{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OOOQSQ6WWOMBDUBYBSUXJ52X6P","short_pith_number":"pith:OOOQSQ6W","canonical_record":{"source":{"id":"1003.5405","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-28T23:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"4c98154108589d292851e11189606d6bb29f8a9b7c64158f66e6f02a81654063","abstract_canon_sha256":"49d40f6ada7073229502666266e6f2819d725efc55a6472fb8bd8e55afff7f18"},"schema_version":"1.0"},"canonical_sha256":"739d0943d6b39811d0380ca974f757f3cf3c11486f438ebdf0ae671ff3c969e6","source":{"kind":"arxiv","id":"1003.5405","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5405","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5405v2","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5405","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"OOOQSQ6WWOMB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OOOQSQ6WWOMBDUBY","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OOOQSQ6W","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OOOQSQ6WWOMBDUBYBSUXJ52X6P","target":"record","payload":{"canonical_record":{"source":{"id":"1003.5405","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-28T23:40:19Z","cross_cats_sorted":[],"title_canon_sha256":"4c98154108589d292851e11189606d6bb29f8a9b7c64158f66e6f02a81654063","abstract_canon_sha256":"49d40f6ada7073229502666266e6f2819d725efc55a6472fb8bd8e55afff7f18"},"schema_version":"1.0"},"canonical_sha256":"739d0943d6b39811d0380ca974f757f3cf3c11486f438ebdf0ae671ff3c969e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:59.291079Z","signature_b64":"zUd+3U+DCr2m4SoggfLxDNarjG6TMWggkjL2xqCpMe5zyHkzLB3gJkMcKPC5R/zJvqM+P1tIV6X1HEPDeg1sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"739d0943d6b39811d0380ca974f757f3cf3c11486f438ebdf0ae671ff3c969e6","last_reissued_at":"2026-05-18T04:39:59.290495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:59.290495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.5405","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"81Z50IN9a/l9/jeRISCDSUSf8AGDAzTkaJJa/4Wo+9GCmS2oZ+GXa84gnxe/MGq5W9SG/i2A5Nh8Ecr3G2LeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:27:50.113476Z"},"content_sha256":"f297ffe40f2da3a6630a226d79b76cf5af26d13a18a45d84f8292c45ebf19bdb","schema_version":"1.0","event_id":"sha256:f297ffe40f2da3a6630a226d79b76cf5af26d13a18a45d84f8292c45ebf19bdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OOOQSQ6WWOMBDUBYBSUXJ52X6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On q-skew Iterated Ore Extensions Satisfying a Polynomial Identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Andr\\'e Leroy, Jerzy Matczuk","submitted_at":"2010-03-28T23:40:19Z","abstract_excerpt":"For iterated Ore extensions satisfying a polynomial identity we present an elementary way of erasing derivations. As a consequence we recover some results obtained by Haynal in \"PI degree parity in q-skew polynomial rings\" (J. Algebra 319, 2008, 4199-4221). We also prove, under mild assumptions on $R_n=R[x_1;\\si_1,\\de_1]...[x_n;\\si_n;\\de_n]$ that the Ore extension $R[x_1;\\si_1]...[x_n;\\si_n]$ exists and is PI if $R_n$ is PI."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5405","kind":"arxiv","version":2},"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":"2026-05-18T04:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xt+Kosna0i89JGWlufZxB8C9u/pTZvujB8HwsT1iKwd3YcjQN0+VdIlCAscRoQ4G4v2/Pk9nx5Z4OVyq/XTCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:27:50.113815Z"},"content_sha256":"766982a1a1769d7429fc0002d302378397032a65d2226cb1569cbeb6a813b346","schema_version":"1.0","event_id":"sha256:766982a1a1769d7429fc0002d302378397032a65d2226cb1569cbeb6a813b346"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOOQSQ6WWOMBDUBYBSUXJ52X6P/bundle.json","state_url":"https://pith.science/pith/OOOQSQ6WWOMBDUBYBSUXJ52X6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOOQSQ6WWOMBDUBYBSUXJ52X6P/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":"2026-06-01T08:27:50Z","links":{"resolver":"https://pith.science/pith/OOOQSQ6WWOMBDUBYBSUXJ52X6P","bundle":"https://pith.science/pith/OOOQSQ6WWOMBDUBYBSUXJ52X6P/bundle.json","state":"https://pith.science/pith/OOOQSQ6WWOMBDUBYBSUXJ52X6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOOQSQ6WWOMBDUBYBSUXJ52X6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OOOQSQ6WWOMBDUBYBSUXJ52X6P","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":"49d40f6ada7073229502666266e6f2819d725efc55a6472fb8bd8e55afff7f18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-28T23:40:19Z","title_canon_sha256":"4c98154108589d292851e11189606d6bb29f8a9b7c64158f66e6f02a81654063"},"schema_version":"1.0","source":{"id":"1003.5405","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5405","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5405v2","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5405","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"OOOQSQ6WWOMB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OOOQSQ6WWOMBDUBY","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OOOQSQ6W","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:766982a1a1769d7429fc0002d302378397032a65d2226cb1569cbeb6a813b346","target":"graph","created_at":"2026-05-18T04:39:59Z","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":"For iterated Ore extensions satisfying a polynomial identity we present an elementary way of erasing derivations. As a consequence we recover some results obtained by Haynal in \"PI degree parity in q-skew polynomial rings\" (J. Algebra 319, 2008, 4199-4221). We also prove, under mild assumptions on $R_n=R[x_1;\\si_1,\\de_1]...[x_n;\\si_n;\\de_n]$ that the Ore extension $R[x_1;\\si_1]...[x_n;\\si_n]$ exists and is PI if $R_n$ is PI.","authors_text":"Andr\\'e Leroy, Jerzy Matczuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-28T23:40:19Z","title":"On q-skew Iterated Ore Extensions Satisfying a Polynomial Identity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5405","kind":"arxiv","version":2},"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:f297ffe40f2da3a6630a226d79b76cf5af26d13a18a45d84f8292c45ebf19bdb","target":"record","created_at":"2026-05-18T04:39:59Z","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":"49d40f6ada7073229502666266e6f2819d725efc55a6472fb8bd8e55afff7f18","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-28T23:40:19Z","title_canon_sha256":"4c98154108589d292851e11189606d6bb29f8a9b7c64158f66e6f02a81654063"},"schema_version":"1.0","source":{"id":"1003.5405","kind":"arxiv","version":2}},"canonical_sha256":"739d0943d6b39811d0380ca974f757f3cf3c11486f438ebdf0ae671ff3c969e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"739d0943d6b39811d0380ca974f757f3cf3c11486f438ebdf0ae671ff3c969e6","first_computed_at":"2026-05-18T04:39:59.290495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.290495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zUd+3U+DCr2m4SoggfLxDNarjG6TMWggkjL2xqCpMe5zyHkzLB3gJkMcKPC5R/zJvqM+P1tIV6X1HEPDeg1sCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.291079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5405","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f297ffe40f2da3a6630a226d79b76cf5af26d13a18a45d84f8292c45ebf19bdb","sha256:766982a1a1769d7429fc0002d302378397032a65d2226cb1569cbeb6a813b346"],"state_sha256":"4411791e080c7081a26e561552ba8207219763bb6281f43d50679c3662898629"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5bi8ZQ61c+EjR4siQBt1cRB/6Vr1uS4bHJuTarzUQXyibsWOk1an3TMsWLilTkOaXc+CsbqnIIWfJvS0SIsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:27:50.116036Z","bundle_sha256":"7bd90351970002118dfeaa14ecd12b56b408c51e350e1daa6461f8da8c5af592"}}