{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OP7OFAG3CDQHSII7QJ2HRAOK7I","short_pith_number":"pith:OP7OFAG3","canonical_record":{"source":{"id":"1704.00093","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-01T01:10:13Z","cross_cats_sorted":[],"title_canon_sha256":"a177bc38338c96b8e3d87cda536fa07bb5ed4a0f3966657fb6a50d986a89d741","abstract_canon_sha256":"ec10b3e75cb69ad314745d41af4fbedc986c521cc85f8a2bf42d075c91141c09"},"schema_version":"1.0"},"canonical_sha256":"73fee280db10e079211f82747881cafa19a66dcd09f33dfadaf58f2de72d6c63","source":{"kind":"arxiv","id":"1704.00093","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00093","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00093v3","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00093","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"OP7OFAG3CDQH","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OP7OFAG3CDQHSII7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OP7OFAG3","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OP7OFAG3CDQHSII7QJ2HRAOK7I","target":"record","payload":{"canonical_record":{"source":{"id":"1704.00093","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-01T01:10:13Z","cross_cats_sorted":[],"title_canon_sha256":"a177bc38338c96b8e3d87cda536fa07bb5ed4a0f3966657fb6a50d986a89d741","abstract_canon_sha256":"ec10b3e75cb69ad314745d41af4fbedc986c521cc85f8a2bf42d075c91141c09"},"schema_version":"1.0"},"canonical_sha256":"73fee280db10e079211f82747881cafa19a66dcd09f33dfadaf58f2de72d6c63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:31.899413Z","signature_b64":"9mu9S27qWiqdJGBcPxH5GeOWOceatxM5Zg2DV+MZhfDzYTAx5JkxTpMxOEbHarruvPyvy8t1YaECThLmX8IxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73fee280db10e079211f82747881cafa19a66dcd09f33dfadaf58f2de72d6c63","last_reissued_at":"2026-05-18T00:18:31.898994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:31.898994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.00093","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBCBu5K8CWOAk4COA39OKu+sFDWnMS/zRNCp7UDQOUw3/7kK4k/mN7j8IrtdrjpD9qIK7Xqv2zp0+bhUDKmcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:39:35.078963Z"},"content_sha256":"b621a836fd8994fa4d0c565f52b94699543de7d73cd81deac560c398e0dc8946","schema_version":"1.0","event_id":"sha256:b621a836fd8994fa4d0c565f52b94699543de7d73cd81deac560c398e0dc8946"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OP7OFAG3CDQHSII7QJ2HRAOK7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Carlson's Theorem for Different Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Meredith Sargent","submitted_at":"2017-04-01T01:10:13Z","abstract_excerpt":"We use an observation of Bohr connecting Dirichlet series in the right half plane $\\mathbb{C}_+$ to power series on the polydisk to interpret Carlson's theorem about integrals in the mean as a special case of the ergodic theorem by considering any vertical line in the half plane as an ergodic flow on the polytorus. Of particular interest is the imaginary axis because Carlson's theorem for Lebesgue measure does not hold there. In this note, we construct measures for which Carlson's theorem does hold on the imaginary axis for functions in the Dirichlet series analog of the disk algebra $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00093","kind":"arxiv","version":3},"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":"2026-05-18T00:18:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JaY1DFXagMD4fGcKItPXDmHhGkTvGC9+p0O14/OBF9o82GA2UaDk9y6cQR627IL+GwPkm2TdwweaT+D6V61/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:39:35.079306Z"},"content_sha256":"5433fc3e42d355ad2be2b1b9aa072ad5634fe539da5a23e2a94035f97f9f9f77","schema_version":"1.0","event_id":"sha256:5433fc3e42d355ad2be2b1b9aa072ad5634fe539da5a23e2a94035f97f9f9f77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OP7OFAG3CDQHSII7QJ2HRAOK7I/bundle.json","state_url":"https://pith.science/pith/OP7OFAG3CDQHSII7QJ2HRAOK7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OP7OFAG3CDQHSII7QJ2HRAOK7I/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":"2026-06-22T22:39:35Z","links":{"resolver":"https://pith.science/pith/OP7OFAG3CDQHSII7QJ2HRAOK7I","bundle":"https://pith.science/pith/OP7OFAG3CDQHSII7QJ2HRAOK7I/bundle.json","state":"https://pith.science/pith/OP7OFAG3CDQHSII7QJ2HRAOK7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OP7OFAG3CDQHSII7QJ2HRAOK7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OP7OFAG3CDQHSII7QJ2HRAOK7I","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":"ec10b3e75cb69ad314745d41af4fbedc986c521cc85f8a2bf42d075c91141c09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-01T01:10:13Z","title_canon_sha256":"a177bc38338c96b8e3d87cda536fa07bb5ed4a0f3966657fb6a50d986a89d741"},"schema_version":"1.0","source":{"id":"1704.00093","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00093","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00093v3","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00093","created_at":"2026-05-18T00:18:31Z"},{"alias_kind":"pith_short_12","alias_value":"OP7OFAG3CDQH","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OP7OFAG3CDQHSII7","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OP7OFAG3","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:5433fc3e42d355ad2be2b1b9aa072ad5634fe539da5a23e2a94035f97f9f9f77","target":"graph","created_at":"2026-05-18T00:18:31Z","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 use an observation of Bohr connecting Dirichlet series in the right half plane $\\mathbb{C}_+$ to power series on the polydisk to interpret Carlson's theorem about integrals in the mean as a special case of the ergodic theorem by considering any vertical line in the half plane as an ergodic flow on the polytorus. Of particular interest is the imaginary axis because Carlson's theorem for Lebesgue measure does not hold there. In this note, we construct measures for which Carlson's theorem does hold on the imaginary axis for functions in the Dirichlet series analog of the disk algebra $\\mathcal","authors_text":"Meredith Sargent","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-01T01:10:13Z","title":"Carlson's Theorem for Different Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00093","kind":"arxiv","version":3},"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:b621a836fd8994fa4d0c565f52b94699543de7d73cd81deac560c398e0dc8946","target":"record","created_at":"2026-05-18T00:18:31Z","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":"ec10b3e75cb69ad314745d41af4fbedc986c521cc85f8a2bf42d075c91141c09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-04-01T01:10:13Z","title_canon_sha256":"a177bc38338c96b8e3d87cda536fa07bb5ed4a0f3966657fb6a50d986a89d741"},"schema_version":"1.0","source":{"id":"1704.00093","kind":"arxiv","version":3}},"canonical_sha256":"73fee280db10e079211f82747881cafa19a66dcd09f33dfadaf58f2de72d6c63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73fee280db10e079211f82747881cafa19a66dcd09f33dfadaf58f2de72d6c63","first_computed_at":"2026-05-18T00:18:31.898994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:31.898994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9mu9S27qWiqdJGBcPxH5GeOWOceatxM5Zg2DV+MZhfDzYTAx5JkxTpMxOEbHarruvPyvy8t1YaECThLmX8IxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:31.899413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00093","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b621a836fd8994fa4d0c565f52b94699543de7d73cd81deac560c398e0dc8946","sha256:5433fc3e42d355ad2be2b1b9aa072ad5634fe539da5a23e2a94035f97f9f9f77"],"state_sha256":"fac511d8d508cea359af13a59b57a663f95ece2c3f98b42155097f30e2bc9eaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1fzSXRCv3+LvFJE1Vm2LGrVhf1+5i11shsIeMsjPu/i9FKenOcD0DalSzis4o2SwMRtJU7P4wnkKHk4CcMJDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:39:35.081206Z","bundle_sha256":"1b634b546fd1dd9c4ce73a2a921f27ca4da31486e10169b93c56f904a3f28eb4"}}