{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WI7SELW3CBINVFR2NFJGJFY35E","short_pith_number":"pith:WI7SELW3","canonical_record":{"source":{"id":"1312.2283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-08T23:59:44Z","cross_cats_sorted":[],"title_canon_sha256":"f948f48c7fdc6738ee6505dac6ad1c0648b08b3f4b9dd48f7569281806f08365","abstract_canon_sha256":"9a412c02e7af323c6275854a1a1a66e728cf2699af5eab391d57a42af718935b"},"schema_version":"1.0"},"canonical_sha256":"b23f222edb1050da963a695264971be90bd91b1bdb8114f7df64ff2c01466944","source":{"kind":"arxiv","id":"1312.2283","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2283","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2283v2","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2283","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"WI7SELW3CBIN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WI7SELW3CBINVFR2","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WI7SELW3","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WI7SELW3CBINVFR2NFJGJFY35E","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2283","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-08T23:59:44Z","cross_cats_sorted":[],"title_canon_sha256":"f948f48c7fdc6738ee6505dac6ad1c0648b08b3f4b9dd48f7569281806f08365","abstract_canon_sha256":"9a412c02e7af323c6275854a1a1a66e728cf2699af5eab391d57a42af718935b"},"schema_version":"1.0"},"canonical_sha256":"b23f222edb1050da963a695264971be90bd91b1bdb8114f7df64ff2c01466944","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:24.614356Z","signature_b64":"/kl1klAxKlEAOqfvo3Vx58TOJqvQICANKOVpX9n/QH+KyRgxJtXJs4M/RRFq0rbRdk581Z3ilj7QKGuKVC7QAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b23f222edb1050da963a695264971be90bd91b1bdb8114f7df64ff2c01466944","last_reissued_at":"2026-05-18T01:22:24.613657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:24.613657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2283","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":"2026-05-18T01:22:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gt9IDTn2yp3zBMJGtkTDzTwC+lL7KkAEDZ+3gcNhkJMR1g0cpY3RluWfQGM1j+K/gu7rhypJM8myHTGFfy+vDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:32:49.810993Z"},"content_sha256":"cef3e6f477563a8c39265f613da26882888eb2ac8fbf5b42f09f2a2274ba7bfd","schema_version":"1.0","event_id":"sha256:cef3e6f477563a8c39265f613da26882888eb2ac8fbf5b42f09f2a2274ba7bfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WI7SELW3CBINVFR2NFJGJFY35E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Real Zero Decreasing Operators Related to Orthogonal Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andre Bunton, Andrzej Piotrowski, Charles McKenry Jr., Louis Scott, Nicole Jacobs, Samantha Jenkins","submitted_at":"2013-12-08T23:59:44Z","abstract_excerpt":"Laguerre's theorem regarding the number of non-real zeros of a polynomial and its image under certain linear operators is generalized. This generalization is then used to (1) exhibit a number of previously undiscovered complex zero decreasing sequences for the Chebyshev, Legendre, and generalized Laguerre polynomial bases and (2) simultaneously generate a basis $B$ and a corresponding $B$-CZDS. Some extensions to transcendental entire functions in the Laguerre-Polya class are given which, in turn, give a new and short proof of a previously known result due to one of the authors. The paper conc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2283","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":"2026-05-18T01:22:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDxUkroK7yGOCle72KruGjoXEjFYrCHeVQ2LXRT4xFfx3IWRabtvJy+jVuQaVPW64bJ9sqld6LzBBRkxLsktDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:32:49.811339Z"},"content_sha256":"6996ab717583c44b5cf4b626ee91ec460724164da6f5e8944fbdbfb359d77a85","schema_version":"1.0","event_id":"sha256:6996ab717583c44b5cf4b626ee91ec460724164da6f5e8944fbdbfb359d77a85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WI7SELW3CBINVFR2NFJGJFY35E/bundle.json","state_url":"https://pith.science/pith/WI7SELW3CBINVFR2NFJGJFY35E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WI7SELW3CBINVFR2NFJGJFY35E/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":"2026-06-09T12:32:49Z","links":{"resolver":"https://pith.science/pith/WI7SELW3CBINVFR2NFJGJFY35E","bundle":"https://pith.science/pith/WI7SELW3CBINVFR2NFJGJFY35E/bundle.json","state":"https://pith.science/pith/WI7SELW3CBINVFR2NFJGJFY35E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WI7SELW3CBINVFR2NFJGJFY35E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WI7SELW3CBINVFR2NFJGJFY35E","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":"9a412c02e7af323c6275854a1a1a66e728cf2699af5eab391d57a42af718935b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-08T23:59:44Z","title_canon_sha256":"f948f48c7fdc6738ee6505dac6ad1c0648b08b3f4b9dd48f7569281806f08365"},"schema_version":"1.0","source":{"id":"1312.2283","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2283","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2283v2","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2283","created_at":"2026-05-18T01:22:24Z"},{"alias_kind":"pith_short_12","alias_value":"WI7SELW3CBIN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WI7SELW3CBINVFR2","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WI7SELW3","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:6996ab717583c44b5cf4b626ee91ec460724164da6f5e8944fbdbfb359d77a85","target":"graph","created_at":"2026-05-18T01:22:24Z","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":"Laguerre's theorem regarding the number of non-real zeros of a polynomial and its image under certain linear operators is generalized. This generalization is then used to (1) exhibit a number of previously undiscovered complex zero decreasing sequences for the Chebyshev, Legendre, and generalized Laguerre polynomial bases and (2) simultaneously generate a basis $B$ and a corresponding $B$-CZDS. Some extensions to transcendental entire functions in the Laguerre-Polya class are given which, in turn, give a new and short proof of a previously known result due to one of the authors. The paper conc","authors_text":"Andre Bunton, Andrzej Piotrowski, Charles McKenry Jr., Louis Scott, Nicole Jacobs, Samantha Jenkins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-08T23:59:44Z","title":"Non-Real Zero Decreasing Operators Related to Orthogonal Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2283","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:cef3e6f477563a8c39265f613da26882888eb2ac8fbf5b42f09f2a2274ba7bfd","target":"record","created_at":"2026-05-18T01:22:24Z","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":"9a412c02e7af323c6275854a1a1a66e728cf2699af5eab391d57a42af718935b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-12-08T23:59:44Z","title_canon_sha256":"f948f48c7fdc6738ee6505dac6ad1c0648b08b3f4b9dd48f7569281806f08365"},"schema_version":"1.0","source":{"id":"1312.2283","kind":"arxiv","version":2}},"canonical_sha256":"b23f222edb1050da963a695264971be90bd91b1bdb8114f7df64ff2c01466944","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b23f222edb1050da963a695264971be90bd91b1bdb8114f7df64ff2c01466944","first_computed_at":"2026-05-18T01:22:24.613657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:24.613657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/kl1klAxKlEAOqfvo3Vx58TOJqvQICANKOVpX9n/QH+KyRgxJtXJs4M/RRFq0rbRdk581Z3ilj7QKGuKVC7QAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:24.614356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2283","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cef3e6f477563a8c39265f613da26882888eb2ac8fbf5b42f09f2a2274ba7bfd","sha256:6996ab717583c44b5cf4b626ee91ec460724164da6f5e8944fbdbfb359d77a85"],"state_sha256":"037aa6cd6e369c1d8551f523e11b9df1863d57e4467022d519fcc9f7cea6a22e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJ0hxGT0mHfrVgG+cjFU95H5RZRUaArUZgjSpV2uL192IU0iu62ICRfBwGA43IunWyHohin3zuOF/8e/7fWBAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:32:49.813232Z","bundle_sha256":"0f22bf36e7ebd73df8928b67869b4d871abdf6b4e468cd59fe2928895676034a"}}