{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:U26IXM3RKLGNBQE5ELBE3UURL4","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":"296cc920fa922bd1762ec8ce7593294cef24a7ea058c8ccdc806cef21a88818d","cross_cats_sorted":["cs.IT","math.IT","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-07T11:12:11Z","title_canon_sha256":"2befe0005fda628298c3278aef235cbb33c7d8fe8902ca10f87a7eaac9f27353"},"schema_version":"1.0","source":{"id":"1511.02339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02339","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02339v1","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02339","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"U26IXM3RKLGN","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"U26IXM3RKLGNBQE5","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"U26IXM3R","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:6cda17e20f08e9627a2e4709fbe4c666f360344955aee0ec7b2a6ccff42c7507","target":"graph","created_at":"2026-05-18T01:27:30Z","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":"Besides the different approaches suggested in the literature, accurate estimation of the order of a Markov chain from a given symbol sequence is an open issue, especially when the order is moderately large. Here, parametric significance tests of conditional mutual information (CMI) of increasing order $m$, $I_c(m)$, on a symbol sequence are conducted for increasing orders $m$ in order to estimate the true order $L$ of the underlying Markov chain. CMI of order $m$ is the mutual information of two variables in the Markov chain being $m$ time steps apart, conditioning on the intermediate variable","authors_text":"Dimitris Kugiumtzis, Maria Papapetrou","cross_cats":["cs.IT","math.IT","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-07T11:12:11Z","title":"Markov chain order estimation with parametric significance tests of conditional mutual information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02339","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":"sha256:6e0675f1cc499ab6b845082d82134739ec26547ab844014eefca613accc556cf","target":"record","created_at":"2026-05-18T01:27:30Z","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":"296cc920fa922bd1762ec8ce7593294cef24a7ea058c8ccdc806cef21a88818d","cross_cats_sorted":["cs.IT","math.IT","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-11-07T11:12:11Z","title_canon_sha256":"2befe0005fda628298c3278aef235cbb33c7d8fe8902ca10f87a7eaac9f27353"},"schema_version":"1.0","source":{"id":"1511.02339","kind":"arxiv","version":1}},"canonical_sha256":"a6bc8bb37152ccd0c09d22c24dd2915f3cbb19c61781a6005a3b51b7cad126a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6bc8bb37152ccd0c09d22c24dd2915f3cbb19c61781a6005a3b51b7cad126a6","first_computed_at":"2026-05-18T01:27:30.598001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:30.598001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+bkoPP2Ytt/yjJMAHMceJ5dfvTWCPkQCGcHBo0wsacw1wxVcEr4PK9VhKB58XHzylcxiPZ/DT3ly8r//fcOsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:30.598549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e0675f1cc499ab6b845082d82134739ec26547ab844014eefca613accc556cf","sha256:6cda17e20f08e9627a2e4709fbe4c666f360344955aee0ec7b2a6ccff42c7507"],"state_sha256":"656cc752cee62681a292031632219ea1ae1873b25fe4051bc26f320118f55a87"}