{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DC5IDYJWOQEZRWRENEJZAKOYIV","short_pith_number":"pith:DC5IDYJW","schema_version":"1.0","canonical_sha256":"18ba81e136740998da2469139029d8455df35a59684d67728be5d6da19d02efe","source":{"kind":"arxiv","id":"1802.00136","version":3},"attestation_state":"computed","paper":{"title":"Redundancy of unbounded memory Markov classes with continuity conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Changlong Wu, Maryam Hosseini, Narayana Santhanam","submitted_at":"2018-02-01T03:03:31Z","abstract_excerpt":"We study the redundancy of universally compressing strings $X_1,\\dots, X_n$ generated by a binary Markov source $p$ without any bound on the memory. To better understand the connection between compression and estimation in the Markov regime, we consider a class of Markov sources restricted by a continuity condition. In the absence of an upper bound on memory, the continuity condition implies that $p(X_0|X^{-1}_{-m})$ gets closer to the true probability $p(X_0|X_{-\\infty}^{-1})$ as $m$ increases, rather than vary around arbitrarily. For such sources, we prove asymptotically matching upper and l"},"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":"1802.00136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-02-01T03:03:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"16c8996ae27b253b5825ae342a08b173e657e69731a2bdbc2939c4a9ceb6e113","abstract_canon_sha256":"341bf4b255a332fb158713fa80b5f0ddb9c623b30cd8ac10008dd13528283ce2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:48.394270Z","signature_b64":"o8A0D+FkyYu89YJEdNIYXGrAuf+wQTNHiGbQw7IWPzdKDuxWw2LXt34oBP8DieHDWdVajr+HdpFPRCmolzmWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18ba81e136740998da2469139029d8455df35a59684d67728be5d6da19d02efe","last_reissued_at":"2026-05-18T00:12:48.393787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:48.393787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Redundancy of unbounded memory Markov classes with continuity conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Changlong Wu, Maryam Hosseini, Narayana Santhanam","submitted_at":"2018-02-01T03:03:31Z","abstract_excerpt":"We study the redundancy of universally compressing strings $X_1,\\dots, X_n$ generated by a binary Markov source $p$ without any bound on the memory. To better understand the connection between compression and estimation in the Markov regime, we consider a class of Markov sources restricted by a continuity condition. In the absence of an upper bound on memory, the continuity condition implies that $p(X_0|X^{-1}_{-m})$ gets closer to the true probability $p(X_0|X_{-\\infty}^{-1})$ as $m$ increases, rather than vary around arbitrarily. For such sources, we prove asymptotically matching upper and l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00136","kind":"arxiv","version":3},"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":"1802.00136","created_at":"2026-05-18T00:12:48.393857+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.00136v3","created_at":"2026-05-18T00:12:48.393857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00136","created_at":"2026-05-18T00:12:48.393857+00:00"},{"alias_kind":"pith_short_12","alias_value":"DC5IDYJWOQEZ","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DC5IDYJWOQEZRWRE","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DC5IDYJW","created_at":"2026-05-18T12:32:19.392346+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/DC5IDYJWOQEZRWRENEJZAKOYIV","json":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV.json","graph_json":"https://pith.science/api/pith-number/DC5IDYJWOQEZRWRENEJZAKOYIV/graph.json","events_json":"https://pith.science/api/pith-number/DC5IDYJWOQEZRWRENEJZAKOYIV/events.json","paper":"https://pith.science/paper/DC5IDYJW"},"agent_actions":{"view_html":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV","download_json":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV.json","view_paper":"https://pith.science/paper/DC5IDYJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.00136&json=true","fetch_graph":"https://pith.science/api/pith-number/DC5IDYJWOQEZRWRENEJZAKOYIV/graph.json","fetch_events":"https://pith.science/api/pith-number/DC5IDYJWOQEZRWRENEJZAKOYIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV/action/storage_attestation","attest_author":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV/action/author_attestation","sign_citation":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV/action/citation_signature","submit_replication":"https://pith.science/pith/DC5IDYJWOQEZRWRENEJZAKOYIV/action/replication_record"}},"created_at":"2026-05-18T00:12:48.393857+00:00","updated_at":"2026-05-18T00:12:48.393857+00:00"}