{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:ERRLWDCWXEP7YLG4ZI62HNXXCT","short_pith_number":"pith:ERRLWDCW","canonical_record":{"source":{"id":"2007.05375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-10T13:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"7e5638758d986e49d97ad7db4b21d648179106f6321e5e69979f59bcf90a2e5b","abstract_canon_sha256":"b2aa1c3c0d7edcdec07a408e1477a4d8705787027b15bdc32e33d70d71be68a7"},"schema_version":"1.0"},"canonical_sha256":"2462bb0c56b91ffc2cdcca3da3b6f714dc26b52e0bee0780f6b065dee5c0e998","source":{"kind":"arxiv","id":"2007.05375","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.05375","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2007.05375v1","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.05375","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"ERRLWDCWXEP7","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"ERRLWDCWXEP7YLG4","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"ERRLWDCW","created_at":"2026-07-05T01:17:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:ERRLWDCWXEP7YLG4ZI62HNXXCT","target":"record","payload":{"canonical_record":{"source":{"id":"2007.05375","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-10T13:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"7e5638758d986e49d97ad7db4b21d648179106f6321e5e69979f59bcf90a2e5b","abstract_canon_sha256":"b2aa1c3c0d7edcdec07a408e1477a4d8705787027b15bdc32e33d70d71be68a7"},"schema_version":"1.0"},"canonical_sha256":"2462bb0c56b91ffc2cdcca3da3b6f714dc26b52e0bee0780f6b065dee5c0e998","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:46.031468Z","signature_b64":"mZZbiqj6cnMoWkKuv6KDEtPillGzlQxcaFg6Vr8TmtV/VzH8bd7OboTcodlPGf/iZCbk3U21U4qSpDJnd6tlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2462bb0c56b91ffc2cdcca3da3b6f714dc26b52e0bee0780f6b065dee5c0e998","last_reissued_at":"2026-07-05T01:17:46.031119Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:46.031119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.05375","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":"2026-07-05T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nXoU+1Dy7WsB5jvpo3O7DmhflivhYUZpecstmtoiALM7KS3+v5+wAWn98pUpB4fgKxPZqEhPM9bvT2sXF1dlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:11:59.738590Z"},"content_sha256":"2a447dbb6aa7383ae840c9d814e3b4fa25ec8acabbfca85cfa4ea5fad765b4d2","schema_version":"1.0","event_id":"sha256:2a447dbb6aa7383ae840c9d814e3b4fa25ec8acabbfca85cfa4ea5fad765b4d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:ERRLWDCWXEP7YLG4ZI62HNXXCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Octonionic bimodule","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Guangbin Ren, Qinghai Huo","submitted_at":"2020-07-10T13:29:52Z","abstract_excerpt":"The structure of octonionic bimodules is formulated in this paper. It turns out that every octonionic bimodule is a tensor product, the category of octonionic bimodules is isomorphic to the category of real vector spaces. We show that there is also a real part structure on octonionic bimodules similar to the quaternion case. Different from the quaternion setting , the octonionic bimodule sturcture is uniquely determined by its left module structure and hence the real part can be obtained only by left multiplication. The structure of octonionic submodules generated by one element is more involv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.05375","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.05375/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:17:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HJt57cPvClUMakzucSeBt58jTOt+tADi9WaisCeEe7UTDcCcIcTee3Ng7x47JbC/c+jinM56fHrMugHK7/KJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:11:59.738959Z"},"content_sha256":"0fd86615daaadaf5a3a44b68e77e2740179c11c7eb220439945f5ceff5589176","schema_version":"1.0","event_id":"sha256:0fd86615daaadaf5a3a44b68e77e2740179c11c7eb220439945f5ceff5589176"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERRLWDCWXEP7YLG4ZI62HNXXCT/bundle.json","state_url":"https://pith.science/pith/ERRLWDCWXEP7YLG4ZI62HNXXCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERRLWDCWXEP7YLG4ZI62HNXXCT/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":"2026-07-07T11:11:59Z","links":{"resolver":"https://pith.science/pith/ERRLWDCWXEP7YLG4ZI62HNXXCT","bundle":"https://pith.science/pith/ERRLWDCWXEP7YLG4ZI62HNXXCT/bundle.json","state":"https://pith.science/pith/ERRLWDCWXEP7YLG4ZI62HNXXCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERRLWDCWXEP7YLG4ZI62HNXXCT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:ERRLWDCWXEP7YLG4ZI62HNXXCT","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":"b2aa1c3c0d7edcdec07a408e1477a4d8705787027b15bdc32e33d70d71be68a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-10T13:29:52Z","title_canon_sha256":"7e5638758d986e49d97ad7db4b21d648179106f6321e5e69979f59bcf90a2e5b"},"schema_version":"1.0","source":{"id":"2007.05375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.05375","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"arxiv_version","alias_value":"2007.05375v1","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.05375","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"pith_short_12","alias_value":"ERRLWDCWXEP7","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"pith_short_16","alias_value":"ERRLWDCWXEP7YLG4","created_at":"2026-07-05T01:17:46Z"},{"alias_kind":"pith_short_8","alias_value":"ERRLWDCW","created_at":"2026-07-05T01:17:46Z"}],"graph_snapshots":[{"event_id":"sha256:0fd86615daaadaf5a3a44b68e77e2740179c11c7eb220439945f5ceff5589176","target":"graph","created_at":"2026-07-05T01:17:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.05375/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The structure of octonionic bimodules is formulated in this paper. It turns out that every octonionic bimodule is a tensor product, the category of octonionic bimodules is isomorphic to the category of real vector spaces. We show that there is also a real part structure on octonionic bimodules similar to the quaternion case. Different from the quaternion setting , the octonionic bimodule sturcture is uniquely determined by its left module structure and hence the real part can be obtained only by left multiplication. The structure of octonionic submodules generated by one element is more involv","authors_text":"Guangbin Ren, Qinghai Huo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-10T13:29:52Z","title":"Octonionic bimodule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.05375","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":"sha256:2a447dbb6aa7383ae840c9d814e3b4fa25ec8acabbfca85cfa4ea5fad765b4d2","target":"record","created_at":"2026-07-05T01:17:46Z","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":"b2aa1c3c0d7edcdec07a408e1477a4d8705787027b15bdc32e33d70d71be68a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-07-10T13:29:52Z","title_canon_sha256":"7e5638758d986e49d97ad7db4b21d648179106f6321e5e69979f59bcf90a2e5b"},"schema_version":"1.0","source":{"id":"2007.05375","kind":"arxiv","version":1}},"canonical_sha256":"2462bb0c56b91ffc2cdcca3da3b6f714dc26b52e0bee0780f6b065dee5c0e998","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2462bb0c56b91ffc2cdcca3da3b6f714dc26b52e0bee0780f6b065dee5c0e998","first_computed_at":"2026-07-05T01:17:46.031119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:46.031119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mZZbiqj6cnMoWkKuv6KDEtPillGzlQxcaFg6Vr8TmtV/VzH8bd7OboTcodlPGf/iZCbk3U21U4qSpDJnd6tlAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:46.031468Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.05375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a447dbb6aa7383ae840c9d814e3b4fa25ec8acabbfca85cfa4ea5fad765b4d2","sha256:0fd86615daaadaf5a3a44b68e77e2740179c11c7eb220439945f5ceff5589176"],"state_sha256":"50cf418d8bd7cbd7122075632ec9cf79128f5806e4d419b1756dada42cb6c238"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1eApM44uQeaKFg63CPFOdmt8r2/bJ6JzVfcYN+TdJMN16r6LR5PAtUMsV/TNUgAko3sGWvrB+5tF41r58RiNCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:11:59.740845Z","bundle_sha256":"a1b50262e6cb64ba5e409040239eb41263fd0d89f40b821d434fc8e8537d4bc1"}}