{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EKSDLQ3YM57NHMHWEKWSPPWFBN","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":"200f250a6b1ade237abac0377e35a5242fbba7ed79e7235b0a37af11aab5f936","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-05T19:06:57Z","title_canon_sha256":"f39e48fdbb8b480e5961223e90e398375a75e8b36118a0dc51afa615b12174ab"},"schema_version":"1.0","source":{"id":"1510.01285","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01285","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01285v1","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01285","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"EKSDLQ3YM57N","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EKSDLQ3YM57NHMHW","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EKSDLQ3Y","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:07c0677e27d567da93b1fe0c30df576739931279487d44f46f410184fb1cbc9d","target":"graph","created_at":"2026-05-18T01:31:04Z","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"},"paper":{"abstract_excerpt":"In this paper, we study the zero sets of the confluent hypergeometric function $_{1}F_{1}(\\alpha;\\gamma;z):=\\sum_{n=0}^{\\infty}\\frac{(\\alpha)_{n}}{n!(\\gamma)_{n}}z^{n}$, where $\\alpha, \\gamma, \\gamma-\\alpha\\not\\in \\mathbb{Z}_{\\leq 0}$, and show that if $\\{z_n\\}_{n=1}^{\\infty}$ is the zero set of $_{1}F_{1}(\\alpha;\\gamma;z)$ with multiple zeros repeated and modulus in increasing order, then there exists a constant $M>0$ such that $|z_n|\\geq M n$ for all $n\\geq 1$.","authors_text":"Wei-Chuan Lin, Xu-Dan Luo","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-05T19:06:57Z","title":"On the zeros of Confluent Hypergeometric Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01285","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":"sha256:2f85b5094eef9bc68567073b376a4cf1658558a7b3a184db51fe2ae9617de423","target":"record","created_at":"2026-05-18T01:31:04Z","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":"200f250a6b1ade237abac0377e35a5242fbba7ed79e7235b0a37af11aab5f936","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-05T19:06:57Z","title_canon_sha256":"f39e48fdbb8b480e5961223e90e398375a75e8b36118a0dc51afa615b12174ab"},"schema_version":"1.0","source":{"id":"1510.01285","kind":"arxiv","version":1}},"canonical_sha256":"22a435c378677ed3b0f622ad27bec50b406aeb71f76a057939abb9a2750fb0cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22a435c378677ed3b0f622ad27bec50b406aeb71f76a057939abb9a2750fb0cf","first_computed_at":"2026-05-18T01:31:04.334465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:04.334465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JUByNuKSX3LZwZ7pMMtu6D91IB4vFoAziaeQPRpAN4DEkQGxY5J8Ie2UY2pLug17GEm+V55Ygs9Tlf9MPV29DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:04.335029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01285","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f85b5094eef9bc68567073b376a4cf1658558a7b3a184db51fe2ae9617de423","sha256:07c0677e27d567da93b1fe0c30df576739931279487d44f46f410184fb1cbc9d"],"state_sha256":"4196c9d3a2719902633182e131d35dffda133c365058bf5cfe606d77cf593f5b"}