{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RW5YUGGFNTRTSTFCXJMHMZBI64","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":"ac27f45a7384c328e5951530505003988fc0e8e79d270562b8484cea8bb278ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-02T03:27:15Z","title_canon_sha256":"c6e190dd7064e74b3995ad0e421fc970812cf2106ceb532d4308b9f4d1f7c4c7"},"schema_version":"1.0","source":{"id":"2607.01655","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01655","created_at":"2026-07-03T01:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01655v1","created_at":"2026-07-03T01:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01655","created_at":"2026-07-03T01:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"RW5YUGGFNTRT","created_at":"2026-07-03T01:17:04Z"},{"alias_kind":"pith_short_16","alias_value":"RW5YUGGFNTRTSTFC","created_at":"2026-07-03T01:17:04Z"},{"alias_kind":"pith_short_8","alias_value":"RW5YUGGF","created_at":"2026-07-03T01:17:04Z"}],"graph_snapshots":[{"event_id":"sha256:7d26a656112e8a1b8202cd1011f5805094da01bef224e50c0e3604961cc97284","target":"graph","created_at":"2026-07-03T01:17:04Z","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/2607.01655/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider large Hermitian matrices whose entries are defined by evaluating the exponential function along orbits of the skew-shift \\(\\frac{j(j-1)}{2}\\omega + jy + x \\mod 1\\) for irrational \\(\\omega\\). We establish a rigorous connection between the effective Ratner equidistribution theorem for unipotent orbits in \\(\\SL(3,\\R)/\\SL(3,\\Z)\\) and the global semicircle law for such deterministic matrices. For frequency sequences satisfying a Diophantine condition, we prove that the empirical spectral distribution of these matrices converges to the Wigner semicircle law with optimal polynomial rate \\","authors_text":"Cong Chen, Yong Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-02T03:27:15Z","title":"Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01655","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":"sha256:8dc06f51efc3f2f6ad8ef510a47f82e15e4b61b573721d2fb953ea68ef65fdb5","target":"record","created_at":"2026-07-03T01:17:04Z","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":"ac27f45a7384c328e5951530505003988fc0e8e79d270562b8484cea8bb278ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-02T03:27:15Z","title_canon_sha256":"c6e190dd7064e74b3995ad0e421fc970812cf2106ceb532d4308b9f4d1f7c4c7"},"schema_version":"1.0","source":{"id":"2607.01655","kind":"arxiv","version":1}},"canonical_sha256":"8dbb8a18c56ce3394ca2ba58766428f73eb8b1e26593ae2562ff599aa6afdbde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dbb8a18c56ce3394ca2ba58766428f73eb8b1e26593ae2562ff599aa6afdbde","first_computed_at":"2026-07-03T01:17:04.627454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-03T01:17:04.627454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2fWdZSiRndcpyjaQjLabHXKLFmRiZWrO+VHPsMh4v/xI/eNAbyyRoHPGyJWF6KwKz2IqVvJKT7sV+WtZrLbhAg==","signature_status":"signed_v1","signed_at":"2026-07-03T01:17:04.627886Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dc06f51efc3f2f6ad8ef510a47f82e15e4b61b573721d2fb953ea68ef65fdb5","sha256:7d26a656112e8a1b8202cd1011f5805094da01bef224e50c0e3604961cc97284"],"state_sha256":"eabc253b4aff0f2bc15e32a68f1149f91394c35698b8fb98db3e794cbab147a7"}