{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VLRLMGAMMI2EGI6SD4CMYNWGOG","short_pith_number":"pith:VLRLMGAM","canonical_record":{"source":{"id":"1607.04869","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-17T13:33:19Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"4e3b9d1957e91f0d75eb7d3289efd6506d7d135db28c7872dc0193cff9f410d5","abstract_canon_sha256":"94d54a0ac52e1ef84290fc780428a31ae555cbf93775bea0334c2f4c2e07c68e"},"schema_version":"1.0"},"canonical_sha256":"aae2b6180c62344323d21f04cc36c671a3b0ccd2636ad87ee2af28b9abe0841a","source":{"kind":"arxiv","id":"1607.04869","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04869","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04869v3","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04869","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"VLRLMGAMMI2E","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VLRLMGAMMI2EGI6S","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VLRLMGAM","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VLRLMGAMMI2EGI6SD4CMYNWGOG","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04869","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-17T13:33:19Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"4e3b9d1957e91f0d75eb7d3289efd6506d7d135db28c7872dc0193cff9f410d5","abstract_canon_sha256":"94d54a0ac52e1ef84290fc780428a31ae555cbf93775bea0334c2f4c2e07c68e"},"schema_version":"1.0"},"canonical_sha256":"aae2b6180c62344323d21f04cc36c671a3b0ccd2636ad87ee2af28b9abe0841a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:39.659828Z","signature_b64":"mL253Hfwk1pQKG55uYJzmxFo+GVxaLw+ZCGZo14x9mHL6WpnUsH9M3xukftto047W5G6jh+zUbUPGxhH7DS6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aae2b6180c62344323d21f04cc36c671a3b0ccd2636ad87ee2af28b9abe0841a","last_reissued_at":"2026-05-18T00:43:39.659360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:39.659360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04869","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EkQ+mxs05o8uKKAliqd5rOnEMZvqO/yUvYK6c8JU30Ogis/BOZ6++XJS2DBfwrl1+A1MWfa0EQVDYKPp7wv0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:03:30.112874Z"},"content_sha256":"77d3685c40833721221b837bd7cb32fc194626b1c58c14fd5bf7a6fc117784ab","schema_version":"1.0","event_id":"sha256:77d3685c40833721221b837bd7cb32fc194626b1c58c14fd5bf7a6fc117784ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VLRLMGAMMI2EGI6SD4CMYNWGOG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A quantum version of the algebra of distributions of $\\operatorname{SL}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Iv\\'an Angiono","submitted_at":"2016-07-17T13:33:19Z","abstract_excerpt":"Let $\\lambda$ be a primitive root of unity of order $\\ell$. We introduce a family of finite-dimensional algebras $\\{\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)\\}_{N\\in\\mathbb{N}_0}$ over the complex numbers, such that $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a subalgebra of $\\mathcal{D}_{\\lambda,M}(\\mathfrak{sl}_2)$ if $N<M$, and $\\mathcal{D}_{\\lambda,N-1}(\\mathfrak{sl}_2)\\subset \\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a $\\mathfrak{u}_{\\lambda}(\\mathfrak{sl}_2)$-cleft extension.\n  The simple $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$-modules $(\\mathcal{L}_{N}(p))_{0\\le p<\\ell^{N+1}}$ ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04869","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/8/ScbT4QD9fR8ocKXcA7W56wyOmtXmRwpoItOdcwix8pvWdm5xhRAmM4an8FQlwVt734+gC1sQ/Tj/12uLVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:03:30.113246Z"},"content_sha256":"80decaff30f4bd2dd6e2e56b18f6c61a48907e37d85382003fba298f0f4c9393","schema_version":"1.0","event_id":"sha256:80decaff30f4bd2dd6e2e56b18f6c61a48907e37d85382003fba298f0f4c9393"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/bundle.json","state_url":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T17:03:30Z","links":{"resolver":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG","bundle":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/bundle.json","state":"https://pith.science/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VLRLMGAMMI2EGI6SD4CMYNWGOG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VLRLMGAMMI2EGI6SD4CMYNWGOG","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":"94d54a0ac52e1ef84290fc780428a31ae555cbf93775bea0334c2f4c2e07c68e","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-17T13:33:19Z","title_canon_sha256":"4e3b9d1957e91f0d75eb7d3289efd6506d7d135db28c7872dc0193cff9f410d5"},"schema_version":"1.0","source":{"id":"1607.04869","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04869","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04869v3","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04869","created_at":"2026-05-18T00:43:39Z"},{"alias_kind":"pith_short_12","alias_value":"VLRLMGAMMI2E","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VLRLMGAMMI2EGI6S","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VLRLMGAM","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:80decaff30f4bd2dd6e2e56b18f6c61a48907e37d85382003fba298f0f4c9393","target":"graph","created_at":"2026-05-18T00:43:39Z","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":"Let $\\lambda$ be a primitive root of unity of order $\\ell$. We introduce a family of finite-dimensional algebras $\\{\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)\\}_{N\\in\\mathbb{N}_0}$ over the complex numbers, such that $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a subalgebra of $\\mathcal{D}_{\\lambda,M}(\\mathfrak{sl}_2)$ if $N<M$, and $\\mathcal{D}_{\\lambda,N-1}(\\mathfrak{sl}_2)\\subset \\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$ is a $\\mathfrak{u}_{\\lambda}(\\mathfrak{sl}_2)$-cleft extension.\n  The simple $\\mathcal{D}_{\\lambda,N}(\\mathfrak{sl}_2)$-modules $(\\mathcal{L}_{N}(p))_{0\\le p<\\ell^{N+1}}$ ar","authors_text":"Iv\\'an Angiono","cross_cats":["math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-17T13:33:19Z","title":"A quantum version of the algebra of distributions of $\\operatorname{SL}_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04869","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":"sha256:77d3685c40833721221b837bd7cb32fc194626b1c58c14fd5bf7a6fc117784ab","target":"record","created_at":"2026-05-18T00:43:39Z","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":"94d54a0ac52e1ef84290fc780428a31ae555cbf93775bea0334c2f4c2e07c68e","cross_cats_sorted":["math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-07-17T13:33:19Z","title_canon_sha256":"4e3b9d1957e91f0d75eb7d3289efd6506d7d135db28c7872dc0193cff9f410d5"},"schema_version":"1.0","source":{"id":"1607.04869","kind":"arxiv","version":3}},"canonical_sha256":"aae2b6180c62344323d21f04cc36c671a3b0ccd2636ad87ee2af28b9abe0841a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aae2b6180c62344323d21f04cc36c671a3b0ccd2636ad87ee2af28b9abe0841a","first_computed_at":"2026-05-18T00:43:39.659360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:39.659360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mL253Hfwk1pQKG55uYJzmxFo+GVxaLw+ZCGZo14x9mHL6WpnUsH9M3xukftto047W5G6jh+zUbUPGxhH7DS6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:39.659828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04869","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77d3685c40833721221b837bd7cb32fc194626b1c58c14fd5bf7a6fc117784ab","sha256:80decaff30f4bd2dd6e2e56b18f6c61a48907e37d85382003fba298f0f4c9393"],"state_sha256":"c5f9f45a008208102cf8650de566a0ae9b546f427dabb1f5cbaaf910baa57ea1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4RuGhdgDdAr3VfGMWrl05nKAVaoW9qpTlr3UoN/tN1Qs4jmg7YtddgrCDIWXbut/uSq6Ri+dWOaTGRcEtTwXDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:03:30.115479Z","bundle_sha256":"9cdbe444f0d07e0bc133906d85613134abd18c1f64ae30faee9bed8949f3ad5d"}}