{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XTOIUDZ4K2NAQTTFHBYD5ET2VK","short_pith_number":"pith:XTOIUDZ4","canonical_record":{"source":{"id":"1505.07788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-28T18:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"389ce3fa817ecd20cbbfb43a346eaa45ca5e9552417a684b1b09de4daeed50ec","abstract_canon_sha256":"0d35e955c2eaec636a84905f9f2300fa257b9140e71e48fa059610739f496232"},"schema_version":"1.0"},"canonical_sha256":"bcdc8a0f3c569a084e6538703e927aaa9b3deea9709143d0824bc22c20f1f94a","source":{"kind":"arxiv","id":"1505.07788","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07788","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07788v2","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07788","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"XTOIUDZ4K2NA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XTOIUDZ4K2NAQTTF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XTOIUDZ4","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XTOIUDZ4K2NAQTTFHBYD5ET2VK","target":"record","payload":{"canonical_record":{"source":{"id":"1505.07788","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-28T18:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"389ce3fa817ecd20cbbfb43a346eaa45ca5e9552417a684b1b09de4daeed50ec","abstract_canon_sha256":"0d35e955c2eaec636a84905f9f2300fa257b9140e71e48fa059610739f496232"},"schema_version":"1.0"},"canonical_sha256":"bcdc8a0f3c569a084e6538703e927aaa9b3deea9709143d0824bc22c20f1f94a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:02.733987Z","signature_b64":"3zXvggNuAl3UCRQ0YRPbyLjaR4Uc+PlB4gzLo2ROYqSGnaKixTuP3+Odc17cOl7P4WD9j/rwR8ib7wiXaH1oBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcdc8a0f3c569a084e6538703e927aaa9b3deea9709143d0824bc22c20f1f94a","last_reissued_at":"2026-05-18T00:12:02.733275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:02.733275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.07788","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":"2026-05-18T00:12:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/nl2X99SMemdjkKAWdCulWbgAfdLSe7glkCYel/xWuEvx9mSUFD5PCsTQhMRilUnSZVOydRcswStc5TgUVYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:04:08.019594Z"},"content_sha256":"d044c3eadd7c538a2e37100e59cb06682688787c9af23c1a3fa6d66d14f94c63","schema_version":"1.0","event_id":"sha256:d044c3eadd7c538a2e37100e59cb06682688787c9af23c1a3fa6d66d14f94c63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XTOIUDZ4K2NAQTTFHBYD5ET2VK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Martinez-Finkelshtein, A. Sri Ranga, Daniel O. Veronese","submitted_at":"2015-05-28T18:24:02Z","abstract_excerpt":"Given a non-trivial Borel measure $\\mu$ on the unit circle $\\mathbb T$, the corresponding reproducing (or Christoffel-Darboux) kernels with one of the variables fixed at $z=1$ constitute a family of so-called para-orthogonal polynomials, whose zeros belong to $\\mathbb T$. With a proper normalization they satisfy a three-term recurrence relation determined by two sequence of real coefficients, $\\{c_n\\}$ and $\\{d_n\\}$, where $\\{d_n\\}$ is additionally a positive chain sequence. Coefficients $(c_n,d_n)$ provide a parametrization of a family of measures related to $\\mu$ by addition of a mass point "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07788","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":"2026-05-18T00:12:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vad5KVWUCeTrAF+8t1Bqx/oYMdWENxqFgBl9DQQ8X/OWYfDOLcvkqXWfmN34HDrmoHa7cXNTckBXFpoLctXIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:04:08.020333Z"},"content_sha256":"06ad925743d3d52999f8eebd038e73fb91f4cecf6e7f02331d1d2b988068d431","schema_version":"1.0","event_id":"sha256:06ad925743d3d52999f8eebd038e73fb91f4cecf6e7f02331d1d2b988068d431"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XTOIUDZ4K2NAQTTFHBYD5ET2VK/bundle.json","state_url":"https://pith.science/pith/XTOIUDZ4K2NAQTTFHBYD5ET2VK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XTOIUDZ4K2NAQTTFHBYD5ET2VK/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":"2026-06-08T18:04:08Z","links":{"resolver":"https://pith.science/pith/XTOIUDZ4K2NAQTTFHBYD5ET2VK","bundle":"https://pith.science/pith/XTOIUDZ4K2NAQTTFHBYD5ET2VK/bundle.json","state":"https://pith.science/pith/XTOIUDZ4K2NAQTTFHBYD5ET2VK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XTOIUDZ4K2NAQTTFHBYD5ET2VK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XTOIUDZ4K2NAQTTFHBYD5ET2VK","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":"0d35e955c2eaec636a84905f9f2300fa257b9140e71e48fa059610739f496232","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-28T18:24:02Z","title_canon_sha256":"389ce3fa817ecd20cbbfb43a346eaa45ca5e9552417a684b1b09de4daeed50ec"},"schema_version":"1.0","source":{"id":"1505.07788","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07788","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07788v2","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07788","created_at":"2026-05-18T00:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"XTOIUDZ4K2NA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XTOIUDZ4K2NAQTTF","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XTOIUDZ4","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:06ad925743d3d52999f8eebd038e73fb91f4cecf6e7f02331d1d2b988068d431","target":"graph","created_at":"2026-05-18T00:12:02Z","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":"Given a non-trivial Borel measure $\\mu$ on the unit circle $\\mathbb T$, the corresponding reproducing (or Christoffel-Darboux) kernels with one of the variables fixed at $z=1$ constitute a family of so-called para-orthogonal polynomials, whose zeros belong to $\\mathbb T$. With a proper normalization they satisfy a three-term recurrence relation determined by two sequence of real coefficients, $\\{c_n\\}$ and $\\{d_n\\}$, where $\\{d_n\\}$ is additionally a positive chain sequence. Coefficients $(c_n,d_n)$ provide a parametrization of a family of measures related to $\\mu$ by addition of a mass point ","authors_text":"A. Martinez-Finkelshtein, A. Sri Ranga, Daniel O. Veronese","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-28T18:24:02Z","title":"Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07788","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:d044c3eadd7c538a2e37100e59cb06682688787c9af23c1a3fa6d66d14f94c63","target":"record","created_at":"2026-05-18T00:12:02Z","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":"0d35e955c2eaec636a84905f9f2300fa257b9140e71e48fa059610739f496232","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-05-28T18:24:02Z","title_canon_sha256":"389ce3fa817ecd20cbbfb43a346eaa45ca5e9552417a684b1b09de4daeed50ec"},"schema_version":"1.0","source":{"id":"1505.07788","kind":"arxiv","version":2}},"canonical_sha256":"bcdc8a0f3c569a084e6538703e927aaa9b3deea9709143d0824bc22c20f1f94a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcdc8a0f3c569a084e6538703e927aaa9b3deea9709143d0824bc22c20f1f94a","first_computed_at":"2026-05-18T00:12:02.733275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:02.733275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3zXvggNuAl3UCRQ0YRPbyLjaR4Uc+PlB4gzLo2ROYqSGnaKixTuP3+Odc17cOl7P4WD9j/rwR8ib7wiXaH1oBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:02.733987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07788","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d044c3eadd7c538a2e37100e59cb06682688787c9af23c1a3fa6d66d14f94c63","sha256:06ad925743d3d52999f8eebd038e73fb91f4cecf6e7f02331d1d2b988068d431"],"state_sha256":"531b2a402f67fe452d396a17604ce2c8617832890bf35ea26763a9fe4c1db1d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8QZzGFpkxHPPEWkdXXlwmda3hnFC9TPx8OYQ0LkZi1rO6wnVCSA1r2174bsQ7/CgArhVYK22udhLxAHVK3YAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:04:08.023941Z","bundle_sha256":"636468097c12e35612ec00d2f6d94035794306d07ac7e9d9d630d398f23b809a"}}