{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LNN6OX25QHL2NSYN2D4PVUBQGX","short_pith_number":"pith:LNN6OX25","schema_version":"1.0","canonical_sha256":"5b5be75f5d81d7a6cb0dd0f8fad03035d901ab33b820676d393cbe44ccce3190","source":{"kind":"arxiv","id":"1612.00597","version":1},"attestation_state":"computed","paper":{"title":"On the Bohr inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Rosihan M. Ali, Saminathan Ponnusamy, Yusuf Abu Muhanna","submitted_at":"2016-12-02T08:57:44Z","abstract_excerpt":"The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\\sum_{n=0}^\\infty |a_n|r^n \\leq 1$ holds whenever $|\\sum_{n=0}^\\infty a_nz^n|\\leq 1$ in the unit disk $\\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \\emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\\mathbb{D},$ as well as for analytic functions from $\\mathbb{D}$ into particular domains. Thes"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.00597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-02T08:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"23f2ef7096665819029363200883463d1345b26b21b65a892a69be6861328b52","abstract_canon_sha256":"051f98b4d0e8fb2abf9be15b819f9b4128841bc04435b99ea4d244efd7b14fba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:59.578090Z","signature_b64":"/84kwEOyhFvOT6qAhv6PMSujX4OHjiEmitsvthsIq5Wd65rlUjhavly/zHt36Bd91LmF0DFE+tnbxc1gPzr6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b5be75f5d81d7a6cb0dd0f8fad03035d901ab33b820676d393cbe44ccce3190","last_reissued_at":"2026-05-18T00:55:59.577506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:59.577506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Bohr inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Rosihan M. Ali, Saminathan Ponnusamy, Yusuf Abu Muhanna","submitted_at":"2016-12-02T08:57:44Z","abstract_excerpt":"The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\\sum_{n=0}^\\infty |a_n|r^n \\leq 1$ holds whenever $|\\sum_{n=0}^\\infty a_nz^n|\\leq 1$ in the unit disk $\\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \\emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\\mathbb{D},$ as well as for analytic functions from $\\mathbb{D}$ into particular domains. Thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00597","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.00597","created_at":"2026-05-18T00:55:59.577617+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.00597v1","created_at":"2026-05-18T00:55:59.577617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00597","created_at":"2026-05-18T00:55:59.577617+00:00"},{"alias_kind":"pith_short_12","alias_value":"LNN6OX25QHL2","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LNN6OX25QHL2NSYN","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LNN6OX25","created_at":"2026-05-18T12:30:29.479603+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX","json":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX.json","graph_json":"https://pith.science/api/pith-number/LNN6OX25QHL2NSYN2D4PVUBQGX/graph.json","events_json":"https://pith.science/api/pith-number/LNN6OX25QHL2NSYN2D4PVUBQGX/events.json","paper":"https://pith.science/paper/LNN6OX25"},"agent_actions":{"view_html":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX","download_json":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX.json","view_paper":"https://pith.science/paper/LNN6OX25","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.00597&json=true","fetch_graph":"https://pith.science/api/pith-number/LNN6OX25QHL2NSYN2D4PVUBQGX/graph.json","fetch_events":"https://pith.science/api/pith-number/LNN6OX25QHL2NSYN2D4PVUBQGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX/action/storage_attestation","attest_author":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX/action/author_attestation","sign_citation":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX/action/citation_signature","submit_replication":"https://pith.science/pith/LNN6OX25QHL2NSYN2D4PVUBQGX/action/replication_record"}},"created_at":"2026-05-18T00:55:59.577617+00:00","updated_at":"2026-05-18T00:55:59.577617+00:00"}