{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IHXB26QDSGSXGYHKRNJC2X5OC4","short_pith_number":"pith:IHXB26QD","canonical_record":{"source":{"id":"1202.6021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-02-23T02:07:46Z","cross_cats_sorted":[],"title_canon_sha256":"bce9e47696f31544be019da75dededcf0387e1ee77f1627b04f857823e553448","abstract_canon_sha256":"34f188538e5efbef903e7ba78308bbb4ca5d00386220674f2211ae8fd55d8c8a"},"schema_version":"1.0"},"canonical_sha256":"41ee1d7a0391a57360ea8b522d5fae1708365ccd27c88a54d82d12ec3172c504","source":{"kind":"arxiv","id":"1202.6021","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6021","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6021v2","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6021","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"IHXB26QDSGSX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IHXB26QDSGSXGYHK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IHXB26QD","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IHXB26QDSGSXGYHKRNJC2X5OC4","target":"record","payload":{"canonical_record":{"source":{"id":"1202.6021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-02-23T02:07:46Z","cross_cats_sorted":[],"title_canon_sha256":"bce9e47696f31544be019da75dededcf0387e1ee77f1627b04f857823e553448","abstract_canon_sha256":"34f188538e5efbef903e7ba78308bbb4ca5d00386220674f2211ae8fd55d8c8a"},"schema_version":"1.0"},"canonical_sha256":"41ee1d7a0391a57360ea8b522d5fae1708365ccd27c88a54d82d12ec3172c504","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:54.317157Z","signature_b64":"560Lf7EMl7c58q3TNDx2m12/8uQiWq+NvpWBgk6IN8YRCJwsubpA/Ymt8z+0cr+1T8QKSoCg3URsDJtYfPvNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41ee1d7a0391a57360ea8b522d5fae1708365ccd27c88a54d82d12ec3172c504","last_reissued_at":"2026-05-18T03:53:54.316463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:54.316463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.6021","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":"2026-05-18T03:53:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MBwABjwAI/I7TtHYRjBq091I6Cf1SPX3YmpV+DEZ+DUiLm+C0aeRE9OGP50EH6p7RurD7BSVHno4KBznnL/3Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:01:00.842668Z"},"content_sha256":"a8eb8fb45afb6d6d00731c5a9733d7d475c3288dd77e2e69844fdd071c7668a8","schema_version":"1.0","event_id":"sha256:a8eb8fb45afb6d6d00731c5a9733d7d475c3288dd77e2e69844fdd071c7668a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IHXB26QDSGSXGYHKRNJC2X5OC4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mappings of Conjugation of Quaternion Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Aleks Kleyn","submitted_at":"2012-02-23T02:07:46Z","abstract_excerpt":"In the paper I considered mappings of conjugation of quaternion algebra. I proved the theorem that there is unique expansion of R-linear mapping of quaternion algebra relative to the given set of mappings of conjugation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6021","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":"2026-05-18T03:53:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"utKaCaF8YZh0cyx3jtSGPg+ZQdA6x/7qPaxGdde9GMS8tj4efMv72kkxqUvQ8WKUM8EjCSuHYAiGzN+G9nfyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:01:00.843363Z"},"content_sha256":"277fc39a4210cd82863fec39b20ce38d09f237d26e9d5d220ddef411c6e998b9","schema_version":"1.0","event_id":"sha256:277fc39a4210cd82863fec39b20ce38d09f237d26e9d5d220ddef411c6e998b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHXB26QDSGSXGYHKRNJC2X5OC4/bundle.json","state_url":"https://pith.science/pith/IHXB26QDSGSXGYHKRNJC2X5OC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHXB26QDSGSXGYHKRNJC2X5OC4/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":"2026-06-09T05:01:00Z","links":{"resolver":"https://pith.science/pith/IHXB26QDSGSXGYHKRNJC2X5OC4","bundle":"https://pith.science/pith/IHXB26QDSGSXGYHKRNJC2X5OC4/bundle.json","state":"https://pith.science/pith/IHXB26QDSGSXGYHKRNJC2X5OC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHXB26QDSGSXGYHKRNJC2X5OC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IHXB26QDSGSXGYHKRNJC2X5OC4","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":"34f188538e5efbef903e7ba78308bbb4ca5d00386220674f2211ae8fd55d8c8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-02-23T02:07:46Z","title_canon_sha256":"bce9e47696f31544be019da75dededcf0387e1ee77f1627b04f857823e553448"},"schema_version":"1.0","source":{"id":"1202.6021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6021","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6021v2","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6021","created_at":"2026-05-18T03:53:54Z"},{"alias_kind":"pith_short_12","alias_value":"IHXB26QDSGSX","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IHXB26QDSGSXGYHK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IHXB26QD","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:277fc39a4210cd82863fec39b20ce38d09f237d26e9d5d220ddef411c6e998b9","target":"graph","created_at":"2026-05-18T03:53:54Z","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":"In the paper I considered mappings of conjugation of quaternion algebra. I proved the theorem that there is unique expansion of R-linear mapping of quaternion algebra relative to the given set of mappings of conjugation.","authors_text":"Aleks Kleyn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-02-23T02:07:46Z","title":"Mappings of Conjugation of Quaternion Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6021","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:a8eb8fb45afb6d6d00731c5a9733d7d475c3288dd77e2e69844fdd071c7668a8","target":"record","created_at":"2026-05-18T03:53:54Z","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":"34f188538e5efbef903e7ba78308bbb4ca5d00386220674f2211ae8fd55d8c8a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-02-23T02:07:46Z","title_canon_sha256":"bce9e47696f31544be019da75dededcf0387e1ee77f1627b04f857823e553448"},"schema_version":"1.0","source":{"id":"1202.6021","kind":"arxiv","version":2}},"canonical_sha256":"41ee1d7a0391a57360ea8b522d5fae1708365ccd27c88a54d82d12ec3172c504","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41ee1d7a0391a57360ea8b522d5fae1708365ccd27c88a54d82d12ec3172c504","first_computed_at":"2026-05-18T03:53:54.316463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:54.316463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"560Lf7EMl7c58q3TNDx2m12/8uQiWq+NvpWBgk6IN8YRCJwsubpA/Ymt8z+0cr+1T8QKSoCg3URsDJtYfPvNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:54.317157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8eb8fb45afb6d6d00731c5a9733d7d475c3288dd77e2e69844fdd071c7668a8","sha256:277fc39a4210cd82863fec39b20ce38d09f237d26e9d5d220ddef411c6e998b9"],"state_sha256":"a49898382de87e10bf7e28aa6766b66901b06e40a938af7d007bbb044fc3e561"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EKZ3ZVI9uFefgt1zgX8qg+lo0hY7o2J9fIFRNaPYl6c9Rm7wgrjZODHn9tY4FhyLD4888K+0xa9Ks1nHVgk0Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:01:00.847180Z","bundle_sha256":"b54445f95862c4c0fb81aad5ee709415e7e8f1a728f2d2fe4298bdc5b633c508"}}