{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QLDLIGMGIILRVSBSJ3OF3Q6MLU","short_pith_number":"pith:QLDLIGMG","canonical_record":{"source":{"id":"1207.4624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:04:06Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"e2e024d2c09193a4e691d8f29d756089746ce35e2663d4359b10af4efde019c4","abstract_canon_sha256":"3f4981c39edef4d4b6e99579d4efb5876afe56dfaccd489a68ecec164178581c"},"schema_version":"1.0"},"canonical_sha256":"82c6b4198642171ac8324edc5dc3cc5d2c06f2ec3fb9fc5ea05a5352a88f0fae","source":{"kind":"arxiv","id":"1207.4624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4624","created_at":"2026-05-18T03:50:36Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4624v1","created_at":"2026-05-18T03:50:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4624","created_at":"2026-05-18T03:50:36Z"},{"alias_kind":"pith_short_12","alias_value":"QLDLIGMGIILR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QLDLIGMGIILRVSBS","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QLDLIGMG","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QLDLIGMGIILRVSBSJ3OF3Q6MLU","target":"record","payload":{"canonical_record":{"source":{"id":"1207.4624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:04:06Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"e2e024d2c09193a4e691d8f29d756089746ce35e2663d4359b10af4efde019c4","abstract_canon_sha256":"3f4981c39edef4d4b6e99579d4efb5876afe56dfaccd489a68ecec164178581c"},"schema_version":"1.0"},"canonical_sha256":"82c6b4198642171ac8324edc5dc3cc5d2c06f2ec3fb9fc5ea05a5352a88f0fae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:36.406865Z","signature_b64":"Ch9XNopu52IMqjaNG/+sPUWmNuLrNrQHBDEfotmhoB5w5CkHzgJ/6AFko2LKROqZjFe+DOoVn42TTxkUhwlsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82c6b4198642171ac8324edc5dc3cc5d2c06f2ec3fb9fc5ea05a5352a88f0fae","last_reissued_at":"2026-05-18T03:50:36.406289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:36.406289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.4624","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":"2026-05-18T03:50:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"71doxnUlUqvnotUVk7giPr3ztMHXmher//oVi7rmHN0j2jPU5065QdC9Oh7fRguI4TxEUXKP5NqRmAv0uqMvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:40:21.990220Z"},"content_sha256":"63101df2035bcea313228db627e07986a83ae0e7ca8fe9b0c66eca60c7864695","schema_version":"1.0","event_id":"sha256:63101df2035bcea313228db627e07986a83ae0e7ca8fe9b0c66eca60c7864695"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QLDLIGMGIILRVSBSJ3OF3Q6MLU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a problem of Ramachandra and approximation of functions by Dirichlet polynomials with bounded coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.NT","authors_text":"Johan Andersson","submitted_at":"2012-07-19T12:04:06Z","abstract_excerpt":"We prove effective results on when a function can be approximated by a Dirichlet polynomial with bounded coefficients. Assuming that \\Phi(n) is an increasing function we prove that the set of polynomials {\\sum_{n=2}^N a_n n^{it-1}: N \\geq 2, |a_n| \\leq \\Phi(n)}, is dense in L^2(0,H) if and only if \\sum_{n=2}^\\infty \\frac{\\log \\Phi(n)} {n \\log^2 n} = \\infty. We also prove variants of this result for generalized Dirichlet polynomials. The main tools are theorems of Paley and Wiener related to quasianalyticity and the Pechersky rearrangement theorem. We use this result to give precise conditions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4624","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":"2026-05-18T03:50:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2r+TnJJWYif8ewS/SRwRE3+XePvRlD6/+4GOfQ5K7gAkfTZOsGyx5Mj5eb5glDykCvEQIJCt2RglzPnuxKkJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T03:40:21.990580Z"},"content_sha256":"c482729aa1263e28981f425fe8af407e8db1ebe54f5a3be9cfac0a0e5e4867aa","schema_version":"1.0","event_id":"sha256:c482729aa1263e28981f425fe8af407e8db1ebe54f5a3be9cfac0a0e5e4867aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QLDLIGMGIILRVSBSJ3OF3Q6MLU/bundle.json","state_url":"https://pith.science/pith/QLDLIGMGIILRVSBSJ3OF3Q6MLU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QLDLIGMGIILRVSBSJ3OF3Q6MLU/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":"2026-06-25T03:40:21Z","links":{"resolver":"https://pith.science/pith/QLDLIGMGIILRVSBSJ3OF3Q6MLU","bundle":"https://pith.science/pith/QLDLIGMGIILRVSBSJ3OF3Q6MLU/bundle.json","state":"https://pith.science/pith/QLDLIGMGIILRVSBSJ3OF3Q6MLU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QLDLIGMGIILRVSBSJ3OF3Q6MLU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QLDLIGMGIILRVSBSJ3OF3Q6MLU","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":"3f4981c39edef4d4b6e99579d4efb5876afe56dfaccd489a68ecec164178581c","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:04:06Z","title_canon_sha256":"e2e024d2c09193a4e691d8f29d756089746ce35e2663d4359b10af4efde019c4"},"schema_version":"1.0","source":{"id":"1207.4624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4624","created_at":"2026-05-18T03:50:36Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4624v1","created_at":"2026-05-18T03:50:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4624","created_at":"2026-05-18T03:50:36Z"},{"alias_kind":"pith_short_12","alias_value":"QLDLIGMGIILR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QLDLIGMGIILRVSBS","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QLDLIGMG","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:c482729aa1263e28981f425fe8af407e8db1ebe54f5a3be9cfac0a0e5e4867aa","target":"graph","created_at":"2026-05-18T03:50:36Z","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 prove effective results on when a function can be approximated by a Dirichlet polynomial with bounded coefficients. Assuming that \\Phi(n) is an increasing function we prove that the set of polynomials {\\sum_{n=2}^N a_n n^{it-1}: N \\geq 2, |a_n| \\leq \\Phi(n)}, is dense in L^2(0,H) if and only if \\sum_{n=2}^\\infty \\frac{\\log \\Phi(n)} {n \\log^2 n} = \\infty. We also prove variants of this result for generalized Dirichlet polynomials. The main tools are theorems of Paley and Wiener related to quasianalyticity and the Pechersky rearrangement theorem. We use this result to give precise conditions ","authors_text":"Johan Andersson","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:04:06Z","title":"On a problem of Ramachandra and approximation of functions by Dirichlet polynomials with bounded coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4624","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":"sha256:63101df2035bcea313228db627e07986a83ae0e7ca8fe9b0c66eca60c7864695","target":"record","created_at":"2026-05-18T03:50:36Z","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":"3f4981c39edef4d4b6e99579d4efb5876afe56dfaccd489a68ecec164178581c","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-07-19T12:04:06Z","title_canon_sha256":"e2e024d2c09193a4e691d8f29d756089746ce35e2663d4359b10af4efde019c4"},"schema_version":"1.0","source":{"id":"1207.4624","kind":"arxiv","version":1}},"canonical_sha256":"82c6b4198642171ac8324edc5dc3cc5d2c06f2ec3fb9fc5ea05a5352a88f0fae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82c6b4198642171ac8324edc5dc3cc5d2c06f2ec3fb9fc5ea05a5352a88f0fae","first_computed_at":"2026-05-18T03:50:36.406289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:36.406289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ch9XNopu52IMqjaNG/+sPUWmNuLrNrQHBDEfotmhoB5w5CkHzgJ/6AFko2LKROqZjFe+DOoVn42TTxkUhwlsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:36.406865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63101df2035bcea313228db627e07986a83ae0e7ca8fe9b0c66eca60c7864695","sha256:c482729aa1263e28981f425fe8af407e8db1ebe54f5a3be9cfac0a0e5e4867aa"],"state_sha256":"65cdaa1dea5c65a9798e466f76e2a5043d5461a954c98474ec6c2056a62ca8ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38iJH0S033Jkbu5Ut2S1UpazoqTm/Wqs4jUgI68rIyHCqfKG50ngUggsleWIiKL9PrTj0eNjKV6Q6zxdKQtBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T03:40:21.992471Z","bundle_sha256":"ea42db724508101b42974e9e752dc361646e8f85968d6a45a22b0941461d2680"}}