{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6UPW6LQ7P426YO5QIXC3ITDLSY","short_pith_number":"pith:6UPW6LQ7","schema_version":"1.0","canonical_sha256":"f51f6f2e1f7f35ec3bb045c5b44c6b960244a7dbce48ebb01f73c4f39742437f","source":{"kind":"arxiv","id":"1501.06013","version":2},"attestation_state":"computed","paper":{"title":"Two and Three-Qubits Geometry, Quaternionic and Octonionic Conformal Maps, and Intertwining Stereographic Projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"B. Seifi, G. Najarbashi, S. Mirzaei","submitted_at":"2015-01-24T07:49:27Z","abstract_excerpt":"In this paper the geometry of two and three-qubit states under local unitary groups is discussed. We first review the one qubit geometry and its relation with Riemannian sphere under the action of group $SU(2)$. We show that the quaternionic stereographic projection intertwines between local unitary group $SU(2)\\otimes SU(2)$ and quaternionic M\\\"{o}bius transformation. The invariant term appearing in this operation is related to concurrence measure. Yet, there exists the same intertwining stereographic projection for much more global group $Sp(2)$, generalizing the familiar Bloch sphere in 2-l"},"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":"1501.06013","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-01-24T07:49:27Z","cross_cats_sorted":[],"title_canon_sha256":"8812cb46664314f12e7801dc4d5038c435216d882134d3cf000d16cf3a9edd75","abstract_canon_sha256":"c2f4b7a3007032227661a6cd0ebadc070ef4af9c22f1627593e80e906342efee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:07.938988Z","signature_b64":"wysJQkUrWrP3SIz7Typdq7zAK36WVIsVnTwADA6nFELuNY0SwWaMakdxW+2RzZTWf8v+DZU/9ip7eWu+0FX6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f51f6f2e1f7f35ec3bb045c5b44c6b960244a7dbce48ebb01f73c4f39742437f","last_reissued_at":"2026-05-18T01:27:07.938344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:07.938344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two and Three-Qubits Geometry, Quaternionic and Octonionic Conformal Maps, and Intertwining Stereographic Projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"B. Seifi, G. Najarbashi, S. Mirzaei","submitted_at":"2015-01-24T07:49:27Z","abstract_excerpt":"In this paper the geometry of two and three-qubit states under local unitary groups is discussed. We first review the one qubit geometry and its relation with Riemannian sphere under the action of group $SU(2)$. We show that the quaternionic stereographic projection intertwines between local unitary group $SU(2)\\otimes SU(2)$ and quaternionic M\\\"{o}bius transformation. The invariant term appearing in this operation is related to concurrence measure. Yet, there exists the same intertwining stereographic projection for much more global group $Sp(2)$, generalizing the familiar Bloch sphere in 2-l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06013","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.06013","created_at":"2026-05-18T01:27:07.938429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06013v2","created_at":"2026-05-18T01:27:07.938429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06013","created_at":"2026-05-18T01:27:07.938429+00:00"},{"alias_kind":"pith_short_12","alias_value":"6UPW6LQ7P426","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6UPW6LQ7P426YO5Q","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6UPW6LQ7","created_at":"2026-05-18T12:29:07.941421+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/6UPW6LQ7P426YO5QIXC3ITDLSY","json":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY.json","graph_json":"https://pith.science/api/pith-number/6UPW6LQ7P426YO5QIXC3ITDLSY/graph.json","events_json":"https://pith.science/api/pith-number/6UPW6LQ7P426YO5QIXC3ITDLSY/events.json","paper":"https://pith.science/paper/6UPW6LQ7"},"agent_actions":{"view_html":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY","download_json":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY.json","view_paper":"https://pith.science/paper/6UPW6LQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06013&json=true","fetch_graph":"https://pith.science/api/pith-number/6UPW6LQ7P426YO5QIXC3ITDLSY/graph.json","fetch_events":"https://pith.science/api/pith-number/6UPW6LQ7P426YO5QIXC3ITDLSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY/action/storage_attestation","attest_author":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY/action/author_attestation","sign_citation":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY/action/citation_signature","submit_replication":"https://pith.science/pith/6UPW6LQ7P426YO5QIXC3ITDLSY/action/replication_record"}},"created_at":"2026-05-18T01:27:07.938429+00:00","updated_at":"2026-05-18T01:27:07.938429+00:00"}