{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LASAZEHPB6EUHEBKJTP4BV2Z2V","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":"8339c2c0091bdfc9023a26bb6e6ff440d536f85c3a4f7b1ad6cb2c9526d08377","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-03-04T10:50:05Z","title_canon_sha256":"66db5ce470c6c0d36bdc3fc72a7a0c05b12d8fd7be776245c0f71baafb4f19c2"},"schema_version":"1.0","source":{"id":"1003.1012","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1012","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1012v3","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1012","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"LASAZEHPB6EU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LASAZEHPB6EUHEBK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LASAZEHP","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:b01a1a1834973ddd88f379bab7312bfeca5c1329aea4ee3a9a979b9e33016757","target":"graph","created_at":"2026-05-18T03:50:09Z","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 construct a genus one analogue of the theory of associators and the Grothendieck-Teichmueller group. The analogue of the Galois action on the profinite braid groups is an action of the arithmetic fundamental group of a moduli space of elliptic curves on the profinite braid groups in genus one. This action factors through an explicit profinite group hat GT_ell, which admits an interpretation in terms of decorations of braided monoidal categories. We relate this group to its prounipotent group scheme version GT_ell(-). We construct a torsor over the latter group, the scheme of elliptic associ","authors_text":"B. Enriquez","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-03-04T10:50:05Z","title":"Elliptic associators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1012","kind":"arxiv","version":3},"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:bd092d2dbef85f43943acd18688ee2cfe25b5333e29dab03a9ed0a5bc164ab79","target":"record","created_at":"2026-05-18T03:50:09Z","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":"8339c2c0091bdfc9023a26bb6e6ff440d536f85c3a4f7b1ad6cb2c9526d08377","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-03-04T10:50:05Z","title_canon_sha256":"66db5ce470c6c0d36bdc3fc72a7a0c05b12d8fd7be776245c0f71baafb4f19c2"},"schema_version":"1.0","source":{"id":"1003.1012","kind":"arxiv","version":3}},"canonical_sha256":"58240c90ef0f8943902a4cdfc0d759d5475546fdf6b7783acb1a2ea0d73d3670","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58240c90ef0f8943902a4cdfc0d759d5475546fdf6b7783acb1a2ea0d73d3670","first_computed_at":"2026-05-18T03:50:09.381488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:09.381488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j3hhvmjiFzv1Q6Y/oJRB/mm9gyPyjvdjYOOU7nwHGOD7Ibn04qo655IzIZAzF0fqY3YUTuolh/Lz+kHsIteABw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:09.382112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1012","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd092d2dbef85f43943acd18688ee2cfe25b5333e29dab03a9ed0a5bc164ab79","sha256:b01a1a1834973ddd88f379bab7312bfeca5c1329aea4ee3a9a979b9e33016757"],"state_sha256":"2bb4ad3ef029c781a38a6c04331c75ba26c5f3ab4669f905135eaa38a988d5a2"}