{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:HZSYZ5MFOXPRC3COHHPP43QSPU","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":"5951ab93c1bec1bf75834044ff45cf20435408f16d71eb704c272564bc8db5ed","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.AG","submitted_at":"2001-01-31T00:37:35Z","title_canon_sha256":"ae63acf11a4777ac873977cdad8a08a98dc531da501250112698c007a103da0d"},"schema_version":"1.0","source":{"id":"math/0101256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101256","created_at":"2026-07-04T14:35:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101256v1","created_at":"2026-07-04T14:35:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101256","created_at":"2026-07-04T14:35:03Z"},{"alias_kind":"pith_short_12","alias_value":"HZSYZ5MFOXPR","created_at":"2026-07-04T14:35:03Z"},{"alias_kind":"pith_short_16","alias_value":"HZSYZ5MFOXPRC3CO","created_at":"2026-07-04T14:35:03Z"},{"alias_kind":"pith_short_8","alias_value":"HZSYZ5MF","created_at":"2026-07-04T14:35:03Z"}],"graph_snapshots":[{"event_id":"sha256:6e21612405eeb8e0c863e4c7d5dbbb2962ed2da173db56809136cc8fb8755b39","target":"graph","created_at":"2026-07-04T14:35:03Z","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/0101256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show by studying the symplectic geometry of the extended moduli space that the intersection cohomology of the representation space $Hom(\\pi_1(\\Sigma),G)/G$ for a simply connected compact Lie group $G$ is naturally embedded into the $G$ equivariant cohomology of $Hom(\\pi_1(\\Sigma),G)$ where $\\Sigma$ is a closed Riemann surface. This enables us to compute the intersection cohomology as a graded vector space with intersection pairing, in terms of the equivariant cohomology ring. The case where $G=SU(2)$ -- the moduli space of rank 2 holomorphic vector bundles of even degree -- is discussed in ","authors_text":"Young-Hoon Kiem","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-01-31T00:37:35Z","title":"Intersection cohomology of representation spaces of surface groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101256","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":"sha256:00c1ddcb07623d0a8917497249385fed48b9e9db2706915481cefdbf9f50a300","target":"record","created_at":"2026-07-04T14:35:03Z","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":"5951ab93c1bec1bf75834044ff45cf20435408f16d71eb704c272564bc8db5ed","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.AG","submitted_at":"2001-01-31T00:37:35Z","title_canon_sha256":"ae63acf11a4777ac873977cdad8a08a98dc531da501250112698c007a103da0d"},"schema_version":"1.0","source":{"id":"math/0101256","kind":"arxiv","version":1}},"canonical_sha256":"3e658cf58575df116c4e39defe6e127d2a92dac16c9114b05ab43450b1827dac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e658cf58575df116c4e39defe6e127d2a92dac16c9114b05ab43450b1827dac","first_computed_at":"2026-07-04T14:35:03.487938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:03.487938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gXtZRXQGvN9pIOvyJFmWvrlUB82oO+BShnwdksRMF9GyS5vgFYyj4QYc7N3+ysV1fGKmCqCCsqg9duW8p6b5CQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:03.488520Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0101256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00c1ddcb07623d0a8917497249385fed48b9e9db2706915481cefdbf9f50a300","sha256:6e21612405eeb8e0c863e4c7d5dbbb2962ed2da173db56809136cc8fb8755b39"],"state_sha256":"d77170f841cfccd62b78754e42d1f94737498025e8b9c7a82c4a1c24b5ded799"}