{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WW3PZNRBLJATADTPGHMOUZFPIT","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":"20a3b324a16fafe6a068f39382a4aa64af3a971f4f9c35d6605b2a602a60dd50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-05T19:29:59Z","title_canon_sha256":"cb8046280260200b4c08419306028c653c48b6e915b48152511bfc26470b80da"},"schema_version":"1.0","source":{"id":"1511.01860","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01860","created_at":"2026-05-18T00:16:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01860v2","created_at":"2026-05-18T00:16:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01860","created_at":"2026-05-18T00:16:14Z"},{"alias_kind":"pith_short_12","alias_value":"WW3PZNRBLJAT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WW3PZNRBLJATADTP","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WW3PZNRB","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:422e269a367cfd1b83f34772fd8633a087c5328f9d44c4bd524f59191e3354bb","target":"graph","created_at":"2026-05-18T00:16:14Z","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":"Let $S$ be a finite semigroup and let $A$ be a finite dimensional $S$-graded algebra. We investigate the exponential rate of growth of the sequence of graded codimensions $c_n^S(A)$ of $A$, i.e $\\lim\\limits_{n \\rightarrow \\infty} \\sqrt[n]{c_n^S(A)}$. For group gradings this is always an integer. Recently in [20] the first example of an algebra with a non-integer growth rate was found. We present a large class of algebras for which we prove that their growth rate can be equal to arbitrarily large non-integers. An explicit formula is given. Surprisingly, this class consists of an infinite family","authors_text":"Alexey Gordienko, Eric Jespers, Geoffrey Janssens","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-05T19:29:59Z","title":"Semigroup graded algebras and graded PI-exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01860","kind":"arxiv","version":2},"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":"sha256:423b92971023220b7926628c353377b8e042e9e25627adae94675e022f08ad07","target":"record","created_at":"2026-05-18T00:16:14Z","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":"20a3b324a16fafe6a068f39382a4aa64af3a971f4f9c35d6605b2a602a60dd50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-11-05T19:29:59Z","title_canon_sha256":"cb8046280260200b4c08419306028c653c48b6e915b48152511bfc26470b80da"},"schema_version":"1.0","source":{"id":"1511.01860","kind":"arxiv","version":2}},"canonical_sha256":"b5b6fcb6215a41300e6f31d8ea64af44f144223a75aedcf7829ad352ab319438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5b6fcb6215a41300e6f31d8ea64af44f144223a75aedcf7829ad352ab319438","first_computed_at":"2026-05-18T00:16:14.926800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:14.926800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b1YafMHRqoh2pyyfA0+c/0IdlV6hKN859kFjRqxgMxZcmV8+02sf6bwfVueUsSt/K2l2zJU7ga/6dKv/IDNsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:14.927413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01860","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:423b92971023220b7926628c353377b8e042e9e25627adae94675e022f08ad07","sha256:422e269a367cfd1b83f34772fd8633a087c5328f9d44c4bd524f59191e3354bb"],"state_sha256":"7a1e3457a0998b6b15b18441b63b889d7d0597cfbe650e6a709583976d9271a4"}