{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ECMOIEGAYFYYTX3FP5J2RWMAJO","short_pith_number":"pith:ECMOIEGA","canonical_record":{"source":{"id":"2608.08714","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CV","submitted_at":"2026-08-09T13:58:26Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"51241ecc06bd856a8a4af93572c6c5f7129b4dd2868183c2fe63c3909deda2c3","abstract_canon_sha256":"e82a6bca9ab8ff6415a97872365b0a18944ed606febd83b980c30277f4af25b5"},"schema_version":"1.0"},"canonical_sha256":"2098e410c0c17189df657f53a8d9804b9b38398342609fd1df053cf50f630664","source":{"kind":"arxiv","id":"2608.08714","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08714","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08714v1","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08714","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"ECMOIEGAYFYY","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"pith_short_16","alias_value":"ECMOIEGAYFYYTX3F","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"pith_short_8","alias_value":"ECMOIEGA","created_at":"2026-08-11T01:25:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ECMOIEGAYFYYTX3FP5J2RWMAJO","target":"record","payload":{"canonical_record":{"source":{"id":"2608.08714","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CV","submitted_at":"2026-08-09T13:58:26Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"51241ecc06bd856a8a4af93572c6c5f7129b4dd2868183c2fe63c3909deda2c3","abstract_canon_sha256":"e82a6bca9ab8ff6415a97872365b0a18944ed606febd83b980c30277f4af25b5"},"schema_version":"1.0"},"canonical_sha256":"2098e410c0c17189df657f53a8d9804b9b38398342609fd1df053cf50f630664","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:25:07.577710Z","signature_b64":"38u+Nx7ytHR0UYoyoi5fTxfLQ8BXnTRRUExE4k8y+4fjkVtG9GTcaLXh2lsN32zONiCkD8OUoEyQGlDCrUbxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2098e410c0c17189df657f53a8d9804b9b38398342609fd1df053cf50f630664","last_reissued_at":"2026-08-11T01:25:07.575287Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:25:07.575287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.08714","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":"2026-08-11T01:25:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4u0BjCyTZG/e+3nId2dLuQ3nKqRJBRF41Y7z+E73ZMXmdZI63Mhm1qPpyiTcYd1CK3LhI3jM1lVNGnzNom6vCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T22:26:00.342271Z"},"content_sha256":"355aba2f80c4f1430f4125613a163eaae4b600334c717db90e8da7b16018ac4b","schema_version":"1.0","event_id":"sha256:355aba2f80c4f1430f4125613a163eaae4b600334c717db90e8da7b16018ac4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ECMOIEGAYFYYTX3FP5J2RWMAJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jacobi Endpoint Pencils and Sharp Interlacing for Centered Binomial Samples","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CV","authors_text":"Seokho Jin","submitted_at":"2026-08-09T13:58:26Z","abstract_excerpt":"For an even or odd real entire function $H$ of order at most one, let $B_{2n+1}[H]$ denote its centered binomial sample of odd degree. After removing the zero at $z=\\pm1$ forced by the parity of $H$ and writing $x=z+z^{-1}$, one obtains a real quotient $C_n(x)$. We prove uniform strip conditions on the zeros of $H$ under which $C_n$ and $C_{n+1}$ generate a real-rooted pencil for every $n$. For even $H$ the optimal uniform half-width is $\\sqrt{15/28}$, whereas for odd $H$ the half-width $1$ is sufficient. This conclusion is genuinely stronger than separate unit-circle-rootedness of the two sam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08714","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08714/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-11T01:25:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SRU9kJiO6fq13LQUWR1SQo5ZRd6UIBYyCaUDM+XjtuAqLeF5IGctcI40Ot2KsPWBrOkMClP1Pj2Pvtlqa1T9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T22:26:00.343270Z"},"content_sha256":"304254a582b9ef70cda4396a117a704ba88f1a705e8682f04480df7c3304c14c","schema_version":"1.0","event_id":"sha256:304254a582b9ef70cda4396a117a704ba88f1a705e8682f04480df7c3304c14c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECMOIEGAYFYYTX3FP5J2RWMAJO/bundle.json","state_url":"https://pith.science/pith/ECMOIEGAYFYYTX3FP5J2RWMAJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECMOIEGAYFYYTX3FP5J2RWMAJO/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":"2026-08-17T22:26:00Z","links":{"resolver":"https://pith.science/pith/ECMOIEGAYFYYTX3FP5J2RWMAJO","bundle":"https://pith.science/pith/ECMOIEGAYFYYTX3FP5J2RWMAJO/bundle.json","state":"https://pith.science/pith/ECMOIEGAYFYYTX3FP5J2RWMAJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECMOIEGAYFYYTX3FP5J2RWMAJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ECMOIEGAYFYYTX3FP5J2RWMAJO","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":"e82a6bca9ab8ff6415a97872365b0a18944ed606febd83b980c30277f4af25b5","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CV","submitted_at":"2026-08-09T13:58:26Z","title_canon_sha256":"51241ecc06bd856a8a4af93572c6c5f7129b4dd2868183c2fe63c3909deda2c3"},"schema_version":"1.0","source":{"id":"2608.08714","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08714","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08714v1","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08714","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"ECMOIEGAYFYY","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"pith_short_16","alias_value":"ECMOIEGAYFYYTX3F","created_at":"2026-08-11T01:25:07Z"},{"alias_kind":"pith_short_8","alias_value":"ECMOIEGA","created_at":"2026-08-11T01:25:07Z"}],"graph_snapshots":[{"event_id":"sha256:304254a582b9ef70cda4396a117a704ba88f1a705e8682f04480df7c3304c14c","target":"graph","created_at":"2026-08-11T01:25:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.08714/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For an even or odd real entire function $H$ of order at most one, let $B_{2n+1}[H]$ denote its centered binomial sample of odd degree. After removing the zero at $z=\\pm1$ forced by the parity of $H$ and writing $x=z+z^{-1}$, one obtains a real quotient $C_n(x)$. We prove uniform strip conditions on the zeros of $H$ under which $C_n$ and $C_{n+1}$ generate a real-rooted pencil for every $n$. For even $H$ the optimal uniform half-width is $\\sqrt{15/28}$, whereas for odd $H$ the half-width $1$ is sufficient. This conclusion is genuinely stronger than separate unit-circle-rootedness of the two sam","authors_text":"Seokho Jin","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CV","submitted_at":"2026-08-09T13:58:26Z","title":"Jacobi Endpoint Pencils and Sharp Interlacing for Centered Binomial Samples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08714","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":"sha256:355aba2f80c4f1430f4125613a163eaae4b600334c717db90e8da7b16018ac4b","target":"record","created_at":"2026-08-11T01:25:07Z","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":"e82a6bca9ab8ff6415a97872365b0a18944ed606febd83b980c30277f4af25b5","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CV","submitted_at":"2026-08-09T13:58:26Z","title_canon_sha256":"51241ecc06bd856a8a4af93572c6c5f7129b4dd2868183c2fe63c3909deda2c3"},"schema_version":"1.0","source":{"id":"2608.08714","kind":"arxiv","version":1}},"canonical_sha256":"2098e410c0c17189df657f53a8d9804b9b38398342609fd1df053cf50f630664","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2098e410c0c17189df657f53a8d9804b9b38398342609fd1df053cf50f630664","first_computed_at":"2026-08-11T01:25:07.575287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:25:07.575287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"38u+Nx7ytHR0UYoyoi5fTxfLQ8BXnTRRUExE4k8y+4fjkVtG9GTcaLXh2lsN32zONiCkD8OUoEyQGlDCrUbxCQ==","signature_status":"signed_v1","signed_at":"2026-08-11T01:25:07.577710Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.08714","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:355aba2f80c4f1430f4125613a163eaae4b600334c717db90e8da7b16018ac4b","sha256:304254a582b9ef70cda4396a117a704ba88f1a705e8682f04480df7c3304c14c"],"state_sha256":"ee908b322aaa432bc9889d1f4ea70d44d98d74eb36f8b1da76455295298199d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fl7P8LNqw7LOKA4IuDVlCVQ9IY2E/475FGUwK4eWCIuVQtd6UKmvCzdise4nX+WSJpx4ovX6x1NG8lNI0y/jBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T22:26:00.350661Z","bundle_sha256":"8def701d4faaffc895911343f5800c308f8bdf3ca01d7a79ba23793afd04f21a"}}