2a29bb9b80ff439d3d4c610e4173ed8dc82ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2014-02-04T18:51:36Z","title_canon_sha256":"928a92e0561c5f1546ff4f122636434f5109436a79c96751b92105d2376999ad"},"schema_version":"1.0","source":{"id":"1402.0829","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0829","created_at":"2026-05-18T03:00:11Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0829v1","created_at":"2026-05-18T03:00:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0829","created_at":"2026-05-18T03:00:11Z"},{"alias_kind":"pith_short_12","alias_value":"MS5FSVUM3YRQ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MS5FSVUM3YRQJABW","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MS5FSVUM","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:def5152f7ecf65cc3ee83e9ca764878171fdac48c0290249e1e3fce8db7e2091","target":"graph","created_at":"2026-05-18T03:00:11Z","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":"Sharp estimates for C - and L - norms of functions that are conjugate with functions from the classes W^rH_\\omega of periodic functions having prescribed concave majorant of moduli of continuity, as well as sharp estimates for the differences of such functions are obtained.","authors_text":"Vladislav Babenko","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2014-02-04T18:51:36Z","title":"Sharp Estimates for Norms of Functions from Conjugate Classes in Metrics C and L"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0829","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:ab053f2706e867307b754bc73a80b734ba34cc1762bff8132da7e6ed9caa35ef","target":"record","created_at":"2026-05-18T03:00:11Z","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":"bc337fecd932defd36cf048d90f2a29bb9b80ff439d3d4c610e4173ed8dc82ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2014-02-04T18:51:36Z","title_canon_sha256":"928a92e0561c5f1546ff4f122636434f5109436a79c96751b92105d2376999ad"},"schema_version":"1.0","source":{"id":"1402.0829","kind":"arxiv","version":1}},"canonical_sha256":"64ba59568cde23048036b2b39eb5f6706fba847f275cce214afa634f31b6a738","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64ba59568cde23048036b2b39eb5f6706fba847f275cce214afa634f31b6a738","first_computed_at":"2026-05-18T03:00:11.892327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:11.892327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hEGaQyfTFusBCUeZQAdXSwuAGamukiiWYvb2Pe9C4LsuYRIJmsuJhPXLdWasGIfSj4MVgymINOJbNFDgmgRFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:11.893130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0829","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab053f2706e867307b754bc73a80b734ba34cc1762bff8132da7e6ed9caa35ef","sha256:def5152f7ecf65cc3ee83e9ca764878171fdac48c0290249e1e3fce8db7e2091"],"state_sha256":"cbdc9d60a88c891a6e7f277e78f48512ac8c51ced325dd0ae2b81f49f2f5a044"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkBZQ8S/PZDonRGRYKxS4LkzfnNJAHL9o1Us0Rz04RFdBnymY/CxXVvVSuONxRkc/19yNgOcbIgN9pfF0cF7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:55:04.066850Z","bundle_sha256":"10ea431e2ab59f8870f4c4ab7ce0701f0df74b2651440917c6da1c1b9d44bb20"}}