{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Y6RZ6CQNNBGWAJ2HQKUDL5MS5B","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":"2505c5a9b5987253feca1d9a0ff1b3ec6eb67fdebb27a439a1eeb98efee7f266","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-04-17T02:35:59Z","title_canon_sha256":"0f06b13a5b6b6060ca64b9ed41b1a853c8eb8677e8826b017f846f7903231f61"},"schema_version":"1.0","source":{"id":"1404.4416","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4416","created_at":"2026-05-18T02:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4416v1","created_at":"2026-05-18T02:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4416","created_at":"2026-05-18T02:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"Y6RZ6CQNNBGW","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"Y6RZ6CQNNBGWAJ2H","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"Y6RZ6CQN","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:3f7c600e6b4c9c0aca71dae07a2cf1801e172e5d266d1dc1e79d2365c6b24182","target":"graph","created_at":"2026-05-18T02:54:04Z","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"},"paper":{"abstract_excerpt":"In this article, we show that the Kamae-Xue complexity function for an infinite sequence classifies eventual periodicity completely. We prove that an infinite binary word $x_1x_2 \\cdots $ is eventually periodic if and only if $\\Sigma(x_1x_2\\cdots x_n)/n^3$ has a positive limit, where $\\Sigma(x_1x_2\\cdots x_n)$ is the sum of the squares of all the numbers of appearance of finite words in $x_1 x_2 \\cdots x_n$, which was introduced by Kamae-Xue as a criterion of randomness in the sense that $x_1x_2\\cdots x_n$ is more random if $\\Sigma(x_1x_2\\cdots x_n)$ is smaller. In fact, it is known that the l","authors_text":"Dong Han Kim, Teturo Kamae","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-04-17T02:35:59Z","title":"A characterization of eventually periodicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4416","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:b0fe07a51faf9306358492f05e2be223257889749b5ba88c31b358a17bd04ffb","target":"record","created_at":"2026-05-18T02:54:04Z","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":"2505c5a9b5987253feca1d9a0ff1b3ec6eb67fdebb27a439a1eeb98efee7f266","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-04-17T02:35:59Z","title_canon_sha256":"0f06b13a5b6b6060ca64b9ed41b1a853c8eb8677e8826b017f846f7903231f61"},"schema_version":"1.0","source":{"id":"1404.4416","kind":"arxiv","version":1}},"canonical_sha256":"c7a39f0a0d684d60274782a835f592e869a9c8d2f8b81c1fb8b3f0a547c64c0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7a39f0a0d684d60274782a835f592e869a9c8d2f8b81c1fb8b3f0a547c64c0d","first_computed_at":"2026-05-18T02:54:04.425404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:04.425404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oB4LplhnWA4WRsnN5ywEf8VsFDYnaLtXN6pYhBza0OQ0GoBQNjaMuM9/top+qO0SI8p7AFCRM6Ee4cys7/WqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:04.425904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4416","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0fe07a51faf9306358492f05e2be223257889749b5ba88c31b358a17bd04ffb","sha256:3f7c600e6b4c9c0aca71dae07a2cf1801e172e5d266d1dc1e79d2365c6b24182"],"state_sha256":"5fbf3df7f9002e9034c83456477d0bbba2aff50f082ce0894b461a69220c2c70"}