{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2EEJNRWUWTO2IWVJ5AN7KXWJXN","short_pith_number":"pith:2EEJNRWU","canonical_record":{"source":{"id":"1403.0200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-02T12:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"5bc4f9facc8a620fef711ea3689f1ba614a0f7691a83586755c6dae634dc6897","abstract_canon_sha256":"54d17cffe34cd7c7ecfd62ce9c71bc113a799d31665d9b685cb8dcc0dce7cc75"},"schema_version":"1.0"},"canonical_sha256":"d10896c6d4b4dda45aa9e81bf55ec9bb6444884236d38a4bcff8a57b7124c761","source":{"kind":"arxiv","id":"1403.0200","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0200","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0200v2","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0200","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"2EEJNRWUWTO2","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2EEJNRWUWTO2IWVJ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2EEJNRWU","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2EEJNRWUWTO2IWVJ5AN7KXWJXN","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-02T12:02:39Z","cross_cats_sorted":[],"title_canon_sha256":"5bc4f9facc8a620fef711ea3689f1ba614a0f7691a83586755c6dae634dc6897","abstract_canon_sha256":"54d17cffe34cd7c7ecfd62ce9c71bc113a799d31665d9b685cb8dcc0dce7cc75"},"schema_version":"1.0"},"canonical_sha256":"d10896c6d4b4dda45aa9e81bf55ec9bb6444884236d38a4bcff8a57b7124c761","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:08.636128Z","signature_b64":"7R6wOIxboQA0S2EDMTHyLFg71pWjxUlVBTST//lVNPv6/Z0e932vR1BS+OMbwhbb0mBZ10KU1dPSH8Hl6PzkCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d10896c6d4b4dda45aa9e81bf55ec9bb6444884236d38a4bcff8a57b7124c761","last_reissued_at":"2026-05-18T00:41:08.635570Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:08.635570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0200","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":"2026-05-18T00:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4O2bNRGXkJF2pq/xqLZFDffBrV+dXDg+ZkF23Qf7nrLn5cDeEkzEaYTjLPggdmEkGQBDqm2A8/wG3zlU31MWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:45:43.330048Z"},"content_sha256":"1f1c1ff12b0e16d5c27c971c392a1a7e81d9a918898940fb24f69d5b89f9db24","schema_version":"1.0","event_id":"sha256:1f1c1ff12b0e16d5c27c971c392a1a7e81d9a918898940fb24f69d5b89f9db24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2EEJNRWUWTO2IWVJ5AN7KXWJXN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On group gradings on PI-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eli Aljadeff, Ofir David","submitted_at":"2014-03-02T12:02:39Z","abstract_excerpt":"We show that there exists a constant K such that for any PI- algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with $[G : U] \\leq exp(W)^K$. A G-grading $W = \\bigoplus_{g \\in G}W_g$ is said to be nondegenerate if $W_{g_1}W_{g_2}... W_{g_r} \\neq 0$ for any $r \\geq 1$ and any $r$ tuple $(g_1, g_2,..., g_r)$ in $G^r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0200","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":"2026-05-18T00:41:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxqvAFLUsQyOAUqdesoOP63Y/AH06HHy3ZdXTwbTnh4V0s/FN1sSCPc5V4lxEAJ/Undom4WpGYVcsrBR4JQXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:45:43.330405Z"},"content_sha256":"2ec3b28c2eeb3b07a59a1f5da87f7a43041e495f95b3efaa175407f0541f4c84","schema_version":"1.0","event_id":"sha256:2ec3b28c2eeb3b07a59a1f5da87f7a43041e495f95b3efaa175407f0541f4c84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2EEJNRWUWTO2IWVJ5AN7KXWJXN/bundle.json","state_url":"https://pith.science/pith/2EEJNRWUWTO2IWVJ5AN7KXWJXN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2EEJNRWUWTO2IWVJ5AN7KXWJXN/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":"2026-06-03T03:45:43Z","links":{"resolver":"https://pith.science/pith/2EEJNRWUWTO2IWVJ5AN7KXWJXN","bundle":"https://pith.science/pith/2EEJNRWUWTO2IWVJ5AN7KXWJXN/bundle.json","state":"https://pith.science/pith/2EEJNRWUWTO2IWVJ5AN7KXWJXN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2EEJNRWUWTO2IWVJ5AN7KXWJXN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2EEJNRWUWTO2IWVJ5AN7KXWJXN","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":"54d17cffe34cd7c7ecfd62ce9c71bc113a799d31665d9b685cb8dcc0dce7cc75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-02T12:02:39Z","title_canon_sha256":"5bc4f9facc8a620fef711ea3689f1ba614a0f7691a83586755c6dae634dc6897"},"schema_version":"1.0","source":{"id":"1403.0200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0200","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0200v2","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0200","created_at":"2026-05-18T00:41:08Z"},{"alias_kind":"pith_short_12","alias_value":"2EEJNRWUWTO2","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2EEJNRWUWTO2IWVJ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2EEJNRWU","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:2ec3b28c2eeb3b07a59a1f5da87f7a43041e495f95b3efaa175407f0541f4c84","target":"graph","created_at":"2026-05-18T00:41:08Z","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 show that there exists a constant K such that for any PI- algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with $[G : U] \\leq exp(W)^K$. A G-grading $W = \\bigoplus_{g \\in G}W_g$ is said to be nondegenerate if $W_{g_1}W_{g_2}... W_{g_r} \\neq 0$ for any $r \\geq 1$ and any $r$ tuple $(g_1, g_2,..., g_r)$ in $G^r$.","authors_text":"Eli Aljadeff, Ofir David","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-02T12:02:39Z","title":"On group gradings on PI-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0200","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":"sha256:1f1c1ff12b0e16d5c27c971c392a1a7e81d9a918898940fb24f69d5b89f9db24","target":"record","created_at":"2026-05-18T00:41:08Z","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":"54d17cffe34cd7c7ecfd62ce9c71bc113a799d31665d9b685cb8dcc0dce7cc75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-02T12:02:39Z","title_canon_sha256":"5bc4f9facc8a620fef711ea3689f1ba614a0f7691a83586755c6dae634dc6897"},"schema_version":"1.0","source":{"id":"1403.0200","kind":"arxiv","version":2}},"canonical_sha256":"d10896c6d4b4dda45aa9e81bf55ec9bb6444884236d38a4bcff8a57b7124c761","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d10896c6d4b4dda45aa9e81bf55ec9bb6444884236d38a4bcff8a57b7124c761","first_computed_at":"2026-05-18T00:41:08.635570Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:08.635570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7R6wOIxboQA0S2EDMTHyLFg71pWjxUlVBTST//lVNPv6/Z0e932vR1BS+OMbwhbb0mBZ10KU1dPSH8Hl6PzkCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:08.636128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f1c1ff12b0e16d5c27c971c392a1a7e81d9a918898940fb24f69d5b89f9db24","sha256:2ec3b28c2eeb3b07a59a1f5da87f7a43041e495f95b3efaa175407f0541f4c84"],"state_sha256":"9bfa45ed64bed5a51c49ca7cca894c105ef79603757639784a49b313f1f52c17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUVKYkyG2jSv9cti3bSvoeD6vpqmCuFZcQ4sSe/BR4aSysPTNkMaYCnJ+EwD427vo63BJfIAsa0/Z5BIgfjNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:45:43.332359Z","bundle_sha256":"290322c891fa9380198566e0640e4533261af0e45198362ca503ba5c7ee5a444"}}