{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XNKZ666ZSH77C6KO3Q7SFA2BHP","short_pith_number":"pith:XNKZ666Z","canonical_record":{"source":{"id":"1603.04694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-12T08:52:40Z","cross_cats_sorted":[],"title_canon_sha256":"be2b05ae039bcaec64d12ebecd6e7e7b972233760bef98219ec44b673d60a865","abstract_canon_sha256":"35c5450b31a0b5ece4a94aa913c77d3d776bcd67de17310f7e0890e1b518acdb"},"schema_version":"1.0"},"canonical_sha256":"bb559f7bd991fff1794edc3f2283413bc1931cd85f9b8b81a9a3798015bf7594","source":{"kind":"arxiv","id":"1603.04694","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04694","created_at":"2026-05-18T01:18:59Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04694v2","created_at":"2026-05-18T01:18:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04694","created_at":"2026-05-18T01:18:59Z"},{"alias_kind":"pith_short_12","alias_value":"XNKZ666ZSH77","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XNKZ666ZSH77C6KO","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XNKZ666Z","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XNKZ666ZSH77C6KO3Q7SFA2BHP","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-12T08:52:40Z","cross_cats_sorted":[],"title_canon_sha256":"be2b05ae039bcaec64d12ebecd6e7e7b972233760bef98219ec44b673d60a865","abstract_canon_sha256":"35c5450b31a0b5ece4a94aa913c77d3d776bcd67de17310f7e0890e1b518acdb"},"schema_version":"1.0"},"canonical_sha256":"bb559f7bd991fff1794edc3f2283413bc1931cd85f9b8b81a9a3798015bf7594","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:59.833035Z","signature_b64":"eaaKw3vx+9qrpD+OVP8CfszvWbdfUbakpXuXdoZUA/+Y116mt2oZga3PQETXE32s162quD8yDf1UltrjUM4WAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb559f7bd991fff1794edc3f2283413bc1931cd85f9b8b81a9a3798015bf7594","last_reissued_at":"2026-05-18T01:18:59.832607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:59.832607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04694","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0s6vlEn4OGEd5gdHs52Tb4HxuwrlBV+o5zHJJyGkv+ny4UBhTnuOcCLl2YEbEXwunWff+Z9N3Fy8feUL7GmSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:39:28.588568Z"},"content_sha256":"848be84dc3e88b7213a6f67a5c7f4a8e95627d01ab43aaff5eea87ea552b6c17","schema_version":"1.0","event_id":"sha256:848be84dc3e88b7213a6f67a5c7f4a8e95627d01ab43aaff5eea87ea552b6c17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XNKZ666ZSH77C6KO3Q7SFA2BHP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeros of Ramanujan Type Entire Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ruiming Zhang","submitted_at":"2016-03-12T08:52:40Z","abstract_excerpt":"In this work we establish some polynomials and entire functions have only real zeros. These polynomials generalize q-Laguerre polynomials $L_{n}^{(\\alpha)}(x;q)$, while the entire functions are generalizations of Ramanujan's entire function $A_{q}(z)$, q-Bessel functions $J_{\\nu}^{(2)}(z;q)$, $J_{\\nu}^{(3)}(z;q)$ and confluent basic hypergeometric series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04694","kind":"arxiv","version":2},"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":"2026-05-18T01:18:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NkAuYvjCnXpZdVmVRZGcudT8g0dLD+JZqpNtvmvl9m7cr5YAukpUur35J92yNHirWKQUbjO5Y01rYrQsSGIhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:39:28.589241Z"},"content_sha256":"e4e1265d0c6b563e68bc0dcc8add4fd0ab13307098315b4a6a76a8a8328a685d","schema_version":"1.0","event_id":"sha256:e4e1265d0c6b563e68bc0dcc8add4fd0ab13307098315b4a6a76a8a8328a685d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNKZ666ZSH77C6KO3Q7SFA2BHP/bundle.json","state_url":"https://pith.science/pith/XNKZ666ZSH77C6KO3Q7SFA2BHP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNKZ666ZSH77C6KO3Q7SFA2BHP/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":"2026-06-21T23:39:28Z","links":{"resolver":"https://pith.science/pith/XNKZ666ZSH77C6KO3Q7SFA2BHP","bundle":"https://pith.science/pith/XNKZ666ZSH77C6KO3Q7SFA2BHP/bundle.json","state":"https://pith.science/pith/XNKZ666ZSH77C6KO3Q7SFA2BHP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNKZ666ZSH77C6KO3Q7SFA2BHP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XNKZ666ZSH77C6KO3Q7SFA2BHP","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":"35c5450b31a0b5ece4a94aa913c77d3d776bcd67de17310f7e0890e1b518acdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-12T08:52:40Z","title_canon_sha256":"be2b05ae039bcaec64d12ebecd6e7e7b972233760bef98219ec44b673d60a865"},"schema_version":"1.0","source":{"id":"1603.04694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04694","created_at":"2026-05-18T01:18:59Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04694v2","created_at":"2026-05-18T01:18:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04694","created_at":"2026-05-18T01:18:59Z"},{"alias_kind":"pith_short_12","alias_value":"XNKZ666ZSH77","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XNKZ666ZSH77C6KO","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XNKZ666Z","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:e4e1265d0c6b563e68bc0dcc8add4fd0ab13307098315b4a6a76a8a8328a685d","target":"graph","created_at":"2026-05-18T01:18:59Z","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 work we establish some polynomials and entire functions have only real zeros. These polynomials generalize q-Laguerre polynomials $L_{n}^{(\\alpha)}(x;q)$, while the entire functions are generalizations of Ramanujan's entire function $A_{q}(z)$, q-Bessel functions $J_{\\nu}^{(2)}(z;q)$, $J_{\\nu}^{(3)}(z;q)$ and confluent basic hypergeometric series.","authors_text":"Ruiming Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-12T08:52:40Z","title":"Zeros of Ramanujan Type Entire Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04694","kind":"arxiv","version":2},"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":"sha256:848be84dc3e88b7213a6f67a5c7f4a8e95627d01ab43aaff5eea87ea552b6c17","target":"record","created_at":"2026-05-18T01:18:59Z","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":"35c5450b31a0b5ece4a94aa913c77d3d776bcd67de17310f7e0890e1b518acdb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-12T08:52:40Z","title_canon_sha256":"be2b05ae039bcaec64d12ebecd6e7e7b972233760bef98219ec44b673d60a865"},"schema_version":"1.0","source":{"id":"1603.04694","kind":"arxiv","version":2}},"canonical_sha256":"bb559f7bd991fff1794edc3f2283413bc1931cd85f9b8b81a9a3798015bf7594","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb559f7bd991fff1794edc3f2283413bc1931cd85f9b8b81a9a3798015bf7594","first_computed_at":"2026-05-18T01:18:59.832607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:59.832607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eaaKw3vx+9qrpD+OVP8CfszvWbdfUbakpXuXdoZUA/+Y116mt2oZga3PQETXE32s162quD8yDf1UltrjUM4WAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:59.833035Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:848be84dc3e88b7213a6f67a5c7f4a8e95627d01ab43aaff5eea87ea552b6c17","sha256:e4e1265d0c6b563e68bc0dcc8add4fd0ab13307098315b4a6a76a8a8328a685d"],"state_sha256":"4e80a5080078e84360fb9c981d0ab38607178d9e7ba87297c399ea4f5d8bac7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLYnY8MNEJvfgBSBy1amuO9rnS8rKNQL+qG6eSV+ChM2tqmFoqSisWT5tekhPbmZi9AsCWPQkTCQeTXh7lgvCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:39:28.592951Z","bundle_sha256":"a03d04d4df709d8f00f6b772b5bec13629c60184f6ad10a7e911962201249878"}}