{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:A5PMRXDUCOOYHQYVUZPYPD3VKR","short_pith_number":"pith:A5PMRXDU","canonical_record":{"source":{"id":"2011.04935","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2020-11-10T06:29:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"65bf98b8ef0c2332af29ab238365d2f4fc021500956a6164a8ee54fad2bd4b75","abstract_canon_sha256":"ef2c273270401b826c4c17b586e2a7ad2022ed3c0ec6a629176b1e743a3353f7"},"schema_version":"1.0"},"canonical_sha256":"075ec8dc74139d83c315a65f878f755468eaae0ebfdf22a503c10e83b3592d33","source":{"kind":"arxiv","id":"2011.04935","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.04935","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"2011.04935v4","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.04935","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"A5PMRXDUCOOY","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"pith_short_16","alias_value":"A5PMRXDUCOOYHQYV","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"pith_short_8","alias_value":"A5PMRXDU","created_at":"2026-07-05T07:20:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:A5PMRXDUCOOYHQYVUZPYPD3VKR","target":"record","payload":{"canonical_record":{"source":{"id":"2011.04935","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2020-11-10T06:29:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"65bf98b8ef0c2332af29ab238365d2f4fc021500956a6164a8ee54fad2bd4b75","abstract_canon_sha256":"ef2c273270401b826c4c17b586e2a7ad2022ed3c0ec6a629176b1e743a3353f7"},"schema_version":"1.0"},"canonical_sha256":"075ec8dc74139d83c315a65f878f755468eaae0ebfdf22a503c10e83b3592d33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:20:46.451382Z","signature_b64":"J+sjaGU8ts2JS/u78gx5iP7haj98bEEXPG4153Q0V+EQiGr7JVCr4XK2PZ2O0SrVlVKigL6+48hpFXSDM44VBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"075ec8dc74139d83c315a65f878f755468eaae0ebfdf22a503c10e83b3592d33","last_reissued_at":"2026-07-05T07:20:46.450816Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:20:46.450816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.04935","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LsOEzNdZqwazxUxBi1x5pquqQLvDXEommgleTMMiCieTbWlFDq1jjXFck7TttK/JEjt9SJ+9LtCA6SqDT2+tDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T07:05:41.751033Z"},"content_sha256":"a7609e24b731cb28f73c4bed6a9c46730aff6adf21895e6083677fde99d16c86","schema_version":"1.0","event_id":"sha256:a7609e24b731cb28f73c4bed6a9c46730aff6adf21895e6083677fde99d16c86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:A5PMRXDUCOOYHQYVUZPYPD3VKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Azumaya Loci Of The Quantum Euclidean $2n$-Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Snehashis Mukherjee","submitted_at":"2020-11-10T06:29:37Z","abstract_excerpt":"This article delves into the Azumaya loci of quantum euclidean 2n-space, providing a comprehensive exploration. We introduce a significant class of maximal-dimensional simple modules associated with this algebra. Moreover, we establish a proof asserting that the maximal-dimensional simple modules are exactly the ones we have constructed. The computation of the algebra's center, coupled with the necessary and sufficient conditions derived for maximal-dimensional simple modules, enables us to determine the Azumaya locus of the algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04935","kind":"arxiv","version":4},"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/2011.04935/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":"2026-07-05T07:20:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"050SBIk+IhSxMMj+VgeZTk/tI1+5nbkT4oqigHc7Y3DdmeLQNoOWROQz8RrGc9PMSZNA+GxPR8IsH4nwbTHsAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T07:05:41.751550Z"},"content_sha256":"7e2f78687ca1362fb16fd825fd2930453fc9d0cfff1e8d4cc8780fce219a8afd","schema_version":"1.0","event_id":"sha256:7e2f78687ca1362fb16fd825fd2930453fc9d0cfff1e8d4cc8780fce219a8afd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5PMRXDUCOOYHQYVUZPYPD3VKR/bundle.json","state_url":"https://pith.science/pith/A5PMRXDUCOOYHQYVUZPYPD3VKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5PMRXDUCOOYHQYVUZPYPD3VKR/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":"2026-08-23T07:05:41Z","links":{"resolver":"https://pith.science/pith/A5PMRXDUCOOYHQYVUZPYPD3VKR","bundle":"https://pith.science/pith/A5PMRXDUCOOYHQYVUZPYPD3VKR/bundle.json","state":"https://pith.science/pith/A5PMRXDUCOOYHQYVUZPYPD3VKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5PMRXDUCOOYHQYVUZPYPD3VKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:A5PMRXDUCOOYHQYVUZPYPD3VKR","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":"ef2c273270401b826c4c17b586e2a7ad2022ed3c0ec6a629176b1e743a3353f7","cross_cats_sorted":["math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2020-11-10T06:29:37Z","title_canon_sha256":"65bf98b8ef0c2332af29ab238365d2f4fc021500956a6164a8ee54fad2bd4b75"},"schema_version":"1.0","source":{"id":"2011.04935","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.04935","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"arxiv_version","alias_value":"2011.04935v4","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.04935","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"pith_short_12","alias_value":"A5PMRXDUCOOY","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"pith_short_16","alias_value":"A5PMRXDUCOOYHQYV","created_at":"2026-07-05T07:20:46Z"},{"alias_kind":"pith_short_8","alias_value":"A5PMRXDU","created_at":"2026-07-05T07:20:46Z"}],"graph_snapshots":[{"event_id":"sha256:7e2f78687ca1362fb16fd825fd2930453fc9d0cfff1e8d4cc8780fce219a8afd","target":"graph","created_at":"2026-07-05T07:20:46Z","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/2011.04935/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article delves into the Azumaya loci of quantum euclidean 2n-space, providing a comprehensive exploration. We introduce a significant class of maximal-dimensional simple modules associated with this algebra. Moreover, we establish a proof asserting that the maximal-dimensional simple modules are exactly the ones we have constructed. The computation of the algebra's center, coupled with the necessary and sufficient conditions derived for maximal-dimensional simple modules, enables us to determine the Azumaya locus of the algebra.","authors_text":"Snehashis Mukherjee","cross_cats":["math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2020-11-10T06:29:37Z","title":"Azumaya Loci Of The Quantum Euclidean $2n$-Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04935","kind":"arxiv","version":4},"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:a7609e24b731cb28f73c4bed6a9c46730aff6adf21895e6083677fde99d16c86","target":"record","created_at":"2026-07-05T07:20:46Z","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":"ef2c273270401b826c4c17b586e2a7ad2022ed3c0ec6a629176b1e743a3353f7","cross_cats_sorted":["math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2020-11-10T06:29:37Z","title_canon_sha256":"65bf98b8ef0c2332af29ab238365d2f4fc021500956a6164a8ee54fad2bd4b75"},"schema_version":"1.0","source":{"id":"2011.04935","kind":"arxiv","version":4}},"canonical_sha256":"075ec8dc74139d83c315a65f878f755468eaae0ebfdf22a503c10e83b3592d33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"075ec8dc74139d83c315a65f878f755468eaae0ebfdf22a503c10e83b3592d33","first_computed_at":"2026-07-05T07:20:46.450816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:20:46.450816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+sjaGU8ts2JS/u78gx5iP7haj98bEEXPG4153Q0V+EQiGr7JVCr4XK2PZ2O0SrVlVKigL6+48hpFXSDM44VBg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:20:46.451382Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.04935","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7609e24b731cb28f73c4bed6a9c46730aff6adf21895e6083677fde99d16c86","sha256:7e2f78687ca1362fb16fd825fd2930453fc9d0cfff1e8d4cc8780fce219a8afd"],"state_sha256":"3b7e0a830e5e6c2bfb6e03c2d15e990665c8dd2126aaab5f65cb2ba7dedfb519"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2f03sUlVMBKwzwaYrw3VSuUF5O4yz6G0g5EnAlua2GN+j0AkSoKEltSxPkVASzGu99Vw28CJM4i4S0ijRB/ACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T07:05:41.756349Z","bundle_sha256":"4f200c254e63ae2ec9d2ae2628109ccab26f7b4338bf638c26fc9e723a4e459a"}}