{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:LWUVUGYTYNHTESLDBICAGK4TZG","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":"8860b954e7171a1aba8c88266275621ac1ff806461197a43afcab7583cfc31b9","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","title_canon_sha256":"b39688a90e8ea3b7930aebcc0d775b6a9010368c8edb8c6b2a53f0e4c6b4f7f7"},"schema_version":"1.0","source":{"id":"math/9307210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9307210","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"math/9307210v1","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9307210","created_at":"2026-05-18T01:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"LWUVUGYTYNHT","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"LWUVUGYTYNHTESLD","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"LWUVUGYT","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:11c53fa8beda6b5c5ef3b00d5f9dde2f2708a4fb0340c41ee03de62ca04299d4","target":"graph","created_at":"2026-05-18T01:05:52Z","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":"It is shown how sums of squares of real valued functions can be used to give new proofs of the reality of the zeros of the Bessel functions $J_\\alpha (z)$ when $\\alpha \\ge -1,$ confluent hypergeometric functions ${}_0F_1(c\\/; z)$ when $c>0$ or $0>c>-1$, Laguerre polynomials $L_n^\\alpha(z)$ when $\\alpha \\ge -2,$ and Jacobi polynomials $P_n^{(\\alpha,\\beta)}(z)$ when $\\alpha \\ge -1$ and $ \\beta \\ge -1.$ Besides yielding new inequalities for $|F(z)|^2,$ where $F(z)$ is one of these functions, the derived identities lead to inequalities for $\\partial |F(z)|^2/\\partial y$ and $\\partial ^2 |F(z)|^2/\\","authors_text":"George Gasper Jr","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","title":"Using sums of squares to prove that certain entire functions have only real zeros"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9307210","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:e79e46a8e6b4a00353c47669ef07ff3eb01bf716aceb6af0f594a6b3a72e9720","target":"record","created_at":"2026-05-18T01:05:52Z","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":"8860b954e7171a1aba8c88266275621ac1ff806461197a43afcab7583cfc31b9","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1993-07-09T00:00:00Z","title_canon_sha256":"b39688a90e8ea3b7930aebcc0d775b6a9010368c8edb8c6b2a53f0e4c6b4f7f7"},"schema_version":"1.0","source":{"id":"math/9307210","kind":"arxiv","version":1}},"canonical_sha256":"5da95a1b13c34f3249630a04032b93c9ae53d2fec3870f863144b7a0a616a719","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5da95a1b13c34f3249630a04032b93c9ae53d2fec3870f863144b7a0a616a719","first_computed_at":"2026-05-18T01:05:52.090356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:52.090356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Vw6uhAc15kLhvvRxthm+VOHOpKe51bx5VBXM2qthrY3+skldHxx3OjnqpC8ExyuhxYTTzpZd0maGj1BBJWECg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:52.090937Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9307210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e79e46a8e6b4a00353c47669ef07ff3eb01bf716aceb6af0f594a6b3a72e9720","sha256:11c53fa8beda6b5c5ef3b00d5f9dde2f2708a4fb0340c41ee03de62ca04299d4"],"state_sha256":"3375b4296e40c0a0451b7445888a73b037b10d9268c21242a93f083b369c7e89"}