{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:P2553T6CFXBZFY43NZBVSAYKML","short_pith_number":"pith:P2553T6C","canonical_record":{"source":{"id":"1903.05575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2019-03-13T16:19:27Z","cross_cats_sorted":[],"title_canon_sha256":"a98f589c8848fe8bf1219278595d81713aa9004c8960316a15230d1fc9a8fd96","abstract_canon_sha256":"6552054322e604656a0fb371494ab8ea08b82a735886f4ff7b72d17ee4ffa615"},"schema_version":"1.0"},"canonical_sha256":"7ebbddcfc22dc392e39b6e4359030a62cfa2a475cd01037ca0f701b5bde5fa29","source":{"kind":"arxiv","id":"1903.05575","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05575","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05575v1","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05575","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"pith_short_12","alias_value":"P2553T6CFXBZ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P2553T6CFXBZFY43","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P2553T6C","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:P2553T6CFXBZFY43NZBVSAYKML","target":"record","payload":{"canonical_record":{"source":{"id":"1903.05575","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2019-03-13T16:19:27Z","cross_cats_sorted":[],"title_canon_sha256":"a98f589c8848fe8bf1219278595d81713aa9004c8960316a15230d1fc9a8fd96","abstract_canon_sha256":"6552054322e604656a0fb371494ab8ea08b82a735886f4ff7b72d17ee4ffa615"},"schema_version":"1.0"},"canonical_sha256":"7ebbddcfc22dc392e39b6e4359030a62cfa2a475cd01037ca0f701b5bde5fa29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:20.590853Z","signature_b64":"b2qpOubzW44mkrijtlGlwNfjMGp/8uEj3UGUZNAo3NekgSHTWhuFW15tFuP6Fg9F7YXooROGCpbTvCgSeWwMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ebbddcfc22dc392e39b6e4359030a62cfa2a475cd01037ca0f701b5bde5fa29","last_reissued_at":"2026-05-17T23:51:20.590165Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:20.590165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.05575","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":"2026-05-17T23:51:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T770V3GI+uwpBkOdgyOuvzf0eKTnEqQ3q6b+t3mUwEngAglFMKQbdr8T6r5bHCvcB4vtnC0y219gpuyHWfz7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T22:19:17.885892Z"},"content_sha256":"020e66529df80365a7fe4a51ac27835b4a0916bc2aecd45a196ea58257da3a00","schema_version":"1.0","event_id":"sha256:020e66529df80365a7fe4a51ac27835b4a0916bc2aecd45a196ea58257da3a00"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:P2553T6CFXBZFY43NZBVSAYKML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.MS","authors_text":"David Williams-Young, Xiaosong Li","submitted_at":"2019-03-13T16:19:27Z","abstract_excerpt":"Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also seen many advances in the formal theoretical development of explicitly quaternion linear algebra with promising applications in image processing and machine learning. Despite these advances, there do not currently exist optimized software implementations of quaternion linear algebra. The leverage of optimized linear algebra software is crucial in the achievem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05575","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":"2026-05-17T23:51:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cm1d4OIS1qOQNfr9Kk/99gg8TV9sjLWbtE10ayHaZx6nXDbx7BM/qaSp1ybWoBBmBpctc/oROIKxnLMHLaN3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T22:19:17.886246Z"},"content_sha256":"6536c88756deb1bde02577e18530f1aa20f8f4db5e4ef700644742bff9b43557","schema_version":"1.0","event_id":"sha256:6536c88756deb1bde02577e18530f1aa20f8f4db5e4ef700644742bff9b43557"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2553T6CFXBZFY43NZBVSAYKML/bundle.json","state_url":"https://pith.science/pith/P2553T6CFXBZFY43NZBVSAYKML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2553T6CFXBZFY43NZBVSAYKML/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":"2026-05-19T22:19:17Z","links":{"resolver":"https://pith.science/pith/P2553T6CFXBZFY43NZBVSAYKML","bundle":"https://pith.science/pith/P2553T6CFXBZFY43NZBVSAYKML/bundle.json","state":"https://pith.science/pith/P2553T6CFXBZFY43NZBVSAYKML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2553T6CFXBZFY43NZBVSAYKML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:P2553T6CFXBZFY43NZBVSAYKML","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":"6552054322e604656a0fb371494ab8ea08b82a735886f4ff7b72d17ee4ffa615","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2019-03-13T16:19:27Z","title_canon_sha256":"a98f589c8848fe8bf1219278595d81713aa9004c8960316a15230d1fc9a8fd96"},"schema_version":"1.0","source":{"id":"1903.05575","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05575","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05575v1","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05575","created_at":"2026-05-17T23:51:20Z"},{"alias_kind":"pith_short_12","alias_value":"P2553T6CFXBZ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P2553T6CFXBZFY43","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P2553T6C","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:6536c88756deb1bde02577e18530f1aa20f8f4db5e4ef700644742bff9b43557","target":"graph","created_at":"2026-05-17T23:51:20Z","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":"Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also seen many advances in the formal theoretical development of explicitly quaternion linear algebra with promising applications in image processing and machine learning. Despite these advances, there do not currently exist optimized software implementations of quaternion linear algebra. The leverage of optimized linear algebra software is crucial in the achievem","authors_text":"David Williams-Young, Xiaosong Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2019-03-13T16:19:27Z","title":"On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05575","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":"sha256:020e66529df80365a7fe4a51ac27835b4a0916bc2aecd45a196ea58257da3a00","target":"record","created_at":"2026-05-17T23:51:20Z","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":"6552054322e604656a0fb371494ab8ea08b82a735886f4ff7b72d17ee4ffa615","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2019-03-13T16:19:27Z","title_canon_sha256":"a98f589c8848fe8bf1219278595d81713aa9004c8960316a15230d1fc9a8fd96"},"schema_version":"1.0","source":{"id":"1903.05575","kind":"arxiv","version":1}},"canonical_sha256":"7ebbddcfc22dc392e39b6e4359030a62cfa2a475cd01037ca0f701b5bde5fa29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ebbddcfc22dc392e39b6e4359030a62cfa2a475cd01037ca0f701b5bde5fa29","first_computed_at":"2026-05-17T23:51:20.590165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:20.590165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b2qpOubzW44mkrijtlGlwNfjMGp/8uEj3UGUZNAo3NekgSHTWhuFW15tFuP6Fg9F7YXooROGCpbTvCgSeWwMAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:20.590853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05575","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:020e66529df80365a7fe4a51ac27835b4a0916bc2aecd45a196ea58257da3a00","sha256:6536c88756deb1bde02577e18530f1aa20f8f4db5e4ef700644742bff9b43557"],"state_sha256":"b79e6bf472783288d6ef2d7c6a4f6e2bf5644c96977db46f2b11b78211bfc98f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uwntb5rDT6B4f2niXH91RWvZk4mRKvnCLp+es/I0Vwkb1Celx5iQHqkDNKP7yJWVEU/3LpVlmE4q1eg/4iihBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T22:19:17.888578Z","bundle_sha256":"22a5ec53f9e40c0fb430eaa4315ea1f6d396abb8c9cebaf53edd5d5ab9330241"}}