{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I273RRBQ5KESJMEEH5OXWWADPT","short_pith_number":"pith:I273RRBQ","canonical_record":{"source":{"id":"1610.03977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-13T08:37:17Z","cross_cats_sorted":[],"title_canon_sha256":"54eea83a60159d9c2b02854e14e0fd74f71338c8c7543e9c3c7817e678db272a","abstract_canon_sha256":"75dbd9a2433985d7062b65d32ca2971d7c7821f872ab4adf1eca91f751b9e0be"},"schema_version":"1.0"},"canonical_sha256":"46bfb8c430ea8924b0843f5d7b58037cc6b59be04a59c6ed5af0b0b82f362746","source":{"kind":"arxiv","id":"1610.03977","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03977","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03977v1","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03977","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"I273RRBQ5KES","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I273RRBQ5KESJMEE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I273RRBQ","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I273RRBQ5KESJMEEH5OXWWADPT","target":"record","payload":{"canonical_record":{"source":{"id":"1610.03977","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-13T08:37:17Z","cross_cats_sorted":[],"title_canon_sha256":"54eea83a60159d9c2b02854e14e0fd74f71338c8c7543e9c3c7817e678db272a","abstract_canon_sha256":"75dbd9a2433985d7062b65d32ca2971d7c7821f872ab4adf1eca91f751b9e0be"},"schema_version":"1.0"},"canonical_sha256":"46bfb8c430ea8924b0843f5d7b58037cc6b59be04a59c6ed5af0b0b82f362746","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:22.821225Z","signature_b64":"1veVbfhb+0j/G90+y0ovIhZBhsyp1Y9ZJJTLX03EHbHpnxOZKA+shPsKWVExMFZ7SzkkANT0rUaS4AOx3X8bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46bfb8c430ea8924b0843f5d7b58037cc6b59be04a59c6ed5af0b0b82f362746","last_reissued_at":"2026-05-18T01:02:22.820581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:22.820581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.03977","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":"2026-05-18T01:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OAFb/6m8TsdUyzrJ2/AtoAWRTMpon0hg7PxZwpmw4nMzJbR91v7kmIHYZWFscIBbF7bu5zjJkYswJDfpY7G2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:37:48.403466Z"},"content_sha256":"9df7e8a7ec2deaaac66a160e326908ef815901df82395743f12306bfff9570c7","schema_version":"1.0","event_id":"sha256:9df7e8a7ec2deaaac66a160e326908ef815901df82395743f12306bfff9570c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I273RRBQ5KESJMEEH5OXWWADPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"G-Graded Central Polynomials and G-Graded Posner's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Yakov Karasik","submitted_at":"2016-10-13T08:37:17Z","abstract_excerpt":"Let F be characteristic zero field, G a residually finite group and W a G-prime and PI F-algebra. By constructing G-graded central polynomials for W, we prove the G-graded version of Posner's theorem. More precisely, if S denotes all non-zero degree e central elements of W, the algebra S^{-1}W is G-graded simple and finite dimensional over its center.\n  Furthermore, we show how to use this theorem in order to recapture the result of Aljadeff and Haile stating that two G-simple algebras of finite dimension are isomorphix iff their ideals of graded identities coincide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03977","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":"2026-05-18T01:02:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GZO7outKOcRhxhTizBCaQ7qnTb9OPsRJve7CiscDcl+ZJQEp+OsR/Lqv0PMDyee+UXfDt01iqmXGiySIqu3vCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:37:48.403816Z"},"content_sha256":"1ff19133dc3c10edfacfa8192ba28b0a7ee091e0c5b5bdb651b6e3e3a5de414a","schema_version":"1.0","event_id":"sha256:1ff19133dc3c10edfacfa8192ba28b0a7ee091e0c5b5bdb651b6e3e3a5de414a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I273RRBQ5KESJMEEH5OXWWADPT/bundle.json","state_url":"https://pith.science/pith/I273RRBQ5KESJMEEH5OXWWADPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I273RRBQ5KESJMEEH5OXWWADPT/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":"2026-06-02T21:37:48Z","links":{"resolver":"https://pith.science/pith/I273RRBQ5KESJMEEH5OXWWADPT","bundle":"https://pith.science/pith/I273RRBQ5KESJMEEH5OXWWADPT/bundle.json","state":"https://pith.science/pith/I273RRBQ5KESJMEEH5OXWWADPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I273RRBQ5KESJMEEH5OXWWADPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I273RRBQ5KESJMEEH5OXWWADPT","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":"75dbd9a2433985d7062b65d32ca2971d7c7821f872ab4adf1eca91f751b9e0be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-13T08:37:17Z","title_canon_sha256":"54eea83a60159d9c2b02854e14e0fd74f71338c8c7543e9c3c7817e678db272a"},"schema_version":"1.0","source":{"id":"1610.03977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03977","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03977v1","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03977","created_at":"2026-05-18T01:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"I273RRBQ5KES","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I273RRBQ5KESJMEE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I273RRBQ","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:1ff19133dc3c10edfacfa8192ba28b0a7ee091e0c5b5bdb651b6e3e3a5de414a","target":"graph","created_at":"2026-05-18T01:02:22Z","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":"Let F be characteristic zero field, G a residually finite group and W a G-prime and PI F-algebra. By constructing G-graded central polynomials for W, we prove the G-graded version of Posner's theorem. More precisely, if S denotes all non-zero degree e central elements of W, the algebra S^{-1}W is G-graded simple and finite dimensional over its center.\n  Furthermore, we show how to use this theorem in order to recapture the result of Aljadeff and Haile stating that two G-simple algebras of finite dimension are isomorphix iff their ideals of graded identities coincide.","authors_text":"Yakov Karasik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-13T08:37:17Z","title":"G-Graded Central Polynomials and G-Graded Posner's Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03977","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":"sha256:9df7e8a7ec2deaaac66a160e326908ef815901df82395743f12306bfff9570c7","target":"record","created_at":"2026-05-18T01:02:22Z","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":"75dbd9a2433985d7062b65d32ca2971d7c7821f872ab4adf1eca91f751b9e0be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-13T08:37:17Z","title_canon_sha256":"54eea83a60159d9c2b02854e14e0fd74f71338c8c7543e9c3c7817e678db272a"},"schema_version":"1.0","source":{"id":"1610.03977","kind":"arxiv","version":1}},"canonical_sha256":"46bfb8c430ea8924b0843f5d7b58037cc6b59be04a59c6ed5af0b0b82f362746","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46bfb8c430ea8924b0843f5d7b58037cc6b59be04a59c6ed5af0b0b82f362746","first_computed_at":"2026-05-18T01:02:22.820581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:22.820581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1veVbfhb+0j/G90+y0ovIhZBhsyp1Y9ZJJTLX03EHbHpnxOZKA+shPsKWVExMFZ7SzkkANT0rUaS4AOx3X8bDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:22.821225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9df7e8a7ec2deaaac66a160e326908ef815901df82395743f12306bfff9570c7","sha256:1ff19133dc3c10edfacfa8192ba28b0a7ee091e0c5b5bdb651b6e3e3a5de414a"],"state_sha256":"4214702e186d9b4a8665308285a2548f3a834e339def87348938e742f1ea340d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2mhp+jgjoy7yDwT3WOYfSYXtsqUb5ZMdyCgNzNVAe/wdYniIm6wo2sYAyQoj1pjopd9ZjgX7e1QLqRiVofG9Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:37:48.405826Z","bundle_sha256":"c0495350c5340058dc3ccd30bc8d711fb84a28143e4afc74752a404041ca9aaa"}}