{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6INTEKVZKOMD2KMPMG2ZTYEVPG","short_pith_number":"pith:6INTEKVZ","schema_version":"1.0","canonical_sha256":"f21b322ab953983d298f61b599e09579aee596db08306ceb8ce3fc0b710a0d93","source":{"kind":"arxiv","id":"1706.08471","version":3},"attestation_state":"computed","paper":{"title":"Loop groups and diffeomorphism groups of the circle as colimits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MP"],"primary_cat":"math-ph","authors_text":"Andre Henriques","submitted_at":"2017-06-26T16:43:50Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.08471","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-06-26T16:43:50Z","cross_cats_sorted":["math.GR","math.MP"],"title_canon_sha256":"f839df2eb44bad184825cdee1354c7c58ab3d170204fdbc6edc2dce44e614630","abstract_canon_sha256":"0e052a581d237511f5ee1fb0cc770b360b46c6cf11fc052e068c12da1e8896a0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:29.910120Z","signature_b64":"EaCM9XPTehHGfsdL8v8myrwol09Jow548AbqmZ+Bsmc5N6sUKcUYHr7RCun2W7Xie+AtIBg64WXKOp64buWIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f21b322ab953983d298f61b599e09579aee596db08306ceb8ce3fc0b710a0d93","last_reissued_at":"2026-05-17T23:55:29.909601Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:29.909601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Loop groups and diffeomorphism groups of the circle as colimits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MP"],"primary_cat":"math-ph","authors_text":"Andre Henriques","submitted_at":"2017-06-26T16:43:50Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08471","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.08471","created_at":"2026-05-17T23:55:29.909675+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.08471v3","created_at":"2026-05-17T23:55:29.909675+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08471","created_at":"2026-05-17T23:55:29.909675+00:00"},{"alias_kind":"pith_short_12","alias_value":"6INTEKVZKOMD","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6INTEKVZKOMD2KMP","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6INTEKVZ","created_at":"2026-05-18T12:31:03.183658+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG","json":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG.json","graph_json":"https://pith.science/api/pith-number/6INTEKVZKOMD2KMPMG2ZTYEVPG/graph.json","events_json":"https://pith.science/api/pith-number/6INTEKVZKOMD2KMPMG2ZTYEVPG/events.json","paper":"https://pith.science/paper/6INTEKVZ"},"agent_actions":{"view_html":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG","download_json":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG.json","view_paper":"https://pith.science/paper/6INTEKVZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.08471&json=true","fetch_graph":"https://pith.science/api/pith-number/6INTEKVZKOMD2KMPMG2ZTYEVPG/graph.json","fetch_events":"https://pith.science/api/pith-number/6INTEKVZKOMD2KMPMG2ZTYEVPG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG/action/storage_attestation","attest_author":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG/action/author_attestation","sign_citation":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG/action/citation_signature","submit_replication":"https://pith.science/pith/6INTEKVZKOMD2KMPMG2ZTYEVPG/action/replication_record"}},"created_at":"2026-05-17T23:55:29.909675+00:00","updated_at":"2026-05-17T23:55:29.909675+00:00"}