{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SHFVQZ3A47GAY4HMEHFF76K2GS","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":"978a3d7d167cad658ddf1233cff3c8842ee76bc91983cb2d97c93987cfdfe7a8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-08T20:08:21Z","title_canon_sha256":"79e1303f145c91611ed27d555ad0f3db4852e2cea6374287df5e40c8538b3d25"},"schema_version":"1.0","source":{"id":"2606.10134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10134","created_at":"2026-06-10T01:08:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10134v1","created_at":"2026-06-10T01:08:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10134","created_at":"2026-06-10T01:08:56Z"},{"alias_kind":"pith_short_12","alias_value":"SHFVQZ3A47GA","created_at":"2026-06-10T01:08:56Z"},{"alias_kind":"pith_short_16","alias_value":"SHFVQZ3A47GAY4HM","created_at":"2026-06-10T01:08:56Z"},{"alias_kind":"pith_short_8","alias_value":"SHFVQZ3A","created_at":"2026-06-10T01:08:56Z"}],"graph_snapshots":[{"event_id":"sha256:36cd13c3c71f09909600307751c39d9b5d6fe6cb526678da7218112ce6ee2526","target":"graph","created_at":"2026-06-10T01:08:56Z","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/2606.10134/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study local eigenvalue spacing for finite truncations of a two-sided Jacobi matrix with two movable endpoints. In particular, we show that a suitable analog of clock spacing follows from a pointwise reflectionlessness condition. We obtain this as a consequence of a new scaling limit for Christoffel--Darboux kernels with a movable starting point. Without reflectionlessness, we obtain a new class of limit kernels, which combine distinct contributions from $\\pm\\infty$.","authors_text":"Benjamin Eichinger, Giorgio Young, Milivoje Luki\\'c","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-08T20:08:21Z","title":"Clock spacing for two-sided Jacobi matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10134","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":"sha256:921b42b66012757d7a3b8cf30f9e97cbf29d2988ef0394a75693e806c69f0894","target":"record","created_at":"2026-06-10T01:08:56Z","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":"978a3d7d167cad658ddf1233cff3c8842ee76bc91983cb2d97c93987cfdfe7a8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-06-08T20:08:21Z","title_canon_sha256":"79e1303f145c91611ed27d555ad0f3db4852e2cea6374287df5e40c8538b3d25"},"schema_version":"1.0","source":{"id":"2606.10134","kind":"arxiv","version":1}},"canonical_sha256":"91cb586760e7cc0c70ec21ca5ff95a34bfce5c5892d0350bab078435eeeb37d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91cb586760e7cc0c70ec21ca5ff95a34bfce5c5892d0350bab078435eeeb37d8","first_computed_at":"2026-06-10T01:08:56.060356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:08:56.060356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Asermr7dXnXAq6LuK6fMyJevTlGtXJPnlQfjd0FBaFL6IyImdgIcIe8cZugj2eRwz1SKZxiCpDs2bFANVQnHAQ==","signature_status":"signed_v1","signed_at":"2026-06-10T01:08:56.061553Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:921b42b66012757d7a3b8cf30f9e97cbf29d2988ef0394a75693e806c69f0894","sha256:36cd13c3c71f09909600307751c39d9b5d6fe6cb526678da7218112ce6ee2526"],"state_sha256":"ecded9a5f215ce8c28e0d8e6bc6c52d073b4b9b217c98ca0f23cd69fa3809e6d"}