{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:XFQ7I7ZNZUVRIDWFG4AWQTQUE5","short_pith_number":"pith:XFQ7I7ZN","schema_version":"1.0","canonical_sha256":"b961f47f2dcd2b140ec53701684e1427540e89814da0fe85260bda201d129b14","source":{"kind":"arxiv","id":"1108.5196","version":3},"attestation_state":"computed","paper":{"title":"Isomorphism conjectures with proper coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.OA"],"primary_cat":"math.KT","authors_text":"Eugenia Ellis, Guillermo Corti\\~nas","submitted_at":"2011-08-25T20:45:55Z","abstract_excerpt":"Let $G$ be a group and let $E$ be a functor from small $\\Z$-linear categories to spectra. Also let $A$ be a ring with a $G$-action. Under mild conditions on $E$ and $A$ one can define an equivariant homology theory of $G$-simplicial sets $H^G(-,E(A))$ with the property that if $H\\subset G$ is a subgroup, then \\[ H^G_*(G/H,E(A))=E_*(A\\rtimes H) \\] If now $\\cF$ is a nonempty family of subgroups of $G$, closed under conjugation and under subgroups, then there is a model category structure on $G$-simplicial sets such that a map $X\\to Y$ is a weak equivalence (resp. a fibration) if and only if $X^H"},"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":"1108.5196","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-08-25T20:45:55Z","cross_cats_sorted":["math.AT","math.OA"],"title_canon_sha256":"ecd075c4f3b16980fb7d86290970505e32ebac1e5694c7f6ba2b40d83a3f1a30","abstract_canon_sha256":"b3c3f7eebfc1f7b117d244360d16b44e714eca1fbc817499052675da2cb185c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:07.054604Z","signature_b64":"2KjCNxO6FZI9nuBennkdRlS9uDHGXDJn1Y/fFPKSdVYTRioB2tKHXO/nmAzn6RI27tfWfRAyh0VuJ9rYUSpvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b961f47f2dcd2b140ec53701684e1427540e89814da0fe85260bda201d129b14","last_reissued_at":"2026-05-18T02:57:07.054044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:07.054044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isomorphism conjectures with proper coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.OA"],"primary_cat":"math.KT","authors_text":"Eugenia Ellis, Guillermo Corti\\~nas","submitted_at":"2011-08-25T20:45:55Z","abstract_excerpt":"Let $G$ be a group and let $E$ be a functor from small $\\Z$-linear categories to spectra. Also let $A$ be a ring with a $G$-action. Under mild conditions on $E$ and $A$ one can define an equivariant homology theory of $G$-simplicial sets $H^G(-,E(A))$ with the property that if $H\\subset G$ is a subgroup, then \\[ H^G_*(G/H,E(A))=E_*(A\\rtimes H) \\] If now $\\cF$ is a nonempty family of subgroups of $G$, closed under conjugation and under subgroups, then there is a model category structure on $G$-simplicial sets such that a map $X\\to Y$ is a weak equivalence (resp. a fibration) if and only if $X^H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5196","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1108.5196","created_at":"2026-05-18T02:57:07.054107+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5196v3","created_at":"2026-05-18T02:57:07.054107+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5196","created_at":"2026-05-18T02:57:07.054107+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFQ7I7ZNZUVR","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFQ7I7ZNZUVRIDWF","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFQ7I7ZN","created_at":"2026-05-18T12:26:44.992195+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/XFQ7I7ZNZUVRIDWFG4AWQTQUE5","json":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5.json","graph_json":"https://pith.science/api/pith-number/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/graph.json","events_json":"https://pith.science/api/pith-number/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/events.json","paper":"https://pith.science/paper/XFQ7I7ZN"},"agent_actions":{"view_html":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5","download_json":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5.json","view_paper":"https://pith.science/paper/XFQ7I7ZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5196&json=true","fetch_graph":"https://pith.science/api/pith-number/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/graph.json","fetch_events":"https://pith.science/api/pith-number/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/action/storage_attestation","attest_author":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/action/author_attestation","sign_citation":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/action/citation_signature","submit_replication":"https://pith.science/pith/XFQ7I7ZNZUVRIDWFG4AWQTQUE5/action/replication_record"}},"created_at":"2026-05-18T02:57:07.054107+00:00","updated_at":"2026-05-18T02:57:07.054107+00:00"}