{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AXFGLXGE24MMZSGERCXA5DDLWQ","short_pith_number":"pith:AXFGLXGE","canonical_record":{"source":{"id":"1708.05432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-17T20:41:47Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c3892f025e397d3fbb361b0a854be8b17bdae0cb1ffe2c1ac0ec484714090751","abstract_canon_sha256":"79661ac72a02fa5c524d7732c180a0433f1b7c9b01495d5782e36dec95c9115b"},"schema_version":"1.0"},"canonical_sha256":"05ca65dcc4d718ccc8c488ae0e8c6bb43647f7e2a5e769b67bb599e19f45989f","source":{"kind":"arxiv","id":"1708.05432","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05432","created_at":"2026-05-18T00:37:50Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05432v1","created_at":"2026-05-18T00:37:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05432","created_at":"2026-05-18T00:37:50Z"},{"alias_kind":"pith_short_12","alias_value":"AXFGLXGE24MM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AXFGLXGE24MMZSGE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AXFGLXGE","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AXFGLXGE24MMZSGERCXA5DDLWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.05432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-17T20:41:47Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c3892f025e397d3fbb361b0a854be8b17bdae0cb1ffe2c1ac0ec484714090751","abstract_canon_sha256":"79661ac72a02fa5c524d7732c180a0433f1b7c9b01495d5782e36dec95c9115b"},"schema_version":"1.0"},"canonical_sha256":"05ca65dcc4d718ccc8c488ae0e8c6bb43647f7e2a5e769b67bb599e19f45989f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:50.091223Z","signature_b64":"b3DoSTIWcrfhPUM3HMMXHFYRaQFKi89P1LIVe38Qwyfql+loFPfg0d/PitC2J74C/xMU7CwpoY+uS6MCaoIvBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05ca65dcc4d718ccc8c488ae0e8c6bb43647f7e2a5e769b67bb599e19f45989f","last_reissued_at":"2026-05-18T00:37:50.090721Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:50.090721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.05432","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":"2026-05-18T00:37:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jatTJHOmQ3WJOfaN+k42ZhPxWhDl8qE/63x3ACG7hms1jm6HrYejDhLt08LmGd6Xo+UkUF4WEELkfRe6V+OqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:22:45.301040Z"},"content_sha256":"0bae1cd678fc25b04bd6a855c7159702f4c8fba7fcd39452e69bce54725929c7","schema_version":"1.0","event_id":"sha256:0bae1cd678fc25b04bd6a855c7159702f4c8fba7fcd39452e69bce54725929c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AXFGLXGE24MMZSGERCXA5DDLWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $q$-commutative power and Laurent series rings at roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Edward S. Letzter, Linhong Wang, Xingting Wang","submitted_at":"2017-08-17T20:41:47Z","abstract_excerpt":"We continue the first and second authors' study of $q$-commutative power series rings $R=k_q[[x_1,\\ldots,x_n]]$ and Laurent series rings $L=k_q[[x^{\\pm 1}_1,\\ldots,x^{\\pm 1}_n]]$, specializing to the case in which the commutation parameters $q_{ij}$ are all roots of unity. In this setting, $R$ is a PI algebra, and we can apply results of De Concini, Kac, and Procesi to show that $L$ is an Azumaya algebra whose degree can be inferred from the $q_{ij}$. Our main result establishes an exact criterion (dependent on the $q_{ij}$) for determining when the centers of $L$ and $R$ are commutative Laure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05432","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":"2026-05-18T00:37:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MhB3njavZ8VzSwSAGeMhEGU/ZnhLU4KnAm9SUo6jyxE4QdA3jddFFeXqc0JgI5X8DIg3PBEDtrt/zf6jvknYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:22:45.301701Z"},"content_sha256":"10f9b2d7da19baeddde73f462d9f4819ee75812139e9aece7b83cb10e35edb97","schema_version":"1.0","event_id":"sha256:10f9b2d7da19baeddde73f462d9f4819ee75812139e9aece7b83cb10e35edb97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXFGLXGE24MMZSGERCXA5DDLWQ/bundle.json","state_url":"https://pith.science/pith/AXFGLXGE24MMZSGERCXA5DDLWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXFGLXGE24MMZSGERCXA5DDLWQ/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":"2026-05-30T20:22:45Z","links":{"resolver":"https://pith.science/pith/AXFGLXGE24MMZSGERCXA5DDLWQ","bundle":"https://pith.science/pith/AXFGLXGE24MMZSGERCXA5DDLWQ/bundle.json","state":"https://pith.science/pith/AXFGLXGE24MMZSGERCXA5DDLWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXFGLXGE24MMZSGERCXA5DDLWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AXFGLXGE24MMZSGERCXA5DDLWQ","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":"79661ac72a02fa5c524d7732c180a0433f1b7c9b01495d5782e36dec95c9115b","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-17T20:41:47Z","title_canon_sha256":"c3892f025e397d3fbb361b0a854be8b17bdae0cb1ffe2c1ac0ec484714090751"},"schema_version":"1.0","source":{"id":"1708.05432","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05432","created_at":"2026-05-18T00:37:50Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05432v1","created_at":"2026-05-18T00:37:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05432","created_at":"2026-05-18T00:37:50Z"},{"alias_kind":"pith_short_12","alias_value":"AXFGLXGE24MM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"AXFGLXGE24MMZSGE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"AXFGLXGE","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:10f9b2d7da19baeddde73f462d9f4819ee75812139e9aece7b83cb10e35edb97","target":"graph","created_at":"2026-05-18T00:37:50Z","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 continue the first and second authors' study of $q$-commutative power series rings $R=k_q[[x_1,\\ldots,x_n]]$ and Laurent series rings $L=k_q[[x^{\\pm 1}_1,\\ldots,x^{\\pm 1}_n]]$, specializing to the case in which the commutation parameters $q_{ij}$ are all roots of unity. In this setting, $R$ is a PI algebra, and we can apply results of De Concini, Kac, and Procesi to show that $L$ is an Azumaya algebra whose degree can be inferred from the $q_{ij}$. Our main result establishes an exact criterion (dependent on the $q_{ij}$) for determining when the centers of $L$ and $R$ are commutative Laure","authors_text":"Edward S. Letzter, Linhong Wang, Xingting Wang","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-17T20:41:47Z","title":"On $q$-commutative power and Laurent series rings at roots of unity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05432","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":"sha256:0bae1cd678fc25b04bd6a855c7159702f4c8fba7fcd39452e69bce54725929c7","target":"record","created_at":"2026-05-18T00:37:50Z","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":"79661ac72a02fa5c524d7732c180a0433f1b7c9b01495d5782e36dec95c9115b","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-08-17T20:41:47Z","title_canon_sha256":"c3892f025e397d3fbb361b0a854be8b17bdae0cb1ffe2c1ac0ec484714090751"},"schema_version":"1.0","source":{"id":"1708.05432","kind":"arxiv","version":1}},"canonical_sha256":"05ca65dcc4d718ccc8c488ae0e8c6bb43647f7e2a5e769b67bb599e19f45989f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05ca65dcc4d718ccc8c488ae0e8c6bb43647f7e2a5e769b67bb599e19f45989f","first_computed_at":"2026-05-18T00:37:50.090721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:50.090721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b3DoSTIWcrfhPUM3HMMXHFYRaQFKi89P1LIVe38Qwyfql+loFPfg0d/PitC2J74C/xMU7CwpoY+uS6MCaoIvBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:50.091223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05432","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bae1cd678fc25b04bd6a855c7159702f4c8fba7fcd39452e69bce54725929c7","sha256:10f9b2d7da19baeddde73f462d9f4819ee75812139e9aece7b83cb10e35edb97"],"state_sha256":"1f68d3d08ff7080b369036e389d7bd28a175b9157730194a91bb50d76656b348"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IIlx1dpu7t+n7O7zGRzOL4RkgbqtJMK0vBhkiy+M4KIanSJDoUuupg8n0C13/ONBGYOeB4mne7nAP4vBwqgxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:22:45.305111Z","bundle_sha256":"7d39cf4e3c45f0d6b38624fa22c7411e1fb7072876b61c76a238558868ab7aed"}}