{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CZJSUKTYSAQ4YFE5ZQVC3KYQKW","short_pith_number":"pith:CZJSUKTY","schema_version":"1.0","canonical_sha256":"16532a2a789021cc149dcc2a2dab1055b3dba7478a67fad96d518144c8cca033","source":{"kind":"arxiv","id":"1301.0148","version":1},"attestation_state":"computed","paper":{"title":"Markov Chain Order estimation with Conditional Mutual Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ME"],"primary_cat":"physics.data-an","authors_text":"Dimitris Kugiumtzis, Maria Papapetrou","submitted_at":"2013-01-01T23:54:15Z","abstract_excerpt":"We introduce the Conditional Mutual Information (CMI) for the estimation of the Markov chain order. For a Markov chain of $K$ symbols, we define CMI of order $m$, $I_c(m)$, as the mutual information of two variables in the chain being $m$ time steps apart, conditioning on the intermediate variables of the chain. We find approximate analytic significance limits based on the estimation bias of CMI and develop a randomization significance test of $I_c(m)$, where the randomized symbol sequences are formed by random permutation of the components of the original symbol sequence. The significance tes"},"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":"1301.0148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.data-an","submitted_at":"2013-01-01T23:54:15Z","cross_cats_sorted":["cs.IT","math.IT","stat.ME"],"title_canon_sha256":"8704e58ef0f71d314cca1c2073078721470f113c68b8d11518e4304a8c6749e1","abstract_canon_sha256":"1d687f61dcd8ee0e57b2de94edcb0f52f12bb7b29241e38a5d7caf2f1b356ad0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:28.059727Z","signature_b64":"uo/UKDavtH2I45SNOMkJa12Ix1P7GCjdBsCYtitFDmVbnAqMX0XJBV7r8KVqh1pNfm8Mo4lUhyAYm8uQzzrfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16532a2a789021cc149dcc2a2dab1055b3dba7478a67fad96d518144c8cca033","last_reissued_at":"2026-05-18T03:37:28.059039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:28.059039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Markov Chain Order estimation with Conditional Mutual Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ME"],"primary_cat":"physics.data-an","authors_text":"Dimitris Kugiumtzis, Maria Papapetrou","submitted_at":"2013-01-01T23:54:15Z","abstract_excerpt":"We introduce the Conditional Mutual Information (CMI) for the estimation of the Markov chain order. For a Markov chain of $K$ symbols, we define CMI of order $m$, $I_c(m)$, as the mutual information of two variables in the chain being $m$ time steps apart, conditioning on the intermediate variables of the chain. We find approximate analytic significance limits based on the estimation bias of CMI and develop a randomization significance test of $I_c(m)$, where the randomized symbol sequences are formed by random permutation of the components of the original symbol sequence. The significance tes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0148","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":""},"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":"1301.0148","created_at":"2026-05-18T03:37:28.059147+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0148v1","created_at":"2026-05-18T03:37:28.059147+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0148","created_at":"2026-05-18T03:37:28.059147+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZJSUKTYSAQ4","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZJSUKTYSAQ4YFE5","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZJSUKTY","created_at":"2026-05-18T12:27:40.988391+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/CZJSUKTYSAQ4YFE5ZQVC3KYQKW","json":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW.json","graph_json":"https://pith.science/api/pith-number/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/graph.json","events_json":"https://pith.science/api/pith-number/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/events.json","paper":"https://pith.science/paper/CZJSUKTY"},"agent_actions":{"view_html":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW","download_json":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW.json","view_paper":"https://pith.science/paper/CZJSUKTY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0148&json=true","fetch_graph":"https://pith.science/api/pith-number/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/graph.json","fetch_events":"https://pith.science/api/pith-number/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/action/storage_attestation","attest_author":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/action/author_attestation","sign_citation":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/action/citation_signature","submit_replication":"https://pith.science/pith/CZJSUKTYSAQ4YFE5ZQVC3KYQKW/action/replication_record"}},"created_at":"2026-05-18T03:37:28.059147+00:00","updated_at":"2026-05-18T03:37:28.059147+00:00"}