{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:ERIUSMA2DCRX7DCXUTWKP2II4V","short_pith_number":"pith:ERIUSMA2","schema_version":"1.0","canonical_sha256":"245149301a18a37f8c57a4eca7e908e575f61e78531b407174fbd6aa15e0837d","source":{"kind":"arxiv","id":"2205.15344","version":1},"attestation_state":"computed","paper":{"title":"Cluster structures for the $A_{\\infty}$ singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RT","authors_text":"Eleonore Faber, Jenny August, Man-Wai Cheung, Sibylle Schroll, Sira Gratz","submitted_at":"2022-05-30T18:00:08Z","abstract_excerpt":"We study a category $\\mathcal{C}_2$ of $\\mathbb{Z}$-graded MCM modules over the $A_\\infty$ curve singularity and demonstrate it has infinite type $A$ cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategory) is stably equivalent to the infinite type $A$ cluster categories of Holm-Jorgensen, Fisher and Paquette-Yildirim. As a consequence, $\\mathcal{C}_2$ has cluster tilting subcategories modelled by certain triangulations of the (completed) $\\infty$-gon. We use the Frobenius structure to extend this further to consider maximal almost rigid subcategor"},"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":"2205.15344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-05-30T18:00:08Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"12fb61cb3394b7454e46b4483fc10f22d79b497b43d98f98e9685e8da15db080","abstract_canon_sha256":"e6ee07bb5cf4d86c486c0631f81dbb11238aa8414de8ab01cd86c0edb2c91b71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:27:32.062709Z","signature_b64":"zQHiEUhPhtmJngk2nstLzNmYeFGxLfNJ/qp/PglwyPJ+goLWKmodiEMH+S+L2aan+tM1+jfwQksf0vNRGyRNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"245149301a18a37f8c57a4eca7e908e575f61e78531b407174fbd6aa15e0837d","last_reissued_at":"2026-07-05T04:27:32.062288Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:27:32.062288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster structures for the $A_{\\infty}$ singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RT","authors_text":"Eleonore Faber, Jenny August, Man-Wai Cheung, Sibylle Schroll, Sira Gratz","submitted_at":"2022-05-30T18:00:08Z","abstract_excerpt":"We study a category $\\mathcal{C}_2$ of $\\mathbb{Z}$-graded MCM modules over the $A_\\infty$ curve singularity and demonstrate it has infinite type $A$ cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategory) is stably equivalent to the infinite type $A$ cluster categories of Holm-Jorgensen, Fisher and Paquette-Yildirim. As a consequence, $\\mathcal{C}_2$ has cluster tilting subcategories modelled by certain triangulations of the (completed) $\\infty$-gon. We use the Frobenius structure to extend this further to consider maximal almost rigid subcategor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.15344","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/2205.15344/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":"2205.15344","created_at":"2026-07-05T04:27:32.062359+00:00"},{"alias_kind":"arxiv_version","alias_value":"2205.15344v1","created_at":"2026-07-05T04:27:32.062359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.15344","created_at":"2026-07-05T04:27:32.062359+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERIUSMA2DCRX","created_at":"2026-07-05T04:27:32.062359+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERIUSMA2DCRX7DCX","created_at":"2026-07-05T04:27:32.062359+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERIUSMA2","created_at":"2026-07-05T04:27:32.062359+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.13137","citing_title":"Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V","json":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V.json","graph_json":"https://pith.science/api/pith-number/ERIUSMA2DCRX7DCXUTWKP2II4V/graph.json","events_json":"https://pith.science/api/pith-number/ERIUSMA2DCRX7DCXUTWKP2II4V/events.json","paper":"https://pith.science/paper/ERIUSMA2"},"agent_actions":{"view_html":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V","download_json":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V.json","view_paper":"https://pith.science/paper/ERIUSMA2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2205.15344&json=true","fetch_graph":"https://pith.science/api/pith-number/ERIUSMA2DCRX7DCXUTWKP2II4V/graph.json","fetch_events":"https://pith.science/api/pith-number/ERIUSMA2DCRX7DCXUTWKP2II4V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V/action/storage_attestation","attest_author":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V/action/author_attestation","sign_citation":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V/action/citation_signature","submit_replication":"https://pith.science/pith/ERIUSMA2DCRX7DCXUTWKP2II4V/action/replication_record"}},"created_at":"2026-07-05T04:27:32.062359+00:00","updated_at":"2026-07-05T04:27:32.062359+00:00"}