{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NZ5KGYI6QVCZEZU4HRLNMUTW7R","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":"e37b150bde3640bcc29e210f0b502f63d3ab825192a145d520ea8e6edc8ccd29","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-04-23T15:26:46Z","title_canon_sha256":"4040857fbc2b128e1be87bc37349f01f1d8b9d6e7e6dbf628326a2f2989cd5a0"},"schema_version":"1.0","source":{"id":"2404.15125","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.15125","created_at":"2026-07-05T09:46:46Z"},{"alias_kind":"arxiv_version","alias_value":"2404.15125v2","created_at":"2026-07-05T09:46:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.15125","created_at":"2026-07-05T09:46:46Z"},{"alias_kind":"pith_short_12","alias_value":"NZ5KGYI6QVCZ","created_at":"2026-07-05T09:46:46Z"},{"alias_kind":"pith_short_16","alias_value":"NZ5KGYI6QVCZEZU4","created_at":"2026-07-05T09:46:46Z"},{"alias_kind":"pith_short_8","alias_value":"NZ5KGYI6","created_at":"2026-07-05T09:46:46Z"}],"graph_snapshots":[{"event_id":"sha256:b3f0a8cd5802e78ae8905f72a4ef0ed15b24dbd569b7bfc8ed38987976b25d79","target":"graph","created_at":"2026-07-05T09:46:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.15125/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we consider representations of certain combinatorial categories, including the poset $\\D$ of positive integers and division, the Young lattice $\\mathscr{Y}$ of partitions of finite sets, the opposite category of the orbit category $\\mathscr{Z}$ of $(\\mathbb{Z}, +)$ with respect to nontrivial subgroups, and the category $\\mathscr{CI}$ of finite cyclic groups and injective homomorphisms. We describe explicit upper bounds for homological degrees of their representations, and deduce that finitely presented representations (resp., representations presented in finite degrees) over a fi","authors_text":"Li Liang, Liping Li, Zhenxing Di","cross_cats":["math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-04-23T15:26:46Z","title":"Representations of $\\mathbb{N}^{\\infty}$-type combinatorial categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.15125","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":"sha256:18959915b5d9e095ea29c92e535c4cf678904f653b81c0ef7932a36555f8010f","target":"record","created_at":"2026-07-05T09:46:46Z","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":"e37b150bde3640bcc29e210f0b502f63d3ab825192a145d520ea8e6edc8ccd29","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-04-23T15:26:46Z","title_canon_sha256":"4040857fbc2b128e1be87bc37349f01f1d8b9d6e7e6dbf628326a2f2989cd5a0"},"schema_version":"1.0","source":{"id":"2404.15125","kind":"arxiv","version":2}},"canonical_sha256":"6e7aa3611e854592669c3c56d65276fc72f306e57665f7f0f27409a875821813","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e7aa3611e854592669c3c56d65276fc72f306e57665f7f0f27409a875821813","first_computed_at":"2026-07-05T09:46:46.495526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:46:46.495526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vwJH4LgxblxxG6XHijxw/Cf7b3QBaIU3CbOhlvktVKlEnj+2T6ntvTskZ7Jm6rwIcl2AF6DEPb4d7QUP7uvpDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:46:46.496078Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.15125","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18959915b5d9e095ea29c92e535c4cf678904f653b81c0ef7932a36555f8010f","sha256:b3f0a8cd5802e78ae8905f72a4ef0ed15b24dbd569b7bfc8ed38987976b25d79"],"state_sha256":"03bcb319b122ed44f1a0586c8d67940d66b4aa3439632db1ed816f8447af3828"}