{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CYPICS6DA7VVT5DW33U5KUVXO3","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":"72a585624bf4c01a3519d382377efe06ec0008b5b957c2b4f98c785d0623076f","cross_cats_sorted":["math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-26T13:52:35Z","title_canon_sha256":"26d7b21121ab2607e28b1248d4e5adee3b381754eec8712268b0d75ea606b732"},"schema_version":"1.0","source":{"id":"1204.5924","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5924","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5924v2","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5924","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"CYPICS6DA7VV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CYPICS6DA7VVT5DW","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CYPICS6D","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:bb375446c56f1056cd6a8e49294798f73a221f10d8bda4e9065d0fe47f020962","target":"graph","created_at":"2026-05-18T03:01:11Z","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 complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectively, Y) be the space of equivalence classes of representations of the free group of m+n generators in G (respectively, K) such that for each i between 1 and m, the image of the i-th free generator is conjugate to h_i. These spaces are parabolic analogues of character varieties of free groups. We prove that Y is a strong deformation retraction of X. In particular, X and Y are homotopy equivalent. We also describe expl","authors_text":"Carlos Florentino, Indranil Biswas, Marina Logares, Sean Lawton","cross_cats":["math.GT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-26T13:52:35Z","title":"The Topology of Parabolic Character Varieties of Free Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5924","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:dfbe294f8abe24e86bcec8f12ee442f775f8299e7472f1396d056bc946cda2b2","target":"record","created_at":"2026-05-18T03:01:11Z","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":"72a585624bf4c01a3519d382377efe06ec0008b5b957c2b4f98c785d0623076f","cross_cats_sorted":["math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-26T13:52:35Z","title_canon_sha256":"26d7b21121ab2607e28b1248d4e5adee3b381754eec8712268b0d75ea606b732"},"schema_version":"1.0","source":{"id":"1204.5924","kind":"arxiv","version":2}},"canonical_sha256":"161e814bc307eb59f476dee9d552b776e0e4f32f518d45353fcb7a266d87ca41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"161e814bc307eb59f476dee9d552b776e0e4f32f518d45353fcb7a266d87ca41","first_computed_at":"2026-05-18T03:01:11.279576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:11.279576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B1l1L7s8qCgKUrs4poCGpx3+NXeG+67w3RP/8ci6wMvvPwTIuuyiTU53ASxdjkzKu+x7Q4YjFj9FM80nGX3ODg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:11.280382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5924","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfbe294f8abe24e86bcec8f12ee442f775f8299e7472f1396d056bc946cda2b2","sha256:bb375446c56f1056cd6a8e49294798f73a221f10d8bda4e9065d0fe47f020962"],"state_sha256":"ed20caf69a69a3458b77df5da79b7907167f6e82e72cdd25541cb365f3454645"}