{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DGXKUPU32XH4S2YQXGMG4UDOK4","short_pith_number":"pith:DGXKUPU3","canonical_record":{"source":{"id":"1201.3392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-01-16T23:38:44Z","cross_cats_sorted":[],"title_canon_sha256":"006f53b5ba5f845bf7f66e439ef46b543820259d5c4ab7558a2eca08634fef17","abstract_canon_sha256":"f1c7014e02a83b1ef889118d8e28825eb6905c14bf94f763c32239276e5f1800"},"schema_version":"1.0"},"canonical_sha256":"19aeaa3e9bd5cfc96b10b9986e506e572b00af458efa2cbfcdfa57c26b9fd7d3","source":{"kind":"arxiv","id":"1201.3392","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3392","created_at":"2026-05-18T03:49:21Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3392v2","created_at":"2026-05-18T03:49:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3392","created_at":"2026-05-18T03:49:21Z"},{"alias_kind":"pith_short_12","alias_value":"DGXKUPU32XH4","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DGXKUPU32XH4S2YQ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DGXKUPU3","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DGXKUPU32XH4S2YQXGMG4UDOK4","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3392","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-01-16T23:38:44Z","cross_cats_sorted":[],"title_canon_sha256":"006f53b5ba5f845bf7f66e439ef46b543820259d5c4ab7558a2eca08634fef17","abstract_canon_sha256":"f1c7014e02a83b1ef889118d8e28825eb6905c14bf94f763c32239276e5f1800"},"schema_version":"1.0"},"canonical_sha256":"19aeaa3e9bd5cfc96b10b9986e506e572b00af458efa2cbfcdfa57c26b9fd7d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:21.971037Z","signature_b64":"j/Sz7I3ooJ7BPBsM35evIiP40xow0q4TgiTOPk9f5yzW50XWEoyY6dlLq5yCTnQqcLJOX4XTD5Exe1WuM5HdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19aeaa3e9bd5cfc96b10b9986e506e572b00af458efa2cbfcdfa57c26b9fd7d3","last_reissued_at":"2026-05-18T03:49:21.970326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:21.970326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3392","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":"2026-05-18T03:49:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IuJg44jGWFH9qsFm9ZibDJ0HpBO8hrcH7eOkM7ueHf2vgPb4EYbQcVt31Fr6R9+B2weANR4dcjLzi2ZAv3RiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:06:30.510811Z"},"content_sha256":"df12f9525309467f4fb2f804a3541b82d2db4d327b8fc65807190913f81df314","schema_version":"1.0","event_id":"sha256:df12f9525309467f4fb2f804a3541b82d2db4d327b8fc65807190913f81df314"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DGXKUPU32XH4S2YQXGMG4UDOK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum isometries and group dual subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jyotishman Bhowmick, Kenny De Commer, Teodor Banica","submitted_at":"2012-01-16T23:38:44Z","abstract_excerpt":"We study the discrete groups $\\Lambda$ whose duals embed into a given compact quantum group, $\\hat{\\Lambda}\\subset G$. In the matrix case $G\\subset U_n^+$ the embedding condition is equivalent to having a quotient map $\\Gamma_U\\to\\Lambda$, where $F=\\{\\Gamma_U|U\\in U_n\\}$ is a certain family of groups associated to $G$. We develop here a number of techniques for computing $F$, partly inspired from Bichon's classification of group dual subgroups $\\hat{\\Lambda}\\subset S_n^+$. These results are motivated by Goswami's notion of quantum isometry group, because a compact connected Riemannian manifold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3392","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":"2026-05-18T03:49:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NMIjARezL9YsF9C5fe/GYjoPuI3jftepoPeo2QpXvOrdgVan3yLVj129+YOFjwgueBz+bX0110CcoR/5XIpnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:06:30.511166Z"},"content_sha256":"b60470ac94479633922456fff73cee7000b0dc129845ca3da9dbefb2c3f83d1a","schema_version":"1.0","event_id":"sha256:b60470ac94479633922456fff73cee7000b0dc129845ca3da9dbefb2c3f83d1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGXKUPU32XH4S2YQXGMG4UDOK4/bundle.json","state_url":"https://pith.science/pith/DGXKUPU32XH4S2YQXGMG4UDOK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGXKUPU32XH4S2YQXGMG4UDOK4/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":"2026-06-01T17:06:30Z","links":{"resolver":"https://pith.science/pith/DGXKUPU32XH4S2YQXGMG4UDOK4","bundle":"https://pith.science/pith/DGXKUPU32XH4S2YQXGMG4UDOK4/bundle.json","state":"https://pith.science/pith/DGXKUPU32XH4S2YQXGMG4UDOK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGXKUPU32XH4S2YQXGMG4UDOK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DGXKUPU32XH4S2YQXGMG4UDOK4","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":"f1c7014e02a83b1ef889118d8e28825eb6905c14bf94f763c32239276e5f1800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-01-16T23:38:44Z","title_canon_sha256":"006f53b5ba5f845bf7f66e439ef46b543820259d5c4ab7558a2eca08634fef17"},"schema_version":"1.0","source":{"id":"1201.3392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3392","created_at":"2026-05-18T03:49:21Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3392v2","created_at":"2026-05-18T03:49:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3392","created_at":"2026-05-18T03:49:21Z"},{"alias_kind":"pith_short_12","alias_value":"DGXKUPU32XH4","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DGXKUPU32XH4S2YQ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DGXKUPU3","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:b60470ac94479633922456fff73cee7000b0dc129845ca3da9dbefb2c3f83d1a","target":"graph","created_at":"2026-05-18T03:49:21Z","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 study the discrete groups $\\Lambda$ whose duals embed into a given compact quantum group, $\\hat{\\Lambda}\\subset G$. In the matrix case $G\\subset U_n^+$ the embedding condition is equivalent to having a quotient map $\\Gamma_U\\to\\Lambda$, where $F=\\{\\Gamma_U|U\\in U_n\\}$ is a certain family of groups associated to $G$. We develop here a number of techniques for computing $F$, partly inspired from Bichon's classification of group dual subgroups $\\hat{\\Lambda}\\subset S_n^+$. These results are motivated by Goswami's notion of quantum isometry group, because a compact connected Riemannian manifold","authors_text":"Jyotishman Bhowmick, Kenny De Commer, Teodor Banica","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-01-16T23:38:44Z","title":"Quantum isometries and group dual subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3392","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:df12f9525309467f4fb2f804a3541b82d2db4d327b8fc65807190913f81df314","target":"record","created_at":"2026-05-18T03:49:21Z","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":"f1c7014e02a83b1ef889118d8e28825eb6905c14bf94f763c32239276e5f1800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-01-16T23:38:44Z","title_canon_sha256":"006f53b5ba5f845bf7f66e439ef46b543820259d5c4ab7558a2eca08634fef17"},"schema_version":"1.0","source":{"id":"1201.3392","kind":"arxiv","version":2}},"canonical_sha256":"19aeaa3e9bd5cfc96b10b9986e506e572b00af458efa2cbfcdfa57c26b9fd7d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19aeaa3e9bd5cfc96b10b9986e506e572b00af458efa2cbfcdfa57c26b9fd7d3","first_computed_at":"2026-05-18T03:49:21.970326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:21.970326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j/Sz7I3ooJ7BPBsM35evIiP40xow0q4TgiTOPk9f5yzW50XWEoyY6dlLq5yCTnQqcLJOX4XTD5Exe1WuM5HdBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:21.971037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df12f9525309467f4fb2f804a3541b82d2db4d327b8fc65807190913f81df314","sha256:b60470ac94479633922456fff73cee7000b0dc129845ca3da9dbefb2c3f83d1a"],"state_sha256":"d6ddb41d0983891bf96afe68c93cd19869d3f2dd4e40121eedfb32379b916814"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjTDzYNGxnnVckTC5eYEqHTHvar5aROEV8BcoBJSXwHH65avA4eRxsliO+eKyVv1IaShnHMWRpQW+KhGzEbMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:06:30.513086Z","bundle_sha256":"b5e3a4d23680bcee244f04c3269788018ef04ee65ab290a77b6fe538233cd970"}}