{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5JKSW2ISZIEC5SQGBAT4XXC2FQ","short_pith_number":"pith:5JKSW2IS","canonical_record":{"source":{"id":"1002.3146","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-02-16T20:42:47Z","cross_cats_sorted":[],"title_canon_sha256":"bd39f4a8b55757567adca5cb28e3eace25b5c4dfd674991dab687305c66cac0e","abstract_canon_sha256":"d3078030ff4254e95fe292f301828208cd9b0483a68e1c0f8acee5bbadea2cc9"},"schema_version":"1.0"},"canonical_sha256":"ea552b6912ca082eca060827cbdc5a2c10e651575ed9288645ff7c75aba7c59e","source":{"kind":"arxiv","id":"1002.3146","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3146","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3146v2","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3146","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"pith_short_12","alias_value":"5JKSW2ISZIEC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5JKSW2ISZIEC5SQG","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5JKSW2IS","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5JKSW2ISZIEC5SQGBAT4XXC2FQ","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3146","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-02-16T20:42:47Z","cross_cats_sorted":[],"title_canon_sha256":"bd39f4a8b55757567adca5cb28e3eace25b5c4dfd674991dab687305c66cac0e","abstract_canon_sha256":"d3078030ff4254e95fe292f301828208cd9b0483a68e1c0f8acee5bbadea2cc9"},"schema_version":"1.0"},"canonical_sha256":"ea552b6912ca082eca060827cbdc5a2c10e651575ed9288645ff7c75aba7c59e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:53.709337Z","signature_b64":"d5Sv/NgqKhZZWphmEofwc00DCGHHf7/lNsLlMQpsrUt4g1ZHCZCbj6+GJep+p5r4ecy4oJuH9p9NLj+jEk3sDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea552b6912ca082eca060827cbdc5a2c10e651575ed9288645ff7c75aba7c59e","last_reissued_at":"2026-05-18T04:16:53.708887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:53.708887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3146","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"od7NOp2nM7LvvDKz+/AdouKJjq64+GNUFpZWlpQJ3JUdZn7Wq5vNq3uFbS7eBxsVZY0Ez4By3LvzTG8uOn3SDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:38:12.365113Z"},"content_sha256":"e46e72c9d2280fea0774e6377c26c360197602b5e8085c5b0e9cfba31380cde8","schema_version":"1.0","event_id":"sha256:e46e72c9d2280fea0774e6377c26c360197602b5e8085c5b0e9cfba31380cde8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5JKSW2ISZIEC5SQGBAT4XXC2FQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum automorphisms of twisted group algebras and free hypergeometric laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Julien Bichon, Stephen Curran, Teodor Banica","submitted_at":"2010-02-16T20:42:47Z","abstract_excerpt":"We prove that we have an isomorphism of type $A_{aut}(\\mathbb C_\\sigma[G])\\simeq A_{aut}(\\mathbb C[G])^\\sigma$, for any finite group $G$, and any 2-cocycle $\\sigma$ on $G$. In the particular case $G=\\mathbb Z_n^2$, this leads to a Haar-measure preserving identification between the subalgebra of $A_o(n)$ generated by the variables $u_{ij}^2$, and the subalgebra of $A_s(n^2)$ generated by the variables $X_{ij}=\\sum_{a,b=1}^np_{ia,jb}$. Since $u_{ij}$ is \"free hyperspherical\" and $X_{ij}$ is \"free hypergeometric\", we obtain in this way a new free probability formula, which at $n=\\infty$ correspon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3146","kind":"arxiv","version":2},"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":"2026-05-18T04:16:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qSj9h+IM9iuwt7FHHC6cTPQVPXAdLGtUgRXsZqd9MeDugtgcJgpXfP2Dgadpx99PswIN8dzx+aiOpUU/vlfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:38:12.365532Z"},"content_sha256":"c0f8f1d2256c1607e02de8d04bbccb5cb686b0959897f480f8e854ffbbfb0934","schema_version":"1.0","event_id":"sha256:c0f8f1d2256c1607e02de8d04bbccb5cb686b0959897f480f8e854ffbbfb0934"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JKSW2ISZIEC5SQGBAT4XXC2FQ/bundle.json","state_url":"https://pith.science/pith/5JKSW2ISZIEC5SQGBAT4XXC2FQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JKSW2ISZIEC5SQGBAT4XXC2FQ/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":"2026-05-31T18:38:12Z","links":{"resolver":"https://pith.science/pith/5JKSW2ISZIEC5SQGBAT4XXC2FQ","bundle":"https://pith.science/pith/5JKSW2ISZIEC5SQGBAT4XXC2FQ/bundle.json","state":"https://pith.science/pith/5JKSW2ISZIEC5SQGBAT4XXC2FQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JKSW2ISZIEC5SQGBAT4XXC2FQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5JKSW2ISZIEC5SQGBAT4XXC2FQ","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":"d3078030ff4254e95fe292f301828208cd9b0483a68e1c0f8acee5bbadea2cc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-02-16T20:42:47Z","title_canon_sha256":"bd39f4a8b55757567adca5cb28e3eace25b5c4dfd674991dab687305c66cac0e"},"schema_version":"1.0","source":{"id":"1002.3146","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3146","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3146v2","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3146","created_at":"2026-05-18T04:16:53Z"},{"alias_kind":"pith_short_12","alias_value":"5JKSW2ISZIEC","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5JKSW2ISZIEC5SQG","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5JKSW2IS","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:c0f8f1d2256c1607e02de8d04bbccb5cb686b0959897f480f8e854ffbbfb0934","target":"graph","created_at":"2026-05-18T04:16:53Z","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":"We prove that we have an isomorphism of type $A_{aut}(\\mathbb C_\\sigma[G])\\simeq A_{aut}(\\mathbb C[G])^\\sigma$, for any finite group $G$, and any 2-cocycle $\\sigma$ on $G$. In the particular case $G=\\mathbb Z_n^2$, this leads to a Haar-measure preserving identification between the subalgebra of $A_o(n)$ generated by the variables $u_{ij}^2$, and the subalgebra of $A_s(n^2)$ generated by the variables $X_{ij}=\\sum_{a,b=1}^np_{ia,jb}$. Since $u_{ij}$ is \"free hyperspherical\" and $X_{ij}$ is \"free hypergeometric\", we obtain in this way a new free probability formula, which at $n=\\infty$ correspon","authors_text":"Julien Bichon, Stephen Curran, Teodor Banica","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-02-16T20:42:47Z","title":"Quantum automorphisms of twisted group algebras and free hypergeometric laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3146","kind":"arxiv","version":2},"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:e46e72c9d2280fea0774e6377c26c360197602b5e8085c5b0e9cfba31380cde8","target":"record","created_at":"2026-05-18T04:16:53Z","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":"d3078030ff4254e95fe292f301828208cd9b0483a68e1c0f8acee5bbadea2cc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-02-16T20:42:47Z","title_canon_sha256":"bd39f4a8b55757567adca5cb28e3eace25b5c4dfd674991dab687305c66cac0e"},"schema_version":"1.0","source":{"id":"1002.3146","kind":"arxiv","version":2}},"canonical_sha256":"ea552b6912ca082eca060827cbdc5a2c10e651575ed9288645ff7c75aba7c59e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea552b6912ca082eca060827cbdc5a2c10e651575ed9288645ff7c75aba7c59e","first_computed_at":"2026-05-18T04:16:53.708887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:53.708887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d5Sv/NgqKhZZWphmEofwc00DCGHHf7/lNsLlMQpsrUt4g1ZHCZCbj6+GJep+p5r4ecy4oJuH9p9NLj+jEk3sDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:53.709337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3146","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e46e72c9d2280fea0774e6377c26c360197602b5e8085c5b0e9cfba31380cde8","sha256:c0f8f1d2256c1607e02de8d04bbccb5cb686b0959897f480f8e854ffbbfb0934"],"state_sha256":"62567fcbeb952ad6377dd7b75d3181895bee9304cd23bc5dc9406b41a87bed23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/xLN69fVcLhXVDGZV3eK6yrhtHnBYbDn14h/JriI3oiby9QbXnuNzbkZ8O+roJGdMqedceub+V7ookpDa1zCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:38:12.372152Z","bundle_sha256":"111f88005c17b7c88f23edd833fa934f037d1d744b78e2e66bc3b474eb6d1588"}}