{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:IOZLM32PEIVEBV64U2FIXYMNTE","short_pith_number":"pith:IOZLM32P","canonical_record":{"source":{"id":"1101.3918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-20T14:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"81b9e3d80df61e8e226d59b095c403904dd84e457b873f8a70615e982fb2236e","abstract_canon_sha256":"59eaf711ce506fc8cc91915d7cb39e0f3667f122d68a40d7777a277e72324bad"},"schema_version":"1.0"},"canonical_sha256":"43b2b66f4f222a40d7dca68a8be18d9911cfefbc1977997ba2e8808a76c72798","source":{"kind":"arxiv","id":"1101.3918","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3918","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3918v2","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3918","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"IOZLM32PEIVE","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IOZLM32PEIVEBV64","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IOZLM32P","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:IOZLM32PEIVEBV64U2FIXYMNTE","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-20T14:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"81b9e3d80df61e8e226d59b095c403904dd84e457b873f8a70615e982fb2236e","abstract_canon_sha256":"59eaf711ce506fc8cc91915d7cb39e0f3667f122d68a40d7777a277e72324bad"},"schema_version":"1.0"},"canonical_sha256":"43b2b66f4f222a40d7dca68a8be18d9911cfefbc1977997ba2e8808a76c72798","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:22.306868Z","signature_b64":"6tQVgJ5jaj9fQ0EwxI0elJy9PysU9YrIMO/PGGiBlDZPP080Pz6IQ5gfTTpL6Nrw3uEHA4vdRRBU2i8y5SJvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43b2b66f4f222a40d7dca68a8be18d9911cfefbc1977997ba2e8808a76c72798","last_reissued_at":"2026-05-18T04:08:22.306463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:22.306463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3918","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":"2026-05-18T04:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYexuRH2TNFgI0ib4ElSi0vVCt62IptCX2JE2QQ/G+nN53DO6XxyhA9DIQpRvywxbiawELaCQjEldcDNNnc9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:31:01.432654Z"},"content_sha256":"4cbf812dbfbb9712970834e48945631bf37de4b6ec5a2e9533a540a456ee6126","schema_version":"1.0","event_id":"sha256:4cbf812dbfbb9712970834e48945631bf37de4b6ec5a2e9533a540a456ee6126"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:IOZLM32PEIVEBV64U2FIXYMNTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hadamard gap series in growth spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kjersti Solberg Eikrem","submitted_at":"2011-01-20T14:44:35Z","abstract_excerpt":"Let $h^\\infty_v$ be the class of harmonic functions in the unit disk which admit a two-sided radial majorant $v(r)$. We consider functions $v $ that fulfill a doubling condition. We characterize functions in $h^\\infty_v$ that are represented by Hadamard gap series in terms of their coefficients, and as a corollary we obtain a characterization of Hadamard gap series in Bloch-type spaces for weights with a doubling property. We show that if $u\\in h^\\infty_v$ is represented by a Hadamard gap series, then $u $ will grow slower than $v$ or oscillate along almost all radii. We use the law of the ite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3918","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":""},"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":"2026-05-18T04:08:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vigDGnPv0NI27luMLEaNVJ2H7tfcFBqZ5agfdGBSP82pd5ZqEOaVENg/YoGXpCYRaiuu8zphJBRFHlcoxvCjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:31:01.433353Z"},"content_sha256":"f138350aad5e7fc2999a56aa72eb0d7ff698be7c84be9a1f481c0f78db121e10","schema_version":"1.0","event_id":"sha256:f138350aad5e7fc2999a56aa72eb0d7ff698be7c84be9a1f481c0f78db121e10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOZLM32PEIVEBV64U2FIXYMNTE/bundle.json","state_url":"https://pith.science/pith/IOZLM32PEIVEBV64U2FIXYMNTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOZLM32PEIVEBV64U2FIXYMNTE/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":"2026-06-09T08:31:01Z","links":{"resolver":"https://pith.science/pith/IOZLM32PEIVEBV64U2FIXYMNTE","bundle":"https://pith.science/pith/IOZLM32PEIVEBV64U2FIXYMNTE/bundle.json","state":"https://pith.science/pith/IOZLM32PEIVEBV64U2FIXYMNTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOZLM32PEIVEBV64U2FIXYMNTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IOZLM32PEIVEBV64U2FIXYMNTE","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":"59eaf711ce506fc8cc91915d7cb39e0f3667f122d68a40d7777a277e72324bad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-20T14:44:35Z","title_canon_sha256":"81b9e3d80df61e8e226d59b095c403904dd84e457b873f8a70615e982fb2236e"},"schema_version":"1.0","source":{"id":"1101.3918","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3918","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3918v2","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3918","created_at":"2026-05-18T04:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"IOZLM32PEIVE","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IOZLM32PEIVEBV64","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IOZLM32P","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:f138350aad5e7fc2999a56aa72eb0d7ff698be7c84be9a1f481c0f78db121e10","target":"graph","created_at":"2026-05-18T04:08:22Z","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 $h^\\infty_v$ be the class of harmonic functions in the unit disk which admit a two-sided radial majorant $v(r)$. We consider functions $v $ that fulfill a doubling condition. We characterize functions in $h^\\infty_v$ that are represented by Hadamard gap series in terms of their coefficients, and as a corollary we obtain a characterization of Hadamard gap series in Bloch-type spaces for weights with a doubling property. We show that if $u\\in h^\\infty_v$ is represented by a Hadamard gap series, then $u $ will grow slower than $v$ or oscillate along almost all radii. We use the law of the ite","authors_text":"Kjersti Solberg Eikrem","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-20T14:44:35Z","title":"Hadamard gap series in growth spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3918","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":"sha256:4cbf812dbfbb9712970834e48945631bf37de4b6ec5a2e9533a540a456ee6126","target":"record","created_at":"2026-05-18T04:08:22Z","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":"59eaf711ce506fc8cc91915d7cb39e0f3667f122d68a40d7777a277e72324bad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-20T14:44:35Z","title_canon_sha256":"81b9e3d80df61e8e226d59b095c403904dd84e457b873f8a70615e982fb2236e"},"schema_version":"1.0","source":{"id":"1101.3918","kind":"arxiv","version":2}},"canonical_sha256":"43b2b66f4f222a40d7dca68a8be18d9911cfefbc1977997ba2e8808a76c72798","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43b2b66f4f222a40d7dca68a8be18d9911cfefbc1977997ba2e8808a76c72798","first_computed_at":"2026-05-18T04:08:22.306463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:22.306463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6tQVgJ5jaj9fQ0EwxI0elJy9PysU9YrIMO/PGGiBlDZPP080Pz6IQ5gfTTpL6Nrw3uEHA4vdRRBU2i8y5SJvAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:22.306868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3918","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cbf812dbfbb9712970834e48945631bf37de4b6ec5a2e9533a540a456ee6126","sha256:f138350aad5e7fc2999a56aa72eb0d7ff698be7c84be9a1f481c0f78db121e10"],"state_sha256":"d7ba3eed4db3a0da2e3c4f5c3765642f9655b792bdc4c7db5b8dc938ca27a109"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CK4EMH3lkdRmhT2YPMpVDR8VfPUHlm4yWmtxMFPEJNa1JCeW174MbSN9Oz1/dtP+2Jq2xfUU32XFJM89yZVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:31:01.437344Z","bundle_sha256":"add050d9cef2fa9ddfb7507c176d7e1bd6a349b31d30c4ae94eadbdae150f417"}}