{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:BKH6ZRQFZOGZK7SGZI66N5VJLC","short_pith_number":"pith:BKH6ZRQF","canonical_record":{"source":{"id":"2208.10626","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2022-08-22T22:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"9c3fd0282ddbf4fbbc53e960b47e3b7e6d6a173116000740fa30ce2d594a4628","abstract_canon_sha256":"4857e4f5166ad8da7dc20c00b7f3b4b778e7fd4f1e89c51058789a2ba5de24f6"},"schema_version":"1.0"},"canonical_sha256":"0a8fecc605cb8d957e46ca3de6f6a958ab8a18be159f45596ff5b4f04ffb2de7","source":{"kind":"arxiv","id":"2208.10626","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.10626","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"2208.10626v2","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.10626","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"BKH6ZRQFZOGZ","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"pith_short_16","alias_value":"BKH6ZRQFZOGZK7SG","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"pith_short_8","alias_value":"BKH6ZRQF","created_at":"2026-07-05T06:35:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:BKH6ZRQFZOGZK7SGZI66N5VJLC","target":"record","payload":{"canonical_record":{"source":{"id":"2208.10626","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2022-08-22T22:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"9c3fd0282ddbf4fbbc53e960b47e3b7e6d6a173116000740fa30ce2d594a4628","abstract_canon_sha256":"4857e4f5166ad8da7dc20c00b7f3b4b778e7fd4f1e89c51058789a2ba5de24f6"},"schema_version":"1.0"},"canonical_sha256":"0a8fecc605cb8d957e46ca3de6f6a958ab8a18be159f45596ff5b4f04ffb2de7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:35:04.887283Z","signature_b64":"RjiJGpktJic/wwofpSvjmlaWfyWcAEUFBAOQeZ1xSeJVox5lupihxOmIx8zjUZzGuh5BeBCCMRMR2qdMaADFDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a8fecc605cb8d957e46ca3de6f6a958ab8a18be159f45596ff5b4f04ffb2de7","last_reissued_at":"2026-07-05T06:35:04.886804Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:35:04.886804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.10626","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":"2026-07-05T06:35:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tvyIEaMzeWvSXJvzBHrWKuTnA1PAscVQIxbNuUatyYA+biEIsBxsRpnAwZ3QVnkyoQCda9XZdRfqTBSJkYxGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:50:51.126330Z"},"content_sha256":"a3002f334140d988d7760e05034a60b25ef4ebb82f6ae1b64fb964774f1d2658","schema_version":"1.0","event_id":"sha256:a3002f334140d988d7760e05034a60b25ef4ebb82f6ae1b64fb964774f1d2658"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:BKH6ZRQFZOGZK7SGZI66N5VJLC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimates for truncated area functionals on the Bloch space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alejandro Mas, Dragan Vukoti\\'c, Iason Efraimidis","submitted_at":"2022-08-22T22:08:28Z","abstract_excerpt":"Recently, Kayumov \\cite{K} obtained a sharp estimate for the $n$-th truncated area functional for normalized functions in the Bloch space for $n\\le 5$ and then, together with Wirths \\cite{KW1}, extended the result for $n=6$. We prove that for the functions with non-negative Taylor coefficients, the same sharp estimate is valid for all $n$. For arbitrary functions, we obtain an estimate that is asymptotically of the same order but slightly larger (roughly by a factor of $4/e$). We also consider related weighted estimates for functionals involving the powers $n^t$, $t>0$, and show that the expon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.10626","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.10626/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:35:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/woiIHOQhDWg4GulCILVT11qevP7DbjxVFTJzB6mxQqA+HGinYohsjhQf5cWrY7pROto4gqKtxFL48ua/IxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:50:51.126701Z"},"content_sha256":"e36ab82d0a42b4df110206125ce775d6fc8f43aa697d1da5249d3d9f4ecd479b","schema_version":"1.0","event_id":"sha256:e36ab82d0a42b4df110206125ce775d6fc8f43aa697d1da5249d3d9f4ecd479b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BKH6ZRQFZOGZK7SGZI66N5VJLC/bundle.json","state_url":"https://pith.science/pith/BKH6ZRQFZOGZK7SGZI66N5VJLC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BKH6ZRQFZOGZK7SGZI66N5VJLC/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":"2026-07-07T13:50:51Z","links":{"resolver":"https://pith.science/pith/BKH6ZRQFZOGZK7SGZI66N5VJLC","bundle":"https://pith.science/pith/BKH6ZRQFZOGZK7SGZI66N5VJLC/bundle.json","state":"https://pith.science/pith/BKH6ZRQFZOGZK7SGZI66N5VJLC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BKH6ZRQFZOGZK7SGZI66N5VJLC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:BKH6ZRQFZOGZK7SGZI66N5VJLC","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":"4857e4f5166ad8da7dc20c00b7f3b4b778e7fd4f1e89c51058789a2ba5de24f6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2022-08-22T22:08:28Z","title_canon_sha256":"9c3fd0282ddbf4fbbc53e960b47e3b7e6d6a173116000740fa30ce2d594a4628"},"schema_version":"1.0","source":{"id":"2208.10626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.10626","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"2208.10626v2","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.10626","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"BKH6ZRQFZOGZ","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"pith_short_16","alias_value":"BKH6ZRQFZOGZK7SG","created_at":"2026-07-05T06:35:04Z"},{"alias_kind":"pith_short_8","alias_value":"BKH6ZRQF","created_at":"2026-07-05T06:35:04Z"}],"graph_snapshots":[{"event_id":"sha256:e36ab82d0a42b4df110206125ce775d6fc8f43aa697d1da5249d3d9f4ecd479b","target":"graph","created_at":"2026-07-05T06:35:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.10626/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, Kayumov \\cite{K} obtained a sharp estimate for the $n$-th truncated area functional for normalized functions in the Bloch space for $n\\le 5$ and then, together with Wirths \\cite{KW1}, extended the result for $n=6$. We prove that for the functions with non-negative Taylor coefficients, the same sharp estimate is valid for all $n$. For arbitrary functions, we obtain an estimate that is asymptotically of the same order but slightly larger (roughly by a factor of $4/e$). We also consider related weighted estimates for functionals involving the powers $n^t$, $t>0$, and show that the expon","authors_text":"Alejandro Mas, Dragan Vukoti\\'c, Iason Efraimidis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2022-08-22T22:08:28Z","title":"Estimates for truncated area functionals on the Bloch space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.10626","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:a3002f334140d988d7760e05034a60b25ef4ebb82f6ae1b64fb964774f1d2658","target":"record","created_at":"2026-07-05T06:35:04Z","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":"4857e4f5166ad8da7dc20c00b7f3b4b778e7fd4f1e89c51058789a2ba5de24f6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2022-08-22T22:08:28Z","title_canon_sha256":"9c3fd0282ddbf4fbbc53e960b47e3b7e6d6a173116000740fa30ce2d594a4628"},"schema_version":"1.0","source":{"id":"2208.10626","kind":"arxiv","version":2}},"canonical_sha256":"0a8fecc605cb8d957e46ca3de6f6a958ab8a18be159f45596ff5b4f04ffb2de7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a8fecc605cb8d957e46ca3de6f6a958ab8a18be159f45596ff5b4f04ffb2de7","first_computed_at":"2026-07-05T06:35:04.886804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:35:04.886804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RjiJGpktJic/wwofpSvjmlaWfyWcAEUFBAOQeZ1xSeJVox5lupihxOmIx8zjUZzGuh5BeBCCMRMR2qdMaADFDw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:35:04.887283Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.10626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3002f334140d988d7760e05034a60b25ef4ebb82f6ae1b64fb964774f1d2658","sha256:e36ab82d0a42b4df110206125ce775d6fc8f43aa697d1da5249d3d9f4ecd479b"],"state_sha256":"33b8f32c8c423a8684e6b1b23ab55a10c4964856569c1cc241c02017b73a3b80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ye9khU++PDqFSABVh4ETXHxwqbC2og6rkIcE10vIw0F+nY/G3Hrfn+3uHW33TTxrFanh8L1yFhZk0WoROcKxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:50:51.128533Z","bundle_sha256":"0fad721ba4c54b7cbca0f5e3253affd4029aa7c793f5c698f78f43ab9d22fbfc"}}