{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QSHTFI435FIKEEDKVTKZIQMYZW","short_pith_number":"pith:QSHTFI43","schema_version":"1.0","canonical_sha256":"848f32a39be950a2106aacd5944198cda95d1c021b87bc509958c27b61c644a0","source":{"kind":"arxiv","id":"2606.30434","version":1},"attestation_state":"computed","paper":{"title":"On homological finiteness properties and free inverse monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Carl-Fredrik Nyberg-Brodda","submitted_at":"2026-06-29T15:11:56Z","abstract_excerpt":"We construct a simple and useful sufficient condition, based on actions on a lattice of idempotents, for monoids admitting homomorphisms to the monogenic free inverse monoid $\\mathrm{FIM}(1)$ to not be of type $\\mathrm{FP}_2$. This recovers a result of Gray and Steinberg that free inverse monoids are not of type $\\mathrm{FP}_2$. The same technique is then used to show that a finitely generated submonoid of $\\mathrm{FIM}(1)$ is of type $\\mathrm{FP}_2$ if and only if it is finitely presented, answering a question of Cho & Ru\\v{s}kuc."},"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":"2606.30434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-29T15:11:56Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"d8b87333b816600d37bb73c7aacb26a154ade244eb274fafb924ce295a47fae5","abstract_canon_sha256":"4926f3432bd6c92c825320c0fddac3c430b2936b8f99100f16c4bf6e1aa1acb6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:15.033560Z","signature_b64":"RtH4bTUmGYDB2Mhnhd+Ao/xmSAUpyeStOa6hfS5xLMn0hwA7nSxxpxV7W3zeRt5uIob5bYS3fRycIfe7uhtSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"848f32a39be950a2106aacd5944198cda95d1c021b87bc509958c27b61c644a0","last_reissued_at":"2026-06-30T02:18:15.033146Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:15.033146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On homological finiteness properties and free inverse monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Carl-Fredrik Nyberg-Brodda","submitted_at":"2026-06-29T15:11:56Z","abstract_excerpt":"We construct a simple and useful sufficient condition, based on actions on a lattice of idempotents, for monoids admitting homomorphisms to the monogenic free inverse monoid $\\mathrm{FIM}(1)$ to not be of type $\\mathrm{FP}_2$. This recovers a result of Gray and Steinberg that free inverse monoids are not of type $\\mathrm{FP}_2$. The same technique is then used to show that a finitely generated submonoid of $\\mathrm{FIM}(1)$ is of type $\\mathrm{FP}_2$ if and only if it is finitely presented, answering a question of Cho & Ru\\v{s}kuc."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30434","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30434/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.30434","created_at":"2026-06-30T02:18:15.033202+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30434v1","created_at":"2026-06-30T02:18:15.033202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30434","created_at":"2026-06-30T02:18:15.033202+00:00"},{"alias_kind":"pith_short_12","alias_value":"QSHTFI435FIK","created_at":"2026-06-30T02:18:15.033202+00:00"},{"alias_kind":"pith_short_16","alias_value":"QSHTFI435FIKEEDK","created_at":"2026-06-30T02:18:15.033202+00:00"},{"alias_kind":"pith_short_8","alias_value":"QSHTFI43","created_at":"2026-06-30T02:18:15.033202+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/QSHTFI435FIKEEDKVTKZIQMYZW","json":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW.json","graph_json":"https://pith.science/api/pith-number/QSHTFI435FIKEEDKVTKZIQMYZW/graph.json","events_json":"https://pith.science/api/pith-number/QSHTFI435FIKEEDKVTKZIQMYZW/events.json","paper":"https://pith.science/paper/QSHTFI43"},"agent_actions":{"view_html":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW","download_json":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW.json","view_paper":"https://pith.science/paper/QSHTFI43","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30434&json=true","fetch_graph":"https://pith.science/api/pith-number/QSHTFI435FIKEEDKVTKZIQMYZW/graph.json","fetch_events":"https://pith.science/api/pith-number/QSHTFI435FIKEEDKVTKZIQMYZW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW/action/storage_attestation","attest_author":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW/action/author_attestation","sign_citation":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW/action/citation_signature","submit_replication":"https://pith.science/pith/QSHTFI435FIKEEDKVTKZIQMYZW/action/replication_record"}},"created_at":"2026-06-30T02:18:15.033202+00:00","updated_at":"2026-06-30T02:18:15.033202+00:00"}