{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:2XJHB4PC4N6MOREKBNU6FGOSQL","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":"95096401c5b43e1ebc1ded4cb3ae165997c874798674f50ec041f0b4452d3716","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.AG","submitted_at":"2005-03-17T18:53:05Z","title_canon_sha256":"ef7aa5cd2ca4d424969b5a8453012c2a9ce3ff295a2bdc1bbca0542a0bedcc83"},"schema_version":"1.0","source":{"id":"math/0503369","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0503369","created_at":"2026-07-04T14:39:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/0503369v1","created_at":"2026-07-04T14:39:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0503369","created_at":"2026-07-04T14:39:48Z"},{"alias_kind":"pith_short_12","alias_value":"2XJHB4PC4N6M","created_at":"2026-07-04T14:39:48Z"},{"alias_kind":"pith_short_16","alias_value":"2XJHB4PC4N6MOREK","created_at":"2026-07-04T14:39:48Z"},{"alias_kind":"pith_short_8","alias_value":"2XJHB4PC","created_at":"2026-07-04T14:39:48Z"}],"graph_snapshots":[{"event_id":"sha256:a6d4164d1248d888c4445c001a8e92032f7e3ea4f9fab7e3ca3d938f254f8f2f","target":"graph","created_at":"2026-07-04T14:39:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0503369/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper provides an introduction to equivariant cohomology and homology using the approach of Goresky, Kottwitz, and MacPherson. When a group G acts suitably on a variety X, the equivariant cohomology of X can be computed using the combinatorial data of a skeleton of G-orbits on X. We give both a geometric definition and the traditional definition of equivariant cohomology. We include a discussion of the moment map and an algorithm for finding a set of generators for the equivariant cohomology of X. Many examples and explicit calculations are provided.","authors_text":"Julianna S. Tymoczko","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-03-17T18:53:05Z","title":"An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503369","kind":"arxiv","version":1},"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":"sha256:039bcafd58643f3f1cb5c57d889245583975ec24807b17ee386401630d634f25","target":"record","created_at":"2026-07-04T14:39:48Z","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":"95096401c5b43e1ebc1ded4cb3ae165997c874798674f50ec041f0b4452d3716","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.AG","submitted_at":"2005-03-17T18:53:05Z","title_canon_sha256":"ef7aa5cd2ca4d424969b5a8453012c2a9ce3ff295a2bdc1bbca0542a0bedcc83"},"schema_version":"1.0","source":{"id":"math/0503369","kind":"arxiv","version":1}},"canonical_sha256":"d5d270f1e2e37cc7448a0b69e299d282c547a9b49958fa2430bc37b385c21794","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5d270f1e2e37cc7448a0b69e299d282c547a9b49958fa2430bc37b385c21794","first_computed_at":"2026-07-04T14:39:48.222224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:48.222224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EoHEOxthwJoDJB2lMDtEw/7F8kQO9qPNFC/rE9vuS/Qli2OtEKDM2UvlNWLIX38j8FfvnNz0l5BV7QMOhB2CAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:48.222625Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0503369","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:039bcafd58643f3f1cb5c57d889245583975ec24807b17ee386401630d634f25","sha256:a6d4164d1248d888c4445c001a8e92032f7e3ea4f9fab7e3ca3d938f254f8f2f"],"state_sha256":"3a7982b2530ad0d1a324dd4f05f77767b9c9ce9f21b8661c0029d07ecdf102f3"}