{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MXO62GHRGSILISSFHOFQW2RQ2Q","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":"3b54777753d84d2b05cf96861bb148aa01146d9a4da8d592fb5b0d5ca60875bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-24T19:48:27Z","title_canon_sha256":"8604044e97bf0df64081392e3a74debaf33b4b4949c62900101592f43e30fa9c"},"schema_version":"1.0","source":{"id":"1403.6101","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6101","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6101v2","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6101","created_at":"2026-05-18T01:19:30Z"},{"alias_kind":"pith_short_12","alias_value":"MXO62GHRGSIL","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MXO62GHRGSILISSF","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MXO62GHR","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:c5fd5bd5a32f0d2a0e3006e1ba9186423ae0182d0810972b7eaf98b97a2eac2c","target":"graph","created_at":"2026-05-18T01:19:30Z","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"},"paper":{"abstract_excerpt":"Let $G$ be a finite group acting on a small category $I$. We study functors $X \\colon I \\to \\mathscr{C}$ equipped with families of compatible natural transformations that give a kind of generalized $G$-action on $X$. Such objects are called $G$-diagrams. When $\\mathscr{C}$ is a sufficiently nice model category we define a model structure on the category of $G$-diagrams in $\\mathscr{C}$. There are natural $G$-actions on Bousfield-Kan style homotopy limits and colimits of $G$-diagrams. We prove that weak equivalences between point-wise (co)fibrant $G$-diagrams induce weak $G$-equivalences on hom","authors_text":"Emanuele Dotto, Kristian Moi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-24T19:48:27Z","title":"Homotopy theory of G-diagrams and equivariant excision"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6101","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":"sha256:0556e70bc2017d10df83e15d8df84eb93a2860045f254d14bcd95ad3b05cfc35","target":"record","created_at":"2026-05-18T01:19:30Z","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":"3b54777753d84d2b05cf96861bb148aa01146d9a4da8d592fb5b0d5ca60875bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-24T19:48:27Z","title_canon_sha256":"8604044e97bf0df64081392e3a74debaf33b4b4949c62900101592f43e30fa9c"},"schema_version":"1.0","source":{"id":"1403.6101","kind":"arxiv","version":2}},"canonical_sha256":"65dded18f13490b44a453b8b0b6a30d42dc20b47225ecb35b02f1b80badbfeea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65dded18f13490b44a453b8b0b6a30d42dc20b47225ecb35b02f1b80badbfeea","first_computed_at":"2026-05-18T01:19:30.903761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:30.903761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UKHuBNPo19zZTJW2aE5NkCEAapJPE/Xo3h5rc4cWOyoHbax78R6q4i/pMfCA2PTDZGiBtBe1BAsGe+JYltiyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:30.904347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0556e70bc2017d10df83e15d8df84eb93a2860045f254d14bcd95ad3b05cfc35","sha256:c5fd5bd5a32f0d2a0e3006e1ba9186423ae0182d0810972b7eaf98b97a2eac2c"],"state_sha256":"049419d87ff0e058c576b1a72eadf67e41cdce4bddda4566ab945d9707771ff9"}