{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2GMSXSFAXA7XAWKBUIAXWGAMSA","short_pith_number":"pith:2GMSXSFA","schema_version":"1.0","canonical_sha256":"d1992bc8a0b83f705941a2017b180c900cbf42cfa7cc8918da57d40909a710ca","source":{"kind":"arxiv","id":"2607.28379","version":1},"attestation_state":"computed","paper":{"title":"New universality classes associated to fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.SP","authors_text":"Alexander Kheifets, Benjamin Eichinger, Milivoje Luki\\'c, Peter Yuditskii","submitted_at":"2026-07-30T15:39:55Z","abstract_excerpt":"The local behavior of zeros of orthogonal polynomials is determined by the local scaling behavior of Christoffel-Darboux (CD) kernels. All previously studied behaviors are described by scaling limits, and different values of the limit kernel correspond to different universality classes. In this paper, we describe new universality classes in which instead of a single limit kernel, there is a limit cycle. These are naturally suited to Cantor spectra and to fractal behaviors of the measure. We show that these new phenomena occur for two canonical models with singular measures: the middle third Ca"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.28379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2026-07-30T15:39:55Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"c8093ca41a70028eea1c21a808ccc876a5afc41a5558f9b7ea66d8deb379e4c9","abstract_canon_sha256":"f97676b930e0007b96ad7ad82546975d2b22f272021c60be2e380fb5e48a7729"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1992bc8a0b83f705941a2017b180c900cbf42cfa7cc8918da57d40909a710ca","last_reissued_at":"2026-07-31T01:37:29.114909Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:37:29.114909Z"},"graph_snapshot":{"paper":{"title":"New universality classes associated to fractals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.SP","authors_text":"Alexander Kheifets, Benjamin Eichinger, Milivoje Luki\\'c, Peter Yuditskii","submitted_at":"2026-07-30T15:39:55Z","abstract_excerpt":"The local behavior of zeros of orthogonal polynomials is determined by the local scaling behavior of Christoffel-Darboux (CD) kernels. All previously studied behaviors are described by scaling limits, and different values of the limit kernel correspond to different universality classes. In this paper, we describe new universality classes in which instead of a single limit kernel, there is a limit cycle. These are naturally suited to Cantor spectra and to fractal behaviors of the measure. We show that these new phenomena occur for two canonical models with singular measures: the middle third Ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28379","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/2607.28379/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.28379","created_at":"2026-07-31T01:37:29.118001+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.28379v1","created_at":"2026-07-31T01:37:29.118001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28379","created_at":"2026-07-31T01:37:29.118001+00:00"},{"alias_kind":"pith_short_12","alias_value":"2GMSXSFAXA7X","created_at":"2026-07-31T01:37:29.118001+00:00"},{"alias_kind":"pith_short_16","alias_value":"2GMSXSFAXA7XAWKB","created_at":"2026-07-31T01:37:29.118001+00:00"},{"alias_kind":"pith_short_8","alias_value":"2GMSXSFA","created_at":"2026-07-31T01:37:29.118001+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA","json":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA.json","graph_json":"https://pith.science/api/pith-number/2GMSXSFAXA7XAWKBUIAXWGAMSA/graph.json","events_json":"https://pith.science/api/pith-number/2GMSXSFAXA7XAWKBUIAXWGAMSA/events.json","paper":"https://pith.science/paper/2GMSXSFA"},"agent_actions":{"view_html":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA","download_json":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA.json","view_paper":"https://pith.science/paper/2GMSXSFA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.28379&json=true","fetch_graph":"https://pith.science/api/pith-number/2GMSXSFAXA7XAWKBUIAXWGAMSA/graph.json","fetch_events":"https://pith.science/api/pith-number/2GMSXSFAXA7XAWKBUIAXWGAMSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA/action/storage_attestation","attest_author":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA/action/author_attestation","sign_citation":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA/action/citation_signature","submit_replication":"https://pith.science/pith/2GMSXSFAXA7XAWKBUIAXWGAMSA/action/replication_record"}},"created_at":"2026-07-31T01:37:29.118001+00:00","updated_at":"2026-07-31T01:37:29.118001+00:00"}