{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6INTEKVZKOMD2KMPMG2ZTYEVPG","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":"0e052a581d237511f5ee1fb0cc770b360b46c6cf11fc052e068c12da1e8896a0","cross_cats_sorted":["math.GR","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-26T16:43:50Z","title_canon_sha256":"f839df2eb44bad184825cdee1354c7c58ab3d170204fdbc6edc2dce44e614630"},"schema_version":"1.0","source":{"id":"1706.08471","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08471","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08471v3","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08471","created_at":"2026-05-17T23:55:29Z"},{"alias_kind":"pith_short_12","alias_value":"6INTEKVZKOMD","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6INTEKVZKOMD2KMP","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6INTEKVZ","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:4efcd841068c8d53f2be864c4a5033b63afaefe36d0dee4f88898a6d17c0bcef","target":"graph","created_at":"2026-05-17T23:55:29Z","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 show that loop groups and the universal cover of $\\mathrm{Diff}_+(S^1)$ can be expressed as colimits of groups of loops/diffeomorphisms supported in subintervals of $S^1$. Analogous results hold for based loop groups and for the based diffeomorphism group of $S^1$. These results continue to hold for the corresponding centrally extended groups.\n  We use the above results to construct a comparison functor from the representations of a loop group conformal net to the representations of the corresponding affine Lie algebra. We also establish an equivalence of categories between solitonic repres","authors_text":"Andre Henriques","cross_cats":["math.GR","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-26T16:43:50Z","title":"Loop groups and diffeomorphism groups of the circle as colimits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08471","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":"sha256:516f51b3d3b6ad22b41dae158176ec16936d7cb8c253a994f6bc4f576496df49","target":"record","created_at":"2026-05-17T23:55:29Z","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":"0e052a581d237511f5ee1fb0cc770b360b46c6cf11fc052e068c12da1e8896a0","cross_cats_sorted":["math.GR","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-26T16:43:50Z","title_canon_sha256":"f839df2eb44bad184825cdee1354c7c58ab3d170204fdbc6edc2dce44e614630"},"schema_version":"1.0","source":{"id":"1706.08471","kind":"arxiv","version":3}},"canonical_sha256":"f21b322ab953983d298f61b599e09579aee596db08306ceb8ce3fc0b710a0d93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f21b322ab953983d298f61b599e09579aee596db08306ceb8ce3fc0b710a0d93","first_computed_at":"2026-05-17T23:55:29.909601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:29.909601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EaCM9XPTehHGfsdL8v8myrwol09Jow548AbqmZ+Bsmc5N6sUKcUYHr7RCun2W7Xie+AtIBg64WXKOp64buWIBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:29.910120Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08471","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:516f51b3d3b6ad22b41dae158176ec16936d7cb8c253a994f6bc4f576496df49","sha256:4efcd841068c8d53f2be864c4a5033b63afaefe36d0dee4f88898a6d17c0bcef"],"state_sha256":"869f2e81fa521d8dbadb34282fa3fa6cc21a16c17d17dd1d00ef2237fae196e6"}