{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EFQC6DMPQBXE4JY3VDP6LXHD5V","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":"2e1ef407a2c7ff1b0d878ad49dbfb65b3f2b4254932921cdae8a1aa5f60b8e90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-31T20:02:20Z","title_canon_sha256":"32decf2396e1fbb5d4563754796991c792096156a028f92849566ec2c414986b"},"schema_version":"1.0","source":{"id":"1508.00005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00005","created_at":"2026-05-18T01:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00005v1","created_at":"2026-05-18T01:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00005","created_at":"2026-05-18T01:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"EFQC6DMPQBXE","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EFQC6DMPQBXE4JY3","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EFQC6DMP","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:d937c6596aba6ae09050bcd23e5fb118ddfba5632fe3c88051c80070eed991dd","target":"graph","created_at":"2026-05-18T01:24:53Z","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":"Motivated by physical and topological applications, we study representations of the group $\\mathcal{LB}_3$ of motions of $3$ unlinked oriented circles in $\\mathbb{R}^3$. Our point of view is to regard the three strand braid group $\\mathcal{B}_3$ as a subgroup of $\\mathcal{LB}_3$ and study the problem of extending $\\mathcal{B}_3$ representations. We introduce the notion of a \\emph{standard extension} and characterize $\\mathcal{B}_3$ representations admiting such an extension. In particular we show, using a classification result of Tuba and Wenzl, that every irreducible $\\mathcal{B}_3$ represent","authors_text":"Eric C. Rowell, Julia Yael Plavnik, Liang Chang, Michael Yuan Sun, Paul Bruillard, Seung-Moon Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-31T20:02:20Z","title":"Low-dimensional representations of the three component loop braid group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00005","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":"sha256:9d83b37dea0d7e641991e6d9493913a65e9bc51ed18c9455b95be86bbe604fa4","target":"record","created_at":"2026-05-18T01:24:53Z","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":"2e1ef407a2c7ff1b0d878ad49dbfb65b3f2b4254932921cdae8a1aa5f60b8e90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-07-31T20:02:20Z","title_canon_sha256":"32decf2396e1fbb5d4563754796991c792096156a028f92849566ec2c414986b"},"schema_version":"1.0","source":{"id":"1508.00005","kind":"arxiv","version":1}},"canonical_sha256":"21602f0d8f806e4e271ba8dfe5dce3ed5af54fbb21de327c282eac83c764d0f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21602f0d8f806e4e271ba8dfe5dce3ed5af54fbb21de327c282eac83c764d0f5","first_computed_at":"2026-05-18T01:24:53.505361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:53.505361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SQO2A4xVZTLZR9Jdzx3BdpdQPsZ+k6dOd82O09jZ0BjSqa0KURcwy1RcTnS+L4uLWEIoc0VrNM12JeDKvpETBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:53.506021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d83b37dea0d7e641991e6d9493913a65e9bc51ed18c9455b95be86bbe604fa4","sha256:d937c6596aba6ae09050bcd23e5fb118ddfba5632fe3c88051c80070eed991dd"],"state_sha256":"0353c2ec525767e88f73cca4994b67c968bb6db7c72a71abc255cd375c3cedf8"}