{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:B5OBBPJMTSTLIPVTS6MZKRCNNC","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":"04c1573f1dd343b282846e74f669ad0e545905719de7aa5f8ae650818083c85e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-02T19:54:34Z","title_canon_sha256":"82ba07ee0a6cd0457551e6fb7baf1827284a9ab153df6c53f98fd68814f18805"},"schema_version":"1.0","source":{"id":"0903.0362","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.0362","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"0903.0362v4","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.0362","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"B5OBBPJMTSTL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B5OBBPJMTSTLIPVT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B5OBBPJM","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7dda95446b8b67c37a64b904d2a0494f438111603659faebbe537c3f3c6d770d","target":"graph","created_at":"2026-05-18T00:29:06Z","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 W be an associative PI algebra over a field F of characteristic zero, graded by a finite group G. Let id_{G}(W) denote the T-ideal of G-graded identities of W. We prove: 1. {[G-graded PI equivalence]} There exists a field extension K of F and a finite dimensional Z/2ZxG-graded algebra A over K such that id_{G}(W)=id_{G}(A^{*}) where A^{*} is the Grassmann envelope of A. 2. {[G-graded Specht problem]} The T-ideal id_{G}(W) is finitely generated as a T-ideal. 3. {[G-graded PI-equivalence for affine algebras]} Let W be a G-graded affine algebra over F. Then there exists a field extension K of","authors_text":"Alexei Kanel-Belov, Eli Aljadeff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-02T19:54:34Z","title":"Representability and Specht problem for G-graded algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0362","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:eb26a7a1d1ed1017044fa76e3343af55c9e4df6127f788df097a723eb9fb5dbc","target":"record","created_at":"2026-05-18T00:29:06Z","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":"04c1573f1dd343b282846e74f669ad0e545905719de7aa5f8ae650818083c85e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-03-02T19:54:34Z","title_canon_sha256":"82ba07ee0a6cd0457551e6fb7baf1827284a9ab153df6c53f98fd68814f18805"},"schema_version":"1.0","source":{"id":"0903.0362","kind":"arxiv","version":4}},"canonical_sha256":"0f5c10bd2c9ca6b43eb3979995444d688412d9bf451e91844f7ec2f8ffc590b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f5c10bd2c9ca6b43eb3979995444d688412d9bf451e91844f7ec2f8ffc590b6","first_computed_at":"2026-05-18T00:29:06.191549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:06.191549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GrkbdAd2Z1r/nqhN3S6+HqpEQ+m4rCwxgFJFUfRZaB+pIfCru4OmnWqULVkSAVO+2C7HgFGKKKHLXDxDSOtrBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:06.192075Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.0362","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb26a7a1d1ed1017044fa76e3343af55c9e4df6127f788df097a723eb9fb5dbc","sha256:7dda95446b8b67c37a64b904d2a0494f438111603659faebbe537c3f3c6d770d"],"state_sha256":"90c9f63ae1a5e4649d2cfd40e682284ab469c46bedcddfd17ac8e7f008016908"}