{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C7JZ7K77G3J6B5B363XD2MHWGP","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":"23143b5fbdca5c4e7a92d8de75d53393e00d4eabb2a3c8c5a9350758ff169219","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-29T13:47:14Z","title_canon_sha256":"4e1a0d63a7487df3796e859fddb56678d6c836f998e13db18f8ccfbb39f860f8"},"schema_version":"1.0","source":{"id":"1505.08043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.08043","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1505.08043v1","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.08043","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"C7JZ7K77G3J6","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C7JZ7K77G3J6B5B3","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C7JZ7K77","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:9acefb588a7dde6a6e9f2a53d68e8ee6259eae785d0c1f996768857f4b87a610","target":"graph","created_at":"2026-05-18T01:04:50Z","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":"We prove that a random word of length $n$ over a $k$-ary fixed alphabet contains, on expectation, $\\Theta(\\sqrt{n})$ distinct palindromic factors. We study this number of factors, $E(n,k)$, in detail, showing that the limit $\\lim_{n\\to\\infty}E(n,k)/\\sqrt{n}$ does not exist for any $k\\ge2$, $\\liminf_{n\\to\\infty}E(n,k)/\\sqrt{n}=\\Theta(1)$, and $\\limsup_{n\\to\\infty}E(n,k)/\\sqrt{n}=\\Theta(\\sqrt{k})$. Such a complicated behaviour stems from the asymmetry between the palindromes of even and odd length. We show that a similar, but much simpler, result on the expected number of squares in random words","authors_text":"Arseny M. Shur, Mikhail Rubinchik","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-29T13:47:14Z","title":"The Number of Distinct Subpalindromes in Random Words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08043","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":"sha256:4cd1e642ce3f8c29beb5eac9ad6fab9a2667333daa73274c6b86874149b1af12","target":"record","created_at":"2026-05-18T01:04:50Z","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":"23143b5fbdca5c4e7a92d8de75d53393e00d4eabb2a3c8c5a9350758ff169219","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-29T13:47:14Z","title_canon_sha256":"4e1a0d63a7487df3796e859fddb56678d6c836f998e13db18f8ccfbb39f860f8"},"schema_version":"1.0","source":{"id":"1505.08043","kind":"arxiv","version":1}},"canonical_sha256":"17d39fabff36d3e0f43bf6ee3d30f633d25c7c1a7e8fcdc57a13d7bf03319c41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17d39fabff36d3e0f43bf6ee3d30f633d25c7c1a7e8fcdc57a13d7bf03319c41","first_computed_at":"2026-05-18T01:04:50.576995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.576995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eMaRY7LzMVLYZa/CZPfXjt46oGzADy1p6VWxhWBk+ymFD5P1zNpS2brIT7ppY7zACw7qR2BhioI315sxjJpXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.577396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.08043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cd1e642ce3f8c29beb5eac9ad6fab9a2667333daa73274c6b86874149b1af12","sha256:9acefb588a7dde6a6e9f2a53d68e8ee6259eae785d0c1f996768857f4b87a610"],"state_sha256":"a0ad985b6195eac946f3434996b1da84056e07e5a700815ac2c2e88e8033c1e6"}