{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TSCB43ZHUP7U36FXHACAFLG7V7","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":"c9c603f90ab97d6df69915c12cdda22a7669e2df854dcbcd61ded42e08fc021b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-04T18:10:08Z","title_canon_sha256":"2153c627a4e5d78f6f524133af1cabe470c6de48c0fe72e274a36a2c0ae0da4f"},"schema_version":"1.0","source":{"id":"1211.0708","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0708","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0708v1","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0708","created_at":"2026-05-18T02:28:29Z"},{"alias_kind":"pith_short_12","alias_value":"TSCB43ZHUP7U","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TSCB43ZHUP7U36FX","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TSCB43ZH","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:d43b788bbcc687b55b98da798eeb77003e208894e58d0a4545087d9dae85e59c","target":"graph","created_at":"2026-05-18T02:28:29Z","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":"In this paper we consider the sequence of Kakutani's $\\alpha$-refinements corresponding to the inverse of golden ratio (which we call Kakutani-Fibonacci sequence of partitions) and associate to it an ergodic interval exchange (which we call Kakutani-Fibonacci transformation) using the \"cutting-stacking\" technique. We prove that the orbit of the origin under this map coincides with a low discrepancy sequence (which we call Kakutani-Fibonacci sequence of points), which has been also considered by other authors.","authors_text":"Aljo\\v{s}a Vol\\v{c}i\\v{c}, Ingrid Carbone, Maria Rita Iac\\`o","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-04T18:10:08Z","title":"A dynamical system approach to the Kakutani-Fibonacci sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0708","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":"sha256:84725fb67574347b4036d3d1882209cea7bc6b80bb780f2c771ea9d39d8d8ed6","target":"record","created_at":"2026-05-18T02:28:29Z","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":"c9c603f90ab97d6df69915c12cdda22a7669e2df854dcbcd61ded42e08fc021b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-11-04T18:10:08Z","title_canon_sha256":"2153c627a4e5d78f6f524133af1cabe470c6de48c0fe72e274a36a2c0ae0da4f"},"schema_version":"1.0","source":{"id":"1211.0708","kind":"arxiv","version":1}},"canonical_sha256":"9c841e6f27a3ff4df8b7380402acdfafca08f5b9caf4e71bbb7c70f55021e4e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c841e6f27a3ff4df8b7380402acdfafca08f5b9caf4e71bbb7c70f55021e4e0","first_computed_at":"2026-05-18T02:28:29.529989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:29.529989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"twcDFhzSy/Pb189XEXReAnhfVW7fPr1b3rpvhrriOTHmInh5eWxrVNuEITW+qk+XtRD/AWp8d6bY8jY7KPqPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:29.530376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0708","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84725fb67574347b4036d3d1882209cea7bc6b80bb780f2c771ea9d39d8d8ed6","sha256:d43b788bbcc687b55b98da798eeb77003e208894e58d0a4545087d9dae85e59c"],"state_sha256":"6fb6c06e09dc0f5f9c23cf8e1fc0a6a509446dc241112f5043f3a87550b5efc5"}