{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IDV2EHM2AQXINKPQQA2TC2ILXW","short_pith_number":"pith:IDV2EHM2","schema_version":"1.0","canonical_sha256":"40eba21d9a042e86a9f0803531690bbd88238996df0abf0b7f10b6379ecc7e02","source":{"kind":"arxiv","id":"2607.12499","version":1},"attestation_state":"computed","paper":{"title":"Homomorphisms between standard modules of generalized Reedy categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Liping Li","submitted_at":"2026-07-14T08:31:53Z","abstract_excerpt":"We develop a representation-theoretic approach to generalized Reedy categories through a systematic study of homomorphism spaces between standard modules. For a broad class of these categories, we provide a uniform, computable framework that reduces abstract homological constructions to elementary linear algebra and spectral graph theory via incidence matrices and morphism fibers. As a primary application, we establish a uniform extension of the Dold--Kan correspondence for categories arising from rooted trees, encompassing the categories of finite chains, finite sets and partial injections, a"},"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":"2607.12499","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-07-14T08:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"829e07693fb867075799a0bf374aa246c1259693f9e78e1997b7e9f049c45349","abstract_canon_sha256":"b821ed48489ec379b9ba935a1058780502ac2e8923af4f5730e99a42effc8baa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:21:38.205234Z","signature_b64":"Zyxs17Eerx6NLd65GU+GTSjPYWDVlCsXSO6Gd6AU4gSzFacoEwzfa4ZWPF2YHIUqOlG4LDl1qxbbbe9eg+GxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40eba21d9a042e86a9f0803531690bbd88238996df0abf0b7f10b6379ecc7e02","last_reissued_at":"2026-07-15T01:21:38.204387Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:21:38.204387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homomorphisms between standard modules of generalized Reedy categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Liping Li","submitted_at":"2026-07-14T08:31:53Z","abstract_excerpt":"We develop a representation-theoretic approach to generalized Reedy categories through a systematic study of homomorphism spaces between standard modules. For a broad class of these categories, we provide a uniform, computable framework that reduces abstract homological constructions to elementary linear algebra and spectral graph theory via incidence matrices and morphism fibers. As a primary application, we establish a uniform extension of the Dold--Kan correspondence for categories arising from rooted trees, encompassing the categories of finite chains, finite sets and partial injections, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12499","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/2607.12499/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":"2607.12499","created_at":"2026-07-15T01:21:38.204829+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.12499v1","created_at":"2026-07-15T01:21:38.204829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12499","created_at":"2026-07-15T01:21:38.204829+00:00"},{"alias_kind":"pith_short_12","alias_value":"IDV2EHM2AQXI","created_at":"2026-07-15T01:21:38.204829+00:00"},{"alias_kind":"pith_short_16","alias_value":"IDV2EHM2AQXINKPQ","created_at":"2026-07-15T01:21:38.204829+00:00"},{"alias_kind":"pith_short_8","alias_value":"IDV2EHM2","created_at":"2026-07-15T01:21:38.204829+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/IDV2EHM2AQXINKPQQA2TC2ILXW","json":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW.json","graph_json":"https://pith.science/api/pith-number/IDV2EHM2AQXINKPQQA2TC2ILXW/graph.json","events_json":"https://pith.science/api/pith-number/IDV2EHM2AQXINKPQQA2TC2ILXW/events.json","paper":"https://pith.science/paper/IDV2EHM2"},"agent_actions":{"view_html":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW","download_json":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW.json","view_paper":"https://pith.science/paper/IDV2EHM2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.12499&json=true","fetch_graph":"https://pith.science/api/pith-number/IDV2EHM2AQXINKPQQA2TC2ILXW/graph.json","fetch_events":"https://pith.science/api/pith-number/IDV2EHM2AQXINKPQQA2TC2ILXW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW/action/storage_attestation","attest_author":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW/action/author_attestation","sign_citation":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW/action/citation_signature","submit_replication":"https://pith.science/pith/IDV2EHM2AQXINKPQQA2TC2ILXW/action/replication_record"}},"created_at":"2026-07-15T01:21:38.204829+00:00","updated_at":"2026-07-15T01:21:38.204829+00:00"}