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We describe a normal basis of boundary algebras, i.e. algebras with small growth.\n  Let $\\cal L$ be a factor language over alphabet $\\cal A$. {\\it Growth function} $T_{\\cal L}(n)$ is number of subwords $\\cal L$ of degree $n$. We describe factor languages of small growth such that $T_{\\cal L}(n)\\le n+\\mbox{const}$."},"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":"1602.03510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-10T20:40:29Z","cross_cats_sorted":[],"title_canon_sha256":"3ce69813fa264159917ca7b2cf817e9814884cd84619cc2c6f0231ab2039b161","abstract_canon_sha256":"3209a996fd924e578b73d7b345fb06a5c0553c8f3724c8fe59fd174673855494"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:05.940323Z","signature_b64":"cB3XmnJDQ9/W43ZrRFV5M42bZeDuljt7EskgvH3T/mil0/eur6Yg2MSv5lTNJ4CzALRd3NpO6T60dILrDUJDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e26a04b7c8eeb8c5bda156d81d378dedec9227a385790214da8c4a746192f872","last_reissued_at":"2026-05-18T00:29:05.939873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:05.939873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Describtion of normal basis of boundary algebras and factor languages of small growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. L. Chernyatiev (HSE), Ariel, A. Ya. Belov (BIU, Mipt)","submitted_at":"2016-02-10T20:40:29Z","abstract_excerpt":"Let $A$ be an algebra with fixed set of generators $a_1,\\dots,a_s$. $V_A(n)$ be dimension of the space, generated by worlds of length $\\le n$ over $a_i$, $T_A(n)=V_A(n)-V_A(n-1)$. If $T_A(n)<\\mbox{Const}$, algebra $A$ is a {\\it boundary algebra}. We describe a normal basis of boundary algebras, i.e. algebras with small growth.\n  Let $\\cal L$ be a factor language over alphabet $\\cal A$. {\\it Growth function} $T_{\\cal L}(n)$ is number of subwords $\\cal L$ of degree $n$. We describe factor languages of small growth such that $T_{\\cal L}(n)\\le n+\\mbox{const}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03510","kind":"arxiv","version":2},"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":"1602.03510","created_at":"2026-05-18T00:29:05.939937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.03510v2","created_at":"2026-05-18T00:29:05.939937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03510","created_at":"2026-05-18T00:29:05.939937+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JVAJN6I524M","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JVAJN6I524MLPNB","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JVAJN6I","created_at":"2026-05-18T12:29:58.707656+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/4JVAJN6I524MLPNBK3MB2N4N5X","json":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X.json","graph_json":"https://pith.science/api/pith-number/4JVAJN6I524MLPNBK3MB2N4N5X/graph.json","events_json":"https://pith.science/api/pith-number/4JVAJN6I524MLPNBK3MB2N4N5X/events.json","paper":"https://pith.science/paper/4JVAJN6I"},"agent_actions":{"view_html":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X","download_json":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X.json","view_paper":"https://pith.science/paper/4JVAJN6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.03510&json=true","fetch_graph":"https://pith.science/api/pith-number/4JVAJN6I524MLPNBK3MB2N4N5X/graph.json","fetch_events":"https://pith.science/api/pith-number/4JVAJN6I524MLPNBK3MB2N4N5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X/action/storage_attestation","attest_author":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X/action/author_attestation","sign_citation":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X/action/citation_signature","submit_replication":"https://pith.science/pith/4JVAJN6I524MLPNBK3MB2N4N5X/action/replication_record"}},"created_at":"2026-05-18T00:29:05.939937+00:00","updated_at":"2026-05-18T00:29:05.939937+00:00"}