{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:T2HSXLDWHOCKPXJ357MEWUV3KZ","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":"b408d3928a69151bf532782dbe64641ce9bce2160b7a6a3a4f79d45ec33ee554","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-09-14T13:18:16Z","title_canon_sha256":"abd5f65f22b83a1381cb492edeff9b88ec4e4c8c3ff81edc982bb540c4502cac"},"schema_version":"1.0","source":{"id":"1009.2652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2652","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2652v2","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2652","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"T2HSXLDWHOCK","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T2HSXLDWHOCKPXJ3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T2HSXLDW","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:d9ee1cc884e964346a1b2c1426c1e2545c235cbb70355b5ffeee5473a5a02027","target":"graph","created_at":"2026-05-18T04:40:54Z","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 introduce the notions of a half-balanced braided monoidal category and of its contraction. These notions give rise to an explicit description of the action of the Galois group of QQ on Teichmueller groupoids in genus 0, equivalent to that of L. Schneps. We also show that a prounipotent version of this action is equivalent to a graded action.","authors_text":"Benjamin Enriquez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-09-14T13:18:16Z","title":"Half-balanced braided monoidal categories and Teichmueller groupoids in genus zero"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2652","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":"sha256:36323c333aab46fe5b22c40705f05d9c4b41411c101d23900bea19bc61fb17ec","target":"record","created_at":"2026-05-18T04:40:54Z","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":"b408d3928a69151bf532782dbe64641ce9bce2160b7a6a3a4f79d45ec33ee554","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-09-14T13:18:16Z","title_canon_sha256":"abd5f65f22b83a1381cb492edeff9b88ec4e4c8c3ff81edc982bb540c4502cac"},"schema_version":"1.0","source":{"id":"1009.2652","kind":"arxiv","version":2}},"canonical_sha256":"9e8f2bac763b84a7dd3befd84b52bb565d0628dbde8c31e3d35ed6391dfba867","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e8f2bac763b84a7dd3befd84b52bb565d0628dbde8c31e3d35ed6391dfba867","first_computed_at":"2026-05-18T04:40:54.292196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.292196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jIIwpj6Dc506YzPZwPH+SAi3Xhg27VlahWLwiGVzcGZIEQ0YQiDZH0IKfR7m256efUrPtC82xEReTMOnmKQZAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.292696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36323c333aab46fe5b22c40705f05d9c4b41411c101d23900bea19bc61fb17ec","sha256:d9ee1cc884e964346a1b2c1426c1e2545c235cbb70355b5ffeee5473a5a02027"],"state_sha256":"ace1a46346609d8b41bc8eb3747702363e59740dff762d307518d1c341b0999a"}