{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UY3FEZM3USHJ4YVBAJT2ZYJNA6","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":"050289ee6d54dc5a15f5499ca41c69ca3f0419f0e7eb11eaeb1c466afb437f77","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-31T19:13:17Z","title_canon_sha256":"72ace6fba5b6aa49772f187bf20540aecb02174240ccf9de64b34c71fca57c49"},"schema_version":"1.0","source":{"id":"1512.09345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09345","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09345v1","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09345","created_at":"2026-05-18T01:23:32Z"},{"alias_kind":"pith_short_12","alias_value":"UY3FEZM3USHJ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UY3FEZM3USHJ4YVB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UY3FEZM3","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:416037048d1a1bc1f4afed46dadb0e06a9162d1166d4f6a052eb21538da08877","target":"graph","created_at":"2026-05-18T01:23:32Z","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":"We exhibit the traceless $SU(2)$ character variety of a 6-punctured 2-sphere as a 2-fold branched cover of ${\\mathbb{C}}P^3$, branched over the singular Kummer surface, with the branch locus in $R(S^2,6)$ corresponding to the binary dihedral representations. This follows from an analysis of the map induced on $SU(2)$ character varieties by the 2-fold branched cover $F_{n-1}\\to S^2$ branched over $2n$ points, combined with the theorem of Narasimhan-Ramanan which identifies $R(F_2)$ with ${\\mathbb{C}} P^3$. The singular points of $R(S^2,6)$ correspond to abelian representations, and we prove tha","authors_text":"Paul Kirk","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-31T19:13:17Z","title":"On the traceless SU(2) character variety of the 6-punctured 2-sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09345","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":"sha256:8d9129086d3b1e4a586ec63e108b00dfd93d1dd17afa0226b9d10ebd1dafa19c","target":"record","created_at":"2026-05-18T01:23:32Z","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":"050289ee6d54dc5a15f5499ca41c69ca3f0419f0e7eb11eaeb1c466afb437f77","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-31T19:13:17Z","title_canon_sha256":"72ace6fba5b6aa49772f187bf20540aecb02174240ccf9de64b34c71fca57c49"},"schema_version":"1.0","source":{"id":"1512.09345","kind":"arxiv","version":1}},"canonical_sha256":"a63652659ba48e9e62a10267ace12d0794d74fd9958058aea5f03decca5c2111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a63652659ba48e9e62a10267ace12d0794d74fd9958058aea5f03decca5c2111","first_computed_at":"2026-05-18T01:23:32.590157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:32.590157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uAEIlQrOfT4y8n2MA8MzkXyi8pqFqDj/SkIFFuN58LF6ClKF9V88om1817BUlcQlFMySh/crp2Q4ZgCIYvW9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:32.590860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d9129086d3b1e4a586ec63e108b00dfd93d1dd17afa0226b9d10ebd1dafa19c","sha256:416037048d1a1bc1f4afed46dadb0e06a9162d1166d4f6a052eb21538da08877"],"state_sha256":"b94c57c0bad163cadf392e79cd462a29cfa3ff0875143871091379fda483fbeb"}