{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UHA74W47XIXAQLCF2WJ2LRO7ZR","short_pith_number":"pith:UHA74W47","canonical_record":{"source":{"id":"1808.07133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T21:17:46Z","cross_cats_sorted":[],"title_canon_sha256":"5795afb5002007bf9fb6e371e7eaa1178ff75b3d61efbd50d4a76124caaacc35","abstract_canon_sha256":"84671221c8d3e77aceca1e438fea42ed9f6f276e8c02f9baab0e6e16e4bb3812"},"schema_version":"1.0"},"canonical_sha256":"a1c1fe5b9fba2e082c45d593a5c5dfcc59bf2f6cca2e24a29519b6eff0e95e01","source":{"kind":"arxiv","id":"1808.07133","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07133","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07133v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07133","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"UHA74W47XIXA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UHA74W47XIXAQLCF","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UHA74W47","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UHA74W47XIXAQLCF2WJ2LRO7ZR","target":"record","payload":{"canonical_record":{"source":{"id":"1808.07133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T21:17:46Z","cross_cats_sorted":[],"title_canon_sha256":"5795afb5002007bf9fb6e371e7eaa1178ff75b3d61efbd50d4a76124caaacc35","abstract_canon_sha256":"84671221c8d3e77aceca1e438fea42ed9f6f276e8c02f9baab0e6e16e4bb3812"},"schema_version":"1.0"},"canonical_sha256":"a1c1fe5b9fba2e082c45d593a5c5dfcc59bf2f6cca2e24a29519b6eff0e95e01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:29.867068Z","signature_b64":"fRWyDtfdA+QqkpKfFmgU+jRKHeKMKZcuLEMpbBN6aThQ5t+oZYl7YoHCuzlQ20y0gWotF1gozVYrjwPdhVVaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1c1fe5b9fba2e082c45d593a5c5dfcc59bf2f6cca2e24a29519b6eff0e95e01","last_reissued_at":"2026-05-18T00:07:29.866508Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:29.866508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.07133","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUjg24eDkCLHSiD6vz2VRUAa5hsFa60iTaakKNUzkxfSVs7xXZTTIVPhMGC332Qfg/KU2y1M9NVR77qCZqDGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:34:32.624892Z"},"content_sha256":"0a3c5199fe9c3d16aa2e737aca9cae7ee4fd66086f34e05a1af5750f12c8f96f","schema_version":"1.0","event_id":"sha256:0a3c5199fe9c3d16aa2e737aca9cae7ee4fd66086f34e05a1af5750f12c8f96f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UHA74W47XIXAQLCF2WJ2LRO7ZR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zeros of polynomials with four-term recurrence and linear coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andres Zumba, Khang Tran","submitted_at":"2018-08-21T21:17:46Z","abstract_excerpt":"This paper investigates the zero distribution of a sequence of polynomials $\\left\\{ P_{m}(z)\\right\\} _{m=0}^{\\infty}$ generated by the reciprocal of $1+ct+B(z)t^{2}+A(z)t^{3}$ where $c\\in\\mathbb{R}$ and $A(z)$, $B(z)$ are real linear polynomials. We study necessary and sufficient conditions for the reality of the zeros of $P_{m}(z)$. Under these conditions, we find an explicit interval containing these zeros, whose union forms a dense subset of this interval."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07133","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XxUNVzfNnXqVzn2sbbOn/0cNb4o177vXFqEWfJPUi0frEho/tFiLDwSNYlwscCrpYVLomvCg955Pkz5cn4FiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:34:32.625232Z"},"content_sha256":"beac68e3dade36373b44e18a52df647cd3f91e5b9cd23d1dc163fa4155e7ba99","schema_version":"1.0","event_id":"sha256:beac68e3dade36373b44e18a52df647cd3f91e5b9cd23d1dc163fa4155e7ba99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UHA74W47XIXAQLCF2WJ2LRO7ZR/bundle.json","state_url":"https://pith.science/pith/UHA74W47XIXAQLCF2WJ2LRO7ZR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UHA74W47XIXAQLCF2WJ2LRO7ZR/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":"2026-06-01T14:34:32Z","links":{"resolver":"https://pith.science/pith/UHA74W47XIXAQLCF2WJ2LRO7ZR","bundle":"https://pith.science/pith/UHA74W47XIXAQLCF2WJ2LRO7ZR/bundle.json","state":"https://pith.science/pith/UHA74W47XIXAQLCF2WJ2LRO7ZR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UHA74W47XIXAQLCF2WJ2LRO7ZR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UHA74W47XIXAQLCF2WJ2LRO7ZR","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":"84671221c8d3e77aceca1e438fea42ed9f6f276e8c02f9baab0e6e16e4bb3812","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T21:17:46Z","title_canon_sha256":"5795afb5002007bf9fb6e371e7eaa1178ff75b3d61efbd50d4a76124caaacc35"},"schema_version":"1.0","source":{"id":"1808.07133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07133","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07133v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07133","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"UHA74W47XIXA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UHA74W47XIXAQLCF","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UHA74W47","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:beac68e3dade36373b44e18a52df647cd3f91e5b9cd23d1dc163fa4155e7ba99","target":"graph","created_at":"2026-05-18T00:07:29Z","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":"This paper investigates the zero distribution of a sequence of polynomials $\\left\\{ P_{m}(z)\\right\\} _{m=0}^{\\infty}$ generated by the reciprocal of $1+ct+B(z)t^{2}+A(z)t^{3}$ where $c\\in\\mathbb{R}$ and $A(z)$, $B(z)$ are real linear polynomials. We study necessary and sufficient conditions for the reality of the zeros of $P_{m}(z)$. Under these conditions, we find an explicit interval containing these zeros, whose union forms a dense subset of this interval.","authors_text":"Andres Zumba, Khang Tran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T21:17:46Z","title":"Zeros of polynomials with four-term recurrence and linear coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07133","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":"sha256:0a3c5199fe9c3d16aa2e737aca9cae7ee4fd66086f34e05a1af5750f12c8f96f","target":"record","created_at":"2026-05-18T00:07:29Z","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":"84671221c8d3e77aceca1e438fea42ed9f6f276e8c02f9baab0e6e16e4bb3812","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T21:17:46Z","title_canon_sha256":"5795afb5002007bf9fb6e371e7eaa1178ff75b3d61efbd50d4a76124caaacc35"},"schema_version":"1.0","source":{"id":"1808.07133","kind":"arxiv","version":1}},"canonical_sha256":"a1c1fe5b9fba2e082c45d593a5c5dfcc59bf2f6cca2e24a29519b6eff0e95e01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1c1fe5b9fba2e082c45d593a5c5dfcc59bf2f6cca2e24a29519b6eff0e95e01","first_computed_at":"2026-05-18T00:07:29.866508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:29.866508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fRWyDtfdA+QqkpKfFmgU+jRKHeKMKZcuLEMpbBN6aThQ5t+oZYl7YoHCuzlQ20y0gWotF1gozVYrjwPdhVVaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:29.867068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a3c5199fe9c3d16aa2e737aca9cae7ee4fd66086f34e05a1af5750f12c8f96f","sha256:beac68e3dade36373b44e18a52df647cd3f91e5b9cd23d1dc163fa4155e7ba99"],"state_sha256":"a868a23712db412649df2d536347bf9a3cf1435f163473c43471fe35789f0659"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/X9gANnWQOec43NGpUmM6MfXjM0+IWuaMQyO3Ru7002v/rI1OB+sQZd+gkFR82DE9n4p/r77YRMgiGP4ZMCDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:34:32.627087Z","bundle_sha256":"371243b419b7ebdba261bf2ec7223b24858c4014cdb8fc6b87b6aea716b0e5cb"}}