{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PYIBSMENT6PR2B4JP56CRD2ODC","short_pith_number":"pith:PYIBSMEN","canonical_record":{"source":{"id":"1606.03315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2016-06-10T13:26:53Z","cross_cats_sorted":["physics.hist-ph"],"title_canon_sha256":"0f8f8a8eeb89f1d9c2f3d2e63d250b83e0f8cfdcdd29efb4f498b5fc7a19b1c9","abstract_canon_sha256":"a8a295d19e70dde3dd412bae2a5326c7218de6b82229f4be2fc1ef5ad36492c1"},"schema_version":"1.0"},"canonical_sha256":"7e1019308d9f9f1d07897f7c288f4e18b67182d619a021d7b22c3ba4a9217b90","source":{"kind":"arxiv","id":"1606.03315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03315","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03315v1","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03315","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"PYIBSMENT6PR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYIBSMENT6PR2B4J","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYIBSMEN","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PYIBSMENT6PR2B4JP56CRD2ODC","target":"record","payload":{"canonical_record":{"source":{"id":"1606.03315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2016-06-10T13:26:53Z","cross_cats_sorted":["physics.hist-ph"],"title_canon_sha256":"0f8f8a8eeb89f1d9c2f3d2e63d250b83e0f8cfdcdd29efb4f498b5fc7a19b1c9","abstract_canon_sha256":"a8a295d19e70dde3dd412bae2a5326c7218de6b82229f4be2fc1ef5ad36492c1"},"schema_version":"1.0"},"canonical_sha256":"7e1019308d9f9f1d07897f7c288f4e18b67182d619a021d7b22c3ba4a9217b90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:37.146635Z","signature_b64":"26gAO/S0EJuAAz1rIekwAsMWPa+duUw3BRR3yFG9HaM6sZ85V108BFHwx8ErcRt6UagDe/wONjV5LIMrpgCSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e1019308d9f9f1d07897f7c288f4e18b67182d619a021d7b22c3ba4a9217b90","last_reissued_at":"2026-05-18T01:12:37.146225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:37.146225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.03315","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":"2026-05-18T01:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jjzPGOQz2mXBKRXEbZj6RdUxrigac/7i7JjeJ0VDnL4pvhPCIzP54aDtisbtt//E5MkrS0zO4W65dcfNqsc2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:34:34.816554Z"},"content_sha256":"01265e142a378ff9f1e63775dae35c9c6c1e03a24bf7f1830a3ba622bb51e03f","schema_version":"1.0","event_id":"sha256:01265e142a378ff9f1e63775dae35c9c6c1e03a24bf7f1830a3ba622bb51e03f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PYIBSMENT6PR2B4JP56CRD2ODC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebra and geometry of Hamilton's quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.hist-ph"],"primary_cat":"math.HO","authors_text":"Govind S. Krishnaswami, Sonakshi Sachdev","submitted_at":"2016-06-10T13:26:53Z","abstract_excerpt":"Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03315","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":"2026-05-18T01:12:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RRAh+Xz97HyWzG3V9PMqxPqeBEU9QyA6dkj/kHcuK85riUOGtisPqgrOc9ZRitVL+DoFJzQQGnwiJKnbd4luAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:34:34.817264Z"},"content_sha256":"44c66b7aed58de9d17e265f224b4f73ca5de7ec30f5c75a34a985586f900439a","schema_version":"1.0","event_id":"sha256:44c66b7aed58de9d17e265f224b4f73ca5de7ec30f5c75a34a985586f900439a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYIBSMENT6PR2B4JP56CRD2ODC/bundle.json","state_url":"https://pith.science/pith/PYIBSMENT6PR2B4JP56CRD2ODC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYIBSMENT6PR2B4JP56CRD2ODC/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":"2026-06-08T01:34:34Z","links":{"resolver":"https://pith.science/pith/PYIBSMENT6PR2B4JP56CRD2ODC","bundle":"https://pith.science/pith/PYIBSMENT6PR2B4JP56CRD2ODC/bundle.json","state":"https://pith.science/pith/PYIBSMENT6PR2B4JP56CRD2ODC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYIBSMENT6PR2B4JP56CRD2ODC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PYIBSMENT6PR2B4JP56CRD2ODC","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":"a8a295d19e70dde3dd412bae2a5326c7218de6b82229f4be2fc1ef5ad36492c1","cross_cats_sorted":["physics.hist-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2016-06-10T13:26:53Z","title_canon_sha256":"0f8f8a8eeb89f1d9c2f3d2e63d250b83e0f8cfdcdd29efb4f498b5fc7a19b1c9"},"schema_version":"1.0","source":{"id":"1606.03315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03315","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03315v1","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03315","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"PYIBSMENT6PR","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PYIBSMENT6PR2B4J","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PYIBSMEN","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:44c66b7aed58de9d17e265f224b4f73ca5de7ec30f5c75a34a985586f900439a","target":"graph","created_at":"2026-05-18T01:12:37Z","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":"Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.","authors_text":"Govind S. Krishnaswami, Sonakshi Sachdev","cross_cats":["physics.hist-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2016-06-10T13:26:53Z","title":"Algebra and geometry of Hamilton's quaternions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03315","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":"sha256:01265e142a378ff9f1e63775dae35c9c6c1e03a24bf7f1830a3ba622bb51e03f","target":"record","created_at":"2026-05-18T01:12:37Z","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":"a8a295d19e70dde3dd412bae2a5326c7218de6b82229f4be2fc1ef5ad36492c1","cross_cats_sorted":["physics.hist-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2016-06-10T13:26:53Z","title_canon_sha256":"0f8f8a8eeb89f1d9c2f3d2e63d250b83e0f8cfdcdd29efb4f498b5fc7a19b1c9"},"schema_version":"1.0","source":{"id":"1606.03315","kind":"arxiv","version":1}},"canonical_sha256":"7e1019308d9f9f1d07897f7c288f4e18b67182d619a021d7b22c3ba4a9217b90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e1019308d9f9f1d07897f7c288f4e18b67182d619a021d7b22c3ba4a9217b90","first_computed_at":"2026-05-18T01:12:37.146225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:37.146225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"26gAO/S0EJuAAz1rIekwAsMWPa+duUw3BRR3yFG9HaM6sZ85V108BFHwx8ErcRt6UagDe/wONjV5LIMrpgCSAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:37.146635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01265e142a378ff9f1e63775dae35c9c6c1e03a24bf7f1830a3ba622bb51e03f","sha256:44c66b7aed58de9d17e265f224b4f73ca5de7ec30f5c75a34a985586f900439a"],"state_sha256":"58efee0c5a4518f455f3ca6b087a5e7de05dfee23a6b77f4cd179e241adb0ea2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNib+aRTWpCNU6qGvqDoB51tubCAEyyRlLRToeHv8UoXFX5nDoKngmFLs4uliwZQPys900H9kE0xqgamJaRUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:34:34.821025Z","bundle_sha256":"3c7ae5e3aff3c79f89984f7997cacd60481bbcd77694e51c4541ff2876c520b0"}}