{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DXPBGKDNH3LODVJAOVTHEPQZNA","short_pith_number":"pith:DXPBGKDN","canonical_record":{"source":{"id":"1510.01862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-10-07T08:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"e8aa489ce052dc9da7b1da4f22d97d30ac047d72c5a667970303c85b9c8a3103","abstract_canon_sha256":"eaa10c99271173a4846b6e2f83bc830ad06e2c9580bf004fb504b6f8dec3a09d"},"schema_version":"1.0"},"canonical_sha256":"1dde13286d3ed6e1d5207566723e19682b2d213f44529f60c7557699f43067f6","source":{"kind":"arxiv","id":"1510.01862","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01862","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01862v1","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01862","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"DXPBGKDNH3LO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DXPBGKDNH3LODVJA","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DXPBGKDN","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DXPBGKDNH3LODVJAOVTHEPQZNA","target":"record","payload":{"canonical_record":{"source":{"id":"1510.01862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-10-07T08:51:33Z","cross_cats_sorted":[],"title_canon_sha256":"e8aa489ce052dc9da7b1da4f22d97d30ac047d72c5a667970303c85b9c8a3103","abstract_canon_sha256":"eaa10c99271173a4846b6e2f83bc830ad06e2c9580bf004fb504b6f8dec3a09d"},"schema_version":"1.0"},"canonical_sha256":"1dde13286d3ed6e1d5207566723e19682b2d213f44529f60c7557699f43067f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:50.181681Z","signature_b64":"i45P/naQEODrdk0DltTGRHMSPt1DrJeywcT40FbhSIb192xi8Xm6OrLo1wEix/cO7YLYm8g4EtC5MoNezKC7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dde13286d3ed6e1d5207566723e19682b2d213f44529f60c7557699f43067f6","last_reissued_at":"2026-05-18T01:30:50.181170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:50.181170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.01862","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+VLR6vOGYavuQu2fz/cBZXM3TKKFqF4AgKC0sBm1SPR8quU/D/WogEaI3aIw2i/memFOjrkdzH6v4aIsq09DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:24:34.717469Z"},"content_sha256":"2df40bb0dafaa9f440ac34cf5332f800010aeb114b81c7899ea673e37668dd33","schema_version":"1.0","event_id":"sha256:2df40bb0dafaa9f440ac34cf5332f800010aeb114b81c7899ea673e37668dd33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DXPBGKDNH3LODVJAOVTHEPQZNA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$q$-invariance of quantum quaternion spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Bipul Saurabh","submitted_at":"2015-10-07T08:51:33Z","abstract_excerpt":"The $C^*$-algebra of continuous functions on the quantum quaternion sphere $H_q^{2n}$ can be identified with the quotient algebra $C(SP_q(2n)/SP_q(2n-2))$. In commutative case i.e. for $q=1$, the topological space $SP(2n)/SP(2n-2)$ is homeomorphic to the odd dimensional sphere $S^{4n-1}$. In this paper, we prove the noncommutative analogue of this result. Using homogeneous $C^*$-extension theory, we prove that the $C^*$-algebra $C(H_q^{2n})$ is isomorphic to the $C^*$-algebra $C(S_q^{4n-1})$. This further implies that for different values of $q \\in [0,1)$, the $C^*$-algebras underlying the non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01862","kind":"arxiv","version":1},"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":"2026-05-18T01:30:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLAvl4g/m0c3vsXASwKNMzt+qwYGG2sRRErFSMiMMOyC5S2LuF5KZJ+dAJfM+cJaMTavitlSmhCM04w+bwZyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T00:24:34.717813Z"},"content_sha256":"94399f0a77620cec36151ddae38a1211d6e4549dcd148cc4ab07948d23f67fe8","schema_version":"1.0","event_id":"sha256:94399f0a77620cec36151ddae38a1211d6e4549dcd148cc4ab07948d23f67fe8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DXPBGKDNH3LODVJAOVTHEPQZNA/bundle.json","state_url":"https://pith.science/pith/DXPBGKDNH3LODVJAOVTHEPQZNA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DXPBGKDNH3LODVJAOVTHEPQZNA/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":"2026-06-09T00:24:34Z","links":{"resolver":"https://pith.science/pith/DXPBGKDNH3LODVJAOVTHEPQZNA","bundle":"https://pith.science/pith/DXPBGKDNH3LODVJAOVTHEPQZNA/bundle.json","state":"https://pith.science/pith/DXPBGKDNH3LODVJAOVTHEPQZNA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DXPBGKDNH3LODVJAOVTHEPQZNA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DXPBGKDNH3LODVJAOVTHEPQZNA","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":"eaa10c99271173a4846b6e2f83bc830ad06e2c9580bf004fb504b6f8dec3a09d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-10-07T08:51:33Z","title_canon_sha256":"e8aa489ce052dc9da7b1da4f22d97d30ac047d72c5a667970303c85b9c8a3103"},"schema_version":"1.0","source":{"id":"1510.01862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01862","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01862v1","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01862","created_at":"2026-05-18T01:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"DXPBGKDNH3LO","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DXPBGKDNH3LODVJA","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DXPBGKDN","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:94399f0a77620cec36151ddae38a1211d6e4549dcd148cc4ab07948d23f67fe8","target":"graph","created_at":"2026-05-18T01:30:50Z","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":"The $C^*$-algebra of continuous functions on the quantum quaternion sphere $H_q^{2n}$ can be identified with the quotient algebra $C(SP_q(2n)/SP_q(2n-2))$. In commutative case i.e. for $q=1$, the topological space $SP(2n)/SP(2n-2)$ is homeomorphic to the odd dimensional sphere $S^{4n-1}$. In this paper, we prove the noncommutative analogue of this result. Using homogeneous $C^*$-extension theory, we prove that the $C^*$-algebra $C(H_q^{2n})$ is isomorphic to the $C^*$-algebra $C(S_q^{4n-1})$. This further implies that for different values of $q \\in [0,1)$, the $C^*$-algebras underlying the non","authors_text":"Bipul Saurabh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-10-07T08:51:33Z","title":"$q$-invariance of quantum quaternion spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01862","kind":"arxiv","version":1},"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":"sha256:2df40bb0dafaa9f440ac34cf5332f800010aeb114b81c7899ea673e37668dd33","target":"record","created_at":"2026-05-18T01:30:50Z","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":"eaa10c99271173a4846b6e2f83bc830ad06e2c9580bf004fb504b6f8dec3a09d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-10-07T08:51:33Z","title_canon_sha256":"e8aa489ce052dc9da7b1da4f22d97d30ac047d72c5a667970303c85b9c8a3103"},"schema_version":"1.0","source":{"id":"1510.01862","kind":"arxiv","version":1}},"canonical_sha256":"1dde13286d3ed6e1d5207566723e19682b2d213f44529f60c7557699f43067f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dde13286d3ed6e1d5207566723e19682b2d213f44529f60c7557699f43067f6","first_computed_at":"2026-05-18T01:30:50.181170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:50.181170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i45P/naQEODrdk0DltTGRHMSPt1DrJeywcT40FbhSIb192xi8Xm6OrLo1wEix/cO7YLYm8g4EtC5MoNezKC7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:50.181681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2df40bb0dafaa9f440ac34cf5332f800010aeb114b81c7899ea673e37668dd33","sha256:94399f0a77620cec36151ddae38a1211d6e4549dcd148cc4ab07948d23f67fe8"],"state_sha256":"43211bdc185dc5ed310914063acd902f96e5ea1c9a15dfaee85f547ffb560982"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xi9QZXV6nUp8Y481NyCcjhW8FwbLb7VzXbjcgUDrNmSL8e6MNZoN0HY/xVI4d8dHQXlYNjPIp2wA0NEmx7+vBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T00:24:34.719677Z","bundle_sha256":"260f45d4cff629dc5c6322512ec3a1d0982c04ff3f6a515761ff24a6e170b33d"}}