{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:HSCAJZRQ3TZSLV2RJHLNCAPSSB","short_pith_number":"pith:HSCAJZRQ","canonical_record":{"source":{"id":"0904.4310","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-28T05:41:36Z","cross_cats_sorted":[],"title_canon_sha256":"5d385d0a391b05b313fc8daa2f3336687b992934d987c50c11d3c3689de88cd4","abstract_canon_sha256":"a12a838ee90d52a11c473c3b50db7a9c77fbca8c3ba272187e753993e592fbda"},"schema_version":"1.0"},"canonical_sha256":"3c8404e630dcf325d75149d6d101f29066a5080df05e4d39e5a58580c1a92f2b","source":{"kind":"arxiv","id":"0904.4310","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4310","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4310v5","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4310","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"pith_short_12","alias_value":"HSCAJZRQ3TZS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HSCAJZRQ3TZSLV2R","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HSCAJZRQ","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:HSCAJZRQ3TZSLV2RJHLNCAPSSB","target":"record","payload":{"canonical_record":{"source":{"id":"0904.4310","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-28T05:41:36Z","cross_cats_sorted":[],"title_canon_sha256":"5d385d0a391b05b313fc8daa2f3336687b992934d987c50c11d3c3689de88cd4","abstract_canon_sha256":"a12a838ee90d52a11c473c3b50db7a9c77fbca8c3ba272187e753993e592fbda"},"schema_version":"1.0"},"canonical_sha256":"3c8404e630dcf325d75149d6d101f29066a5080df05e4d39e5a58580c1a92f2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:54.601542Z","signature_b64":"N11wI4AyWopGkO9Xwe6+gEObjgbj16rFCpSauOP5nVfkAqjcZrdKcEguDxz41mUpLyOdqKOwoExbgz3VEDmQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c8404e630dcf325d75149d6d101f29066a5080df05e4d39e5a58580c1a92f2b","last_reissued_at":"2026-05-18T04:23:54.601085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:54.601085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.4310","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CFhPOlgHTZI7cKnZDFIYsM8eQBZh8vocm1UvvSUH19Pv4Xia8nL8pWLYh0zO6ZwLDnZ9t4oshYpqKiO3/xBPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:20:51.291994Z"},"content_sha256":"a025b407e0e6bfc80d6f56daaf3263a45c2455e511e96d9765a18d98c893e41c","schema_version":"1.0","event_id":"sha256:a025b407e0e6bfc80d6f56daaf3263a45c2455e511e96d9765a18d98c893e41c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:HSCAJZRQ3TZSLV2RJHLNCAPSSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing quaternion rings over an arbitrary base","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"John Voight","submitted_at":"2009-04-28T05:41:36Z","abstract_excerpt":"We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4310","kind":"arxiv","version":5},"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":"2026-05-18T04:23:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40EvprECLOk2dgP91GkZJB+LGCJoaNOs56/4MRxNFPgHpFY9rqfgkNUJ6QhP/z+6R8NumKVdHBPIWZvSHRGXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:20:51.292355Z"},"content_sha256":"562e0a3dae6ab9b84396dd797ad46d9c301f4259836a9a8e08171622039e5094","schema_version":"1.0","event_id":"sha256:562e0a3dae6ab9b84396dd797ad46d9c301f4259836a9a8e08171622039e5094"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSCAJZRQ3TZSLV2RJHLNCAPSSB/bundle.json","state_url":"https://pith.science/pith/HSCAJZRQ3TZSLV2RJHLNCAPSSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSCAJZRQ3TZSLV2RJHLNCAPSSB/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":"2026-05-30T05:20:51Z","links":{"resolver":"https://pith.science/pith/HSCAJZRQ3TZSLV2RJHLNCAPSSB","bundle":"https://pith.science/pith/HSCAJZRQ3TZSLV2RJHLNCAPSSB/bundle.json","state":"https://pith.science/pith/HSCAJZRQ3TZSLV2RJHLNCAPSSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSCAJZRQ3TZSLV2RJHLNCAPSSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HSCAJZRQ3TZSLV2RJHLNCAPSSB","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":"a12a838ee90d52a11c473c3b50db7a9c77fbca8c3ba272187e753993e592fbda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-28T05:41:36Z","title_canon_sha256":"5d385d0a391b05b313fc8daa2f3336687b992934d987c50c11d3c3689de88cd4"},"schema_version":"1.0","source":{"id":"0904.4310","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4310","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4310v5","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4310","created_at":"2026-05-18T04:23:54Z"},{"alias_kind":"pith_short_12","alias_value":"HSCAJZRQ3TZS","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HSCAJZRQ3TZSLV2R","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HSCAJZRQ","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:562e0a3dae6ab9b84396dd797ad46d9c301f4259836a9a8e08171622039e5094","target":"graph","created_at":"2026-05-18T04:23:54Z","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":"We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra.","authors_text":"John Voight","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-28T05:41:36Z","title":"Characterizing quaternion rings over an arbitrary base"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4310","kind":"arxiv","version":5},"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:a025b407e0e6bfc80d6f56daaf3263a45c2455e511e96d9765a18d98c893e41c","target":"record","created_at":"2026-05-18T04:23:54Z","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":"a12a838ee90d52a11c473c3b50db7a9c77fbca8c3ba272187e753993e592fbda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-04-28T05:41:36Z","title_canon_sha256":"5d385d0a391b05b313fc8daa2f3336687b992934d987c50c11d3c3689de88cd4"},"schema_version":"1.0","source":{"id":"0904.4310","kind":"arxiv","version":5}},"canonical_sha256":"3c8404e630dcf325d75149d6d101f29066a5080df05e4d39e5a58580c1a92f2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c8404e630dcf325d75149d6d101f29066a5080df05e4d39e5a58580c1a92f2b","first_computed_at":"2026-05-18T04:23:54.601085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:54.601085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N11wI4AyWopGkO9Xwe6+gEObjgbj16rFCpSauOP5nVfkAqjcZrdKcEguDxz41mUpLyOdqKOwoExbgz3VEDmQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:54.601542Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4310","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a025b407e0e6bfc80d6f56daaf3263a45c2455e511e96d9765a18d98c893e41c","sha256:562e0a3dae6ab9b84396dd797ad46d9c301f4259836a9a8e08171622039e5094"],"state_sha256":"dd5fbf3adecf0350a86009979788983fc8001bd02e2a82f7eea546b9d173d271"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5CFjewIfmkhYJk+N8PT7LscxlfChFDEsOIRywtTG5KdEyKseOBFus1qVL/up/Xa73joedQiKssjIcpD7qSDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:20:51.294358Z","bundle_sha256":"b1c2abc0eacebc4d48d1b9d4f53282f3ee129503b599d0645005975fc5845132"}}