{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MQTBG6JCPTGDDU5UVOEAGQ7RI5","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":"cb281e7682819151d4729e018c748f6656b3e13ba5fc7541a3e5e86baff8b6db","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-09-08T08:31:33Z","title_canon_sha256":"92d02f35086fb12e61ea70b2dd7d49e3726f04ac5985d5fae2ef0dbed49c4384"},"schema_version":"1.0","source":{"id":"1609.02321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02321","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02321v1","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02321","created_at":"2026-05-18T01:04:54Z"},{"alias_kind":"pith_short_12","alias_value":"MQTBG6JCPTGD","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MQTBG6JCPTGDDU5U","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MQTBG6JC","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:9374a7b82a898979c662651cdbf2808d5bfcf84cbc32395991d604abb878a36f","target":"graph","created_at":"2026-05-18T01:04:54Z","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 define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This extends substantially Banica and Speicher's approach of the so called easy quantum groups: It enables us to find new examples of quantum subgroups of Wang's free orthogonal quantum group $O_n^+$ which do not contain the symmetric group $S_n$; we may define new kinds of products of quantum groups coming from new products of categories of partitions; and we give a quantum group interpretation of certain categories of part","authors_text":"Guillaume C\\'ebron, Moritz Weber","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-09-08T08:31:33Z","title":"Quantum groups based on spatial partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02321","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":"sha256:78dbb43997ff695f12f40f3f90ed25df89c827ede1c2b3e61daf5a3976b6b0ca","target":"record","created_at":"2026-05-18T01:04:54Z","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":"cb281e7682819151d4729e018c748f6656b3e13ba5fc7541a3e5e86baff8b6db","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-09-08T08:31:33Z","title_canon_sha256":"92d02f35086fb12e61ea70b2dd7d49e3726f04ac5985d5fae2ef0dbed49c4384"},"schema_version":"1.0","source":{"id":"1609.02321","kind":"arxiv","version":1}},"canonical_sha256":"64261379227ccc31d3b4ab880343f1475c2785acb248ead1157b930cfe0ddc36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64261379227ccc31d3b4ab880343f1475c2785acb248ead1157b930cfe0ddc36","first_computed_at":"2026-05-18T01:04:54.940108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:54.940108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FdpJNv+dDxl+VuAHD2JLfnvFr2Js51mfNLevmE2z0XysDucImFAafYBzb+DkTUY4j52F/FBSKwFDiZuVRbUoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:54.940723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78dbb43997ff695f12f40f3f90ed25df89c827ede1c2b3e61daf5a3976b6b0ca","sha256:9374a7b82a898979c662651cdbf2808d5bfcf84cbc32395991d604abb878a36f"],"state_sha256":"b24d41be6d771b9b9b0de73b14239637acfd6831024f115a782cbe7cf0d19996"}