{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:PTWDHMFYZNYDZZV76GZXJK3WPO","short_pith_number":"pith:PTWDHMFY","schema_version":"1.0","canonical_sha256":"7cec33b0b8cb703ce6bff1b374ab767bbd6004cb8a6fbae9b65c9357a95a38f6","source":{"kind":"arxiv","id":"math/0608680","version":2},"attestation_state":"computed","paper":{"title":"Simple omega-categories and chain complexes","license":"","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Richard Steiner","submitted_at":"2006-08-28T08:55:06Z","abstract_excerpt":"The category of strict omega-categories has an important full subcategory whose objects are the simple omega-categories freely generated by planar trees or by globular cardinals. We give a simple description of this subcategory in terms of chain complexes, and we give a similar description of the opposite category, the category of finite discs, in terms of cochain complexes. Berger has shown that the category of simple omega-categories has a filtration by iterated wreath products of the simplex category. We generalise his result by considering wreath products of categories of chain complexes o"},"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":"math/0608680","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CT","submitted_at":"2006-08-28T08:55:06Z","cross_cats_sorted":[],"title_canon_sha256":"a554f0fd0116733831e62957802a4a1f6d1285a0128050fa32e53cb9f886f695","abstract_canon_sha256":"a151825e1a788a5c38de1de369a86ceeac20e42b55f61a11445bfbe023fd3cec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:00:41.143662Z","signature_b64":"FJhg86+IMaEBIapDDtP/eacQioEGsrzeaLlJ+9itoDArhHJ/NoYfJ7akugtliXDC7/fsI7C+nDvegPzVCKW1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cec33b0b8cb703ce6bff1b374ab767bbd6004cb8a6fbae9b65c9357a95a38f6","last_reissued_at":"2026-07-04T15:00:41.143293Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:00:41.143293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple omega-categories and chain complexes","license":"","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Richard Steiner","submitted_at":"2006-08-28T08:55:06Z","abstract_excerpt":"The category of strict omega-categories has an important full subcategory whose objects are the simple omega-categories freely generated by planar trees or by globular cardinals. We give a simple description of this subcategory in terms of chain complexes, and we give a similar description of the opposite category, the category of finite discs, in terms of cochain complexes. Berger has shown that the category of simple omega-categories has a filtration by iterated wreath products of the simplex category. We generalise his result by considering wreath products of categories of chain complexes o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608680","kind":"arxiv","version":2},"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/math/0608680/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":"math/0608680","created_at":"2026-07-04T15:00:41.143367+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608680v2","created_at":"2026-07-04T15:00:41.143367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608680","created_at":"2026-07-04T15:00:41.143367+00:00"},{"alias_kind":"pith_short_12","alias_value":"PTWDHMFYZNYD","created_at":"2026-07-04T15:00:41.143367+00:00"},{"alias_kind":"pith_short_16","alias_value":"PTWDHMFYZNYDZZV7","created_at":"2026-07-04T15:00:41.143367+00:00"},{"alias_kind":"pith_short_8","alias_value":"PTWDHMFY","created_at":"2026-07-04T15:00:41.143367+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.16326","citing_title":"Deformation Theory for $(\\infty,n)$-categories","ref_index":26,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO","json":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO.json","graph_json":"https://pith.science/api/pith-number/PTWDHMFYZNYDZZV76GZXJK3WPO/graph.json","events_json":"https://pith.science/api/pith-number/PTWDHMFYZNYDZZV76GZXJK3WPO/events.json","paper":"https://pith.science/paper/PTWDHMFY"},"agent_actions":{"view_html":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO","download_json":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO.json","view_paper":"https://pith.science/paper/PTWDHMFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608680&json=true","fetch_graph":"https://pith.science/api/pith-number/PTWDHMFYZNYDZZV76GZXJK3WPO/graph.json","fetch_events":"https://pith.science/api/pith-number/PTWDHMFYZNYDZZV76GZXJK3WPO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO/action/storage_attestation","attest_author":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO/action/author_attestation","sign_citation":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO/action/citation_signature","submit_replication":"https://pith.science/pith/PTWDHMFYZNYDZZV76GZXJK3WPO/action/replication_record"}},"created_at":"2026-07-04T15:00:41.143367+00:00","updated_at":"2026-07-04T15:00:41.143367+00:00"}