{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6KNULCNPJS6L2XA262INPEWX6P","short_pith_number":"pith:6KNULCNP","schema_version":"1.0","canonical_sha256":"f29b4589af4cbcbd5c1af690d792d7f3ccbbe2f38d1c8a573f54f97da4d37f96","source":{"kind":"arxiv","id":"1712.06022","version":1},"attestation_state":"computed","paper":{"title":"Homogeneous finitely presented monoids of linear growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Dmitri Piontkovski","submitted_at":"2017-12-16T21:25:47Z","abstract_excerpt":"If a finitely generated monoid M is defined by a finite number of degree-preserving relations, then it has linear growth if and only if it can be decomposed into a finite disjoint union of subsets (which we call \"sandwiches\") of the form $a<w>b$, where $a,b,w$ are elements of $M$ and $<w>$ denotes the monogenic semigroup generated by $w$. Moreover, the decomposition can be chosen in such a way that the sandwiches are either singletons or \"free\" ones (meaning that all elements $a w^n b$ in each sandwich are pairwise different). So, the minimal number of free sandwiches in such a decomposition i"},"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":"1712.06022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-12-16T21:25:47Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"67f7996fd033d41e6ed6cc2f13ab8c06cb581cf52011a5eb0e47e537ca58f2af","abstract_canon_sha256":"9b0026ab0608ab2222aab213d2778f260bd19f9a9c2a2d64633b2e7fcfb68a49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:51.257562Z","signature_b64":"vRmUHAPuc+TomsmaNCYsAGWM64A4VDJ1rjFD3Ar0+3flcDJEhzTyq/ImEznOdMt9ig3So1Ly8vom76yV0eFXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f29b4589af4cbcbd5c1af690d792d7f3ccbbe2f38d1c8a573f54f97da4d37f96","last_reissued_at":"2026-05-18T00:27:51.257161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:51.257161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homogeneous finitely presented monoids of linear growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Dmitri Piontkovski","submitted_at":"2017-12-16T21:25:47Z","abstract_excerpt":"If a finitely generated monoid M is defined by a finite number of degree-preserving relations, then it has linear growth if and only if it can be decomposed into a finite disjoint union of subsets (which we call \"sandwiches\") of the form $a<w>b$, where $a,b,w$ are elements of $M$ and $<w>$ denotes the monogenic semigroup generated by $w$. Moreover, the decomposition can be chosen in such a way that the sandwiches are either singletons or \"free\" ones (meaning that all elements $a w^n b$ in each sandwich are pairwise different). So, the minimal number of free sandwiches in such a decomposition i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06022","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":"1712.06022","created_at":"2026-05-18T00:27:51.257220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.06022v1","created_at":"2026-05-18T00:27:51.257220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06022","created_at":"2026-05-18T00:27:51.257220+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KNULCNPJS6L","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KNULCNPJS6L2XA2","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KNULCNP","created_at":"2026-05-18T12:31:03.183658+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/6KNULCNPJS6L2XA262INPEWX6P","json":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P.json","graph_json":"https://pith.science/api/pith-number/6KNULCNPJS6L2XA262INPEWX6P/graph.json","events_json":"https://pith.science/api/pith-number/6KNULCNPJS6L2XA262INPEWX6P/events.json","paper":"https://pith.science/paper/6KNULCNP"},"agent_actions":{"view_html":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P","download_json":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P.json","view_paper":"https://pith.science/paper/6KNULCNP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.06022&json=true","fetch_graph":"https://pith.science/api/pith-number/6KNULCNPJS6L2XA262INPEWX6P/graph.json","fetch_events":"https://pith.science/api/pith-number/6KNULCNPJS6L2XA262INPEWX6P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P/action/storage_attestation","attest_author":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P/action/author_attestation","sign_citation":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P/action/citation_signature","submit_replication":"https://pith.science/pith/6KNULCNPJS6L2XA262INPEWX6P/action/replication_record"}},"created_at":"2026-05-18T00:27:51.257220+00:00","updated_at":"2026-05-18T00:27:51.257220+00:00"}