{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HAPMOU3AWFB4IURRNQQFALK7E2","short_pith_number":"pith:HAPMOU3A","canonical_record":{"source":{"id":"1512.07006","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-22T09:57:24Z","cross_cats_sorted":[],"title_canon_sha256":"06fca70bcf2d0a73faadd75984de68cfc4235281e58eed408ea43ff7ee93d8b3","abstract_canon_sha256":"7290fee0773e673297cd394cfc049c3698cf9dfe48380c41cc6bf21ef6e02a24"},"schema_version":"1.0"},"canonical_sha256":"381ec75360b143c452316c20502d5f2691ec248c70baa4f2d3301ea841b4d976","source":{"kind":"arxiv","id":"1512.07006","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07006","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07006v2","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07006","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"HAPMOU3AWFB4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"HAPMOU3AWFB4IURR","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"HAPMOU3A","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HAPMOU3AWFB4IURRNQQFALK7E2","target":"record","payload":{"canonical_record":{"source":{"id":"1512.07006","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-22T09:57:24Z","cross_cats_sorted":[],"title_canon_sha256":"06fca70bcf2d0a73faadd75984de68cfc4235281e58eed408ea43ff7ee93d8b3","abstract_canon_sha256":"7290fee0773e673297cd394cfc049c3698cf9dfe48380c41cc6bf21ef6e02a24"},"schema_version":"1.0"},"canonical_sha256":"381ec75360b143c452316c20502d5f2691ec248c70baa4f2d3301ea841b4d976","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:22.700136Z","signature_b64":"Bo24D3yx3TH0DBT6/iRmKrcNaTYQvI0t+dqSzCCWREL7f6gYp4b9j7AY2qLfVnNypA2HeSbQAt35YGsQbDQIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"381ec75360b143c452316c20502d5f2691ec248c70baa4f2d3301ea841b4d976","last_reissued_at":"2026-05-18T01:12:22.699789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:22.699789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.07006","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":"2026-05-18T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dz+kINmvaSPwvv5ZXMMwfzIdGC6fgAxkbCQNanHRbUZ7Nyih8y1lKAMXYuW2h2xoRG5r92rXP522W37nZWshBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:17:49.931628Z"},"content_sha256":"2ba8a0025a6cdf396ad8dfde120b9d913c2c015fdf04f93c50cd0c3fc1e5f6b8","schema_version":"1.0","event_id":"sha256:2ba8a0025a6cdf396ad8dfde120b9d913c2c015fdf04f93c50cd0c3fc1e5f6b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HAPMOU3AWFB4IURRNQQFALK7E2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relation Between Stereographic Projection and Concurrence Measure in Bipartite Pure States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bahman Seifi, Ghader Najarbashi","submitted_at":"2015-12-22T09:57:24Z","abstract_excerpt":"One-qubit pure states, living on the surface of Bloch sphere, can be mapped onto the usual complex plane by using stereographic projection. In this paper, after reviewing the entanglement of two-qubit pure state, it is shown that the \\emph{quaternionic} stereographic projection is related to concurrence measure. This is due to the fact that every two-qubit state, in ordinary complex field, corresponds to the one-qubit state in quaternionic skew field, called quaterbit. Like the one-qubit states in complex field, the stereographic projection maps every quaterbit onto a quaternion number whose c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07006","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":"2026-05-18T01:12:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BacJI6+rUxkOp7j0xke3wbFKTWhiufwPK+wue54r0VQKO4MnXD07S2xehp/703LW1d6jUgFIelNncD+YpY0vAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:17:49.932163Z"},"content_sha256":"02fc056063601bed0ea840ad3b1cd4c719e9f9f6cbccb642eaa8d073db156b70","schema_version":"1.0","event_id":"sha256:02fc056063601bed0ea840ad3b1cd4c719e9f9f6cbccb642eaa8d073db156b70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HAPMOU3AWFB4IURRNQQFALK7E2/bundle.json","state_url":"https://pith.science/pith/HAPMOU3AWFB4IURRNQQFALK7E2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HAPMOU3AWFB4IURRNQQFALK7E2/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":"2026-08-22T14:17:49Z","links":{"resolver":"https://pith.science/pith/HAPMOU3AWFB4IURRNQQFALK7E2","bundle":"https://pith.science/pith/HAPMOU3AWFB4IURRNQQFALK7E2/bundle.json","state":"https://pith.science/pith/HAPMOU3AWFB4IURRNQQFALK7E2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HAPMOU3AWFB4IURRNQQFALK7E2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HAPMOU3AWFB4IURRNQQFALK7E2","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":"7290fee0773e673297cd394cfc049c3698cf9dfe48380c41cc6bf21ef6e02a24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-22T09:57:24Z","title_canon_sha256":"06fca70bcf2d0a73faadd75984de68cfc4235281e58eed408ea43ff7ee93d8b3"},"schema_version":"1.0","source":{"id":"1512.07006","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07006","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07006v2","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07006","created_at":"2026-05-18T01:12:22Z"},{"alias_kind":"pith_short_12","alias_value":"HAPMOU3AWFB4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"HAPMOU3AWFB4IURR","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"HAPMOU3A","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:02fc056063601bed0ea840ad3b1cd4c719e9f9f6cbccb642eaa8d073db156b70","target":"graph","created_at":"2026-05-18T01:12:22Z","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":"One-qubit pure states, living on the surface of Bloch sphere, can be mapped onto the usual complex plane by using stereographic projection. In this paper, after reviewing the entanglement of two-qubit pure state, it is shown that the \\emph{quaternionic} stereographic projection is related to concurrence measure. This is due to the fact that every two-qubit state, in ordinary complex field, corresponds to the one-qubit state in quaternionic skew field, called quaterbit. Like the one-qubit states in complex field, the stereographic projection maps every quaterbit onto a quaternion number whose c","authors_text":"Bahman Seifi, Ghader Najarbashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-22T09:57:24Z","title":"Relation Between Stereographic Projection and Concurrence Measure in Bipartite Pure States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07006","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":"sha256:2ba8a0025a6cdf396ad8dfde120b9d913c2c015fdf04f93c50cd0c3fc1e5f6b8","target":"record","created_at":"2026-05-18T01:12:22Z","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":"7290fee0773e673297cd394cfc049c3698cf9dfe48380c41cc6bf21ef6e02a24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-12-22T09:57:24Z","title_canon_sha256":"06fca70bcf2d0a73faadd75984de68cfc4235281e58eed408ea43ff7ee93d8b3"},"schema_version":"1.0","source":{"id":"1512.07006","kind":"arxiv","version":2}},"canonical_sha256":"381ec75360b143c452316c20502d5f2691ec248c70baa4f2d3301ea841b4d976","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"381ec75360b143c452316c20502d5f2691ec248c70baa4f2d3301ea841b4d976","first_computed_at":"2026-05-18T01:12:22.699789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:22.699789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bo24D3yx3TH0DBT6/iRmKrcNaTYQvI0t+dqSzCCWREL7f6gYp4b9j7AY2qLfVnNypA2HeSbQAt35YGsQbDQIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:22.700136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07006","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ba8a0025a6cdf396ad8dfde120b9d913c2c015fdf04f93c50cd0c3fc1e5f6b8","sha256:02fc056063601bed0ea840ad3b1cd4c719e9f9f6cbccb642eaa8d073db156b70"],"state_sha256":"0b01071289cd8c04b7f780f8456397697ef8fe12e0ca0aded2f58c636d7b8b06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EiQejzFehHh3rcQG///6bbUnC2sN0Tv0fjY47qpnPbQpAghWeBKTvJ2JZH8Oy2pi69b9S6lwFUpdEcTuIWWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T14:17:49.936791Z","bundle_sha256":"62948863fa9223dfc26ae008d5680670fa78b93ad19dd83630029c9d1effcbcb"}}