{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:I7TUKDXBZNGCFPAWIKGKSFC6GM","short_pith_number":"pith:I7TUKDXB","canonical_record":{"source":{"id":"1906.11370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-26T22:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"5737ff06fe5901148e5ad73876bd4342cb1c0988e67fa2fdfac2c522ea7aca32","abstract_canon_sha256":"86e75e670867d8d28c6e90359daa42e30b7d122d9ce7358c18d55f4bce5f7b30"},"schema_version":"1.0"},"canonical_sha256":"47e7450ee1cb4c22bc16428ca9145e332e28909b2390b50bdceadd5010988e7e","source":{"kind":"arxiv","id":"1906.11370","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11370","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11370v1","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11370","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"I7TUKDXBZNGC","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I7TUKDXBZNGCFPAW","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I7TUKDXB","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:I7TUKDXBZNGCFPAWIKGKSFC6GM","target":"record","payload":{"canonical_record":{"source":{"id":"1906.11370","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-26T22:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"5737ff06fe5901148e5ad73876bd4342cb1c0988e67fa2fdfac2c522ea7aca32","abstract_canon_sha256":"86e75e670867d8d28c6e90359daa42e30b7d122d9ce7358c18d55f4bce5f7b30"},"schema_version":"1.0"},"canonical_sha256":"47e7450ee1cb4c22bc16428ca9145e332e28909b2390b50bdceadd5010988e7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:07.332829Z","signature_b64":"J1AVBJA90g9cXkw4lncbr1e0TFqkdiajVMp2a6b70T51P1Qzc/RujFY8Zm2PeY+MxHSXYPHgzHR60Ks+Dxj9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47e7450ee1cb4c22bc16428ca9145e332e28909b2390b50bdceadd5010988e7e","last_reissued_at":"2026-05-17T23:42:07.332188Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:07.332188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.11370","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":"2026-05-17T23:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GE2D4LbmAzmb5yAC6p+NW4eQLBUYyX9vUj9tKuXR1gyBDEq3GgbzMOX9KTLbVGoye7F+S2y9T3TmEUjVc+NuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:05:55.770132Z"},"content_sha256":"911d45b1d980d380f3884fa37e38f66122ddb49ad141c8363a8f75833af3624e","schema_version":"1.0","event_id":"sha256:911d45b1d980d380f3884fa37e38f66122ddb49ad141c8363a8f75833af3624e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:I7TUKDXBZNGCFPAWIKGKSFC6GM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some extensions of quaternions and symmetries of simply connected space forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gerardo Arizmendi, Marco Antonio P\\'erez-de la Rosa","submitted_at":"2019-06-26T22:29:09Z","abstract_excerpt":"It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the groups of unit--norm elements in the algebras of real quaternions, biquaternions (complex quaternions) and dual quaternions, respectively. In this work, we present a unified framework that allows a wider scope on the subject and includes all the classical results related to the action in dimension 3 and 4 of unit--norm elements of the algebras described above and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11370","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":"2026-05-17T23:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AcOHjNdOL/l04dMPduxjIr+SP69viBbXU5sTibdFlpviliw+SiEYe1sUUU/qhgFidkA/8hPLPjfaRi7bBbAFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:05:55.770858Z"},"content_sha256":"18278d4f95824164a01c2288ea12523eac7732aa267ef154e7421a7aac163640","schema_version":"1.0","event_id":"sha256:18278d4f95824164a01c2288ea12523eac7732aa267ef154e7421a7aac163640"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I7TUKDXBZNGCFPAWIKGKSFC6GM/bundle.json","state_url":"https://pith.science/pith/I7TUKDXBZNGCFPAWIKGKSFC6GM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I7TUKDXBZNGCFPAWIKGKSFC6GM/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":"2026-06-11T01:05:55Z","links":{"resolver":"https://pith.science/pith/I7TUKDXBZNGCFPAWIKGKSFC6GM","bundle":"https://pith.science/pith/I7TUKDXBZNGCFPAWIKGKSFC6GM/bundle.json","state":"https://pith.science/pith/I7TUKDXBZNGCFPAWIKGKSFC6GM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I7TUKDXBZNGCFPAWIKGKSFC6GM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I7TUKDXBZNGCFPAWIKGKSFC6GM","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":"86e75e670867d8d28c6e90359daa42e30b7d122d9ce7358c18d55f4bce5f7b30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-26T22:29:09Z","title_canon_sha256":"5737ff06fe5901148e5ad73876bd4342cb1c0988e67fa2fdfac2c522ea7aca32"},"schema_version":"1.0","source":{"id":"1906.11370","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11370","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11370v1","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11370","created_at":"2026-05-17T23:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"I7TUKDXBZNGC","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"I7TUKDXBZNGCFPAW","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"I7TUKDXB","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:18278d4f95824164a01c2288ea12523eac7732aa267ef154e7421a7aac163640","target":"graph","created_at":"2026-05-17T23:42:07Z","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":"It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the groups of unit--norm elements in the algebras of real quaternions, biquaternions (complex quaternions) and dual quaternions, respectively. In this work, we present a unified framework that allows a wider scope on the subject and includes all the classical results related to the action in dimension 3 and 4 of unit--norm elements of the algebras described above and","authors_text":"Gerardo Arizmendi, Marco Antonio P\\'erez-de la Rosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-26T22:29:09Z","title":"Some extensions of quaternions and symmetries of simply connected space forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11370","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":"sha256:911d45b1d980d380f3884fa37e38f66122ddb49ad141c8363a8f75833af3624e","target":"record","created_at":"2026-05-17T23:42:07Z","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":"86e75e670867d8d28c6e90359daa42e30b7d122d9ce7358c18d55f4bce5f7b30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-26T22:29:09Z","title_canon_sha256":"5737ff06fe5901148e5ad73876bd4342cb1c0988e67fa2fdfac2c522ea7aca32"},"schema_version":"1.0","source":{"id":"1906.11370","kind":"arxiv","version":1}},"canonical_sha256":"47e7450ee1cb4c22bc16428ca9145e332e28909b2390b50bdceadd5010988e7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47e7450ee1cb4c22bc16428ca9145e332e28909b2390b50bdceadd5010988e7e","first_computed_at":"2026-05-17T23:42:07.332188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:07.332188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J1AVBJA90g9cXkw4lncbr1e0TFqkdiajVMp2a6b70T51P1Qzc/RujFY8Zm2PeY+MxHSXYPHgzHR60Ks+Dxj9AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:07.332829Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11370","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:911d45b1d980d380f3884fa37e38f66122ddb49ad141c8363a8f75833af3624e","sha256:18278d4f95824164a01c2288ea12523eac7732aa267ef154e7421a7aac163640"],"state_sha256":"14adfab8db58a33713bad0835c698afde470e88db3a0c7dd8a651bc0fb0cc04c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gI68kMaHfx6C5sD1C8LUgaKTYu6aHLkmuGLDlSECfT465VfH6H1b+mugW1+c+iKpP9nLzW0b8de8++vzkCDoAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:05:55.774857Z","bundle_sha256":"8fc29669d3b7640e994c7d69f3de5cbadb25c2b4ac3ce338bbc6a7992b6e6143"}}