{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WXVUUBM2VLLRQCPAWB3YWDV223","short_pith_number":"pith:WXVUUBM2","schema_version":"1.0","canonical_sha256":"b5eb4a059aaad71809e0b0778b0ebad6df45db852f5348f90ca969821cddea4f","source":{"kind":"arxiv","id":"1805.07184","version":4},"attestation_state":"computed","paper":{"title":"Cellular $E_k$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Alexander Kupers, Oscar Randal-Williams, Soren Galatius","submitted_at":"2018-05-18T13:01:55Z","abstract_excerpt":"We give a set of foundations for cellular $E_k$-algebras which are especially convenient for applications to homological stability. We provide conceptual and computational tools in this setting, such as filtrations, a homology theory for $E_k$-algebras with a Hurewicz theorem, CW approximations, and many spectral sequences, which shall be used for such applications in future papers."},"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":"1805.07184","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-05-18T13:01:55Z","cross_cats_sorted":[],"title_canon_sha256":"5535686f527f4a8576e74ea769c36e4b7e0c162d3c6446ec8c09800317954cad","abstract_canon_sha256":"4775a55d16d8225072fd2c10cf3942f84495b1a9fcf12084a51b788c6a2b14f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:28:41.577895Z","signature_b64":"ibSK8ObxA24E/pIYdSuQUKQrGcPwiXc7IipvQECfesX3Iwkhv1ILbjeLtZeW2u7+P1l4hEy1ztWqW9yazIlgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5eb4a059aaad71809e0b0778b0ebad6df45db852f5348f90ca969821cddea4f","last_reissued_at":"2026-07-05T07:28:41.577411Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:28:41.577411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cellular $E_k$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Alexander Kupers, Oscar Randal-Williams, Soren Galatius","submitted_at":"2018-05-18T13:01:55Z","abstract_excerpt":"We give a set of foundations for cellular $E_k$-algebras which are especially convenient for applications to homological stability. We provide conceptual and computational tools in this setting, such as filtrations, a homology theory for $E_k$-algebras with a Hurewicz theorem, CW approximations, and many spectral sequences, which shall be used for such applications in future papers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07184","kind":"arxiv","version":4},"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/1805.07184/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":"1805.07184","created_at":"2026-07-05T07:28:41.577468+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.07184v4","created_at":"2026-07-05T07:28:41.577468+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07184","created_at":"2026-07-05T07:28:41.577468+00:00"},{"alias_kind":"pith_short_12","alias_value":"WXVUUBM2VLLR","created_at":"2026-07-05T07:28:41.577468+00:00"},{"alias_kind":"pith_short_16","alias_value":"WXVUUBM2VLLRQCPA","created_at":"2026-07-05T07:28:41.577468+00:00"},{"alias_kind":"pith_short_8","alias_value":"WXVUUBM2","created_at":"2026-07-05T07:28:41.577468+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.05516","citing_title":"Representation stability for ordered Hurwitz spaces","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223","json":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223.json","graph_json":"https://pith.science/api/pith-number/WXVUUBM2VLLRQCPAWB3YWDV223/graph.json","events_json":"https://pith.science/api/pith-number/WXVUUBM2VLLRQCPAWB3YWDV223/events.json","paper":"https://pith.science/paper/WXVUUBM2"},"agent_actions":{"view_html":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223","download_json":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223.json","view_paper":"https://pith.science/paper/WXVUUBM2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.07184&json=true","fetch_graph":"https://pith.science/api/pith-number/WXVUUBM2VLLRQCPAWB3YWDV223/graph.json","fetch_events":"https://pith.science/api/pith-number/WXVUUBM2VLLRQCPAWB3YWDV223/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223/action/storage_attestation","attest_author":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223/action/author_attestation","sign_citation":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223/action/citation_signature","submit_replication":"https://pith.science/pith/WXVUUBM2VLLRQCPAWB3YWDV223/action/replication_record"}},"created_at":"2026-07-05T07:28:41.577468+00:00","updated_at":"2026-07-05T07:28:41.577468+00:00"}