{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:D7TE6GNR7HME5WXZO4TRGQ5HVB","short_pith_number":"pith:D7TE6GNR","canonical_record":{"source":{"id":"1204.0044","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-30T22:57:38Z","cross_cats_sorted":[],"title_canon_sha256":"032c59ce56d5995954a39a1938e5731618a03bbd1b2908f04a606b3b53919474","abstract_canon_sha256":"dc101a4a360f4e64656ed0bdee2626acfcadf5856c2f2a0e30520cf7ed34cf01"},"schema_version":"1.0"},"canonical_sha256":"1fe64f19b1f9d84edaf977271343a7a8794a03226340ebad8159c666c60706b4","source":{"kind":"arxiv","id":"1204.0044","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0044","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0044v3","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0044","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"D7TE6GNR7HME","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D7TE6GNR7HME5WXZ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D7TE6GNR","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:D7TE6GNR7HME5WXZO4TRGQ5HVB","target":"record","payload":{"canonical_record":{"source":{"id":"1204.0044","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-30T22:57:38Z","cross_cats_sorted":[],"title_canon_sha256":"032c59ce56d5995954a39a1938e5731618a03bbd1b2908f04a606b3b53919474","abstract_canon_sha256":"dc101a4a360f4e64656ed0bdee2626acfcadf5856c2f2a0e30520cf7ed34cf01"},"schema_version":"1.0"},"canonical_sha256":"1fe64f19b1f9d84edaf977271343a7a8794a03226340ebad8159c666c60706b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.611843Z","signature_b64":"FhNoGkkYHMAXPAPCGaOBDbsoCkV7ucK10llcQJQ9gBSqtfyJNYIv4tD1ff0Q2LggjXHbUcxfUVT5JjJySjfwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fe64f19b1f9d84edaf977271343a7a8794a03226340ebad8159c666c60706b4","last_reissued_at":"2026-05-18T02:51:42.611372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.611372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.0044","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mOBMjEQZhn+uEZyqcPjCna0Ff9J8cuNR4WVdvNOr0ZlMSMel65k2GKkPz499Phu3+sWN5A+D7KfwOVmxJbT2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:44:33.720026Z"},"content_sha256":"9021cfdf423e3fe154850b2d04a8a0f53ac1b355265bc1f8fcb0229ab0d8e890","schema_version":"1.0","event_id":"sha256:9021cfdf423e3fe154850b2d04a8a0f53ac1b355265bc1f8fcb0229ab0d8e890"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:D7TE6GNR7HME5WXZO4TRGQ5HVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graded Skew Clifford Algebras that are Twists of Graded Clifford Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Manizheh Nafari, Michaela Vancliff","submitted_at":"2012-03-30T22:57:38Z","abstract_excerpt":"We prove that if $A$ is a regular graded skew Clifford algebra and is a twist of a regular graded Clifford algebra $B$ by an automorphism, then the subalgebra of $A$ generated by a certain normalizing sequence of homogeneous degree-two elements is a twist of a polynomial ring by an automorphism, and is a skew polynomial ring. We also present an example that demonstrates that this can fail when $A$ is not a twist of $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0044","kind":"arxiv","version":3},"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":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0ESNY6fnUzKqxHs12uoJ+FJ2ellTrlKRRkrPZVgJ7OOPdgYbWAonIaJyX2DzTUGxxIhwcqxWDJn5wRS8fPJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:44:33.720808Z"},"content_sha256":"04b0ac3977273edf7bccfb94e6ee94500a26c2f56d2575c395c5f7b6a10eadbb","schema_version":"1.0","event_id":"sha256:04b0ac3977273edf7bccfb94e6ee94500a26c2f56d2575c395c5f7b6a10eadbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D7TE6GNR7HME5WXZO4TRGQ5HVB/bundle.json","state_url":"https://pith.science/pith/D7TE6GNR7HME5WXZO4TRGQ5HVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D7TE6GNR7HME5WXZO4TRGQ5HVB/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":"2026-06-09T05:44:33Z","links":{"resolver":"https://pith.science/pith/D7TE6GNR7HME5WXZO4TRGQ5HVB","bundle":"https://pith.science/pith/D7TE6GNR7HME5WXZO4TRGQ5HVB/bundle.json","state":"https://pith.science/pith/D7TE6GNR7HME5WXZO4TRGQ5HVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D7TE6GNR7HME5WXZO4TRGQ5HVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D7TE6GNR7HME5WXZO4TRGQ5HVB","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":"dc101a4a360f4e64656ed0bdee2626acfcadf5856c2f2a0e30520cf7ed34cf01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-30T22:57:38Z","title_canon_sha256":"032c59ce56d5995954a39a1938e5731618a03bbd1b2908f04a606b3b53919474"},"schema_version":"1.0","source":{"id":"1204.0044","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0044","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0044v3","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0044","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"D7TE6GNR7HME","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D7TE6GNR7HME5WXZ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D7TE6GNR","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:04b0ac3977273edf7bccfb94e6ee94500a26c2f56d2575c395c5f7b6a10eadbb","target":"graph","created_at":"2026-05-18T02:51:42Z","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 prove that if $A$ is a regular graded skew Clifford algebra and is a twist of a regular graded Clifford algebra $B$ by an automorphism, then the subalgebra of $A$ generated by a certain normalizing sequence of homogeneous degree-two elements is a twist of a polynomial ring by an automorphism, and is a skew polynomial ring. We also present an example that demonstrates that this can fail when $A$ is not a twist of $B$.","authors_text":"Manizheh Nafari, Michaela Vancliff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-30T22:57:38Z","title":"Graded Skew Clifford Algebras that are Twists of Graded Clifford Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0044","kind":"arxiv","version":3},"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":"sha256:9021cfdf423e3fe154850b2d04a8a0f53ac1b355265bc1f8fcb0229ab0d8e890","target":"record","created_at":"2026-05-18T02:51:42Z","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":"dc101a4a360f4e64656ed0bdee2626acfcadf5856c2f2a0e30520cf7ed34cf01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-30T22:57:38Z","title_canon_sha256":"032c59ce56d5995954a39a1938e5731618a03bbd1b2908f04a606b3b53919474"},"schema_version":"1.0","source":{"id":"1204.0044","kind":"arxiv","version":3}},"canonical_sha256":"1fe64f19b1f9d84edaf977271343a7a8794a03226340ebad8159c666c60706b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fe64f19b1f9d84edaf977271343a7a8794a03226340ebad8159c666c60706b4","first_computed_at":"2026-05-18T02:51:42.611372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.611372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FhNoGkkYHMAXPAPCGaOBDbsoCkV7ucK10llcQJQ9gBSqtfyJNYIv4tD1ff0Q2LggjXHbUcxfUVT5JjJySjfwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.611843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0044","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9021cfdf423e3fe154850b2d04a8a0f53ac1b355265bc1f8fcb0229ab0d8e890","sha256:04b0ac3977273edf7bccfb94e6ee94500a26c2f56d2575c395c5f7b6a10eadbb"],"state_sha256":"0bf0588b4a1d198ea6ee1dfcb8e33596ae3e43ce64d69438841bd33e1e407f6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e+aPZtXqNkVAidLg7WGgKFYM4dr0eoCU9jA6XBedivHyBdbHD3u+fLxZfLsdY4tLGGA1jfvj85ni7KoZ5GvhAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:44:33.724718Z","bundle_sha256":"330a213d197777d8829b1565c6d1e0a4d074f0ac997ed5057489a00260fb16b1"}}