{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5VGHF5QI5KVCBLTG335QMCU5AT","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":"aa87c401ff5f252edfbd31771ba230f95294550d200fac3dacb2fc36f3821ec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-14T08:11:27Z","title_canon_sha256":"7465b49da3f401bbabb4334364747e8f422341f4a311d45d6dbd0a295d6b064c"},"schema_version":"1.0","source":{"id":"1308.3055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3055","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3055v1","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3055","created_at":"2026-05-18T00:29:06Z"},{"alias_kind":"pith_short_12","alias_value":"5VGHF5QI5KVC","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5VGHF5QI5KVCBLTG","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5VGHF5QI","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:45ab13433f38aea63b138ffc385c2dd54ac7ffa2962b933af6250f26f7c6fd3b","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":"In a series of papers \\cite{BRV1}, \\cite{BRV2}, \\cite{BRV3} we introduced full quivers and pseudo-quivers of representations of algebras, and used them as tools in describing PI-varieties of algebras. In this paper we apply them to obtain a complete proof of Belov's solution of Specht's problem for affine algebras over an arbitrary Noetherian ring. The inductive step relies on a theorem that enables one to find a \"$\\bar q$-characteristic coefficient-absorbing polynomial in each T-ideal $\\Gamma$,\" i.e., a non-identity of the representable algebra $A$ arising from $\\Gamma$, whose ideal of evalua","authors_text":"Alexei Belov-Kanel, Louis Rowen, Uzi Vishne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-14T08:11:27Z","title":"Specht's problem for associative affine algebras over commutative Noetherian rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3055","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":"sha256:985d9f5feac33d9fbb47b3c0901415897bb00fa7c629d8e5cd98967f42e0733c","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":"aa87c401ff5f252edfbd31771ba230f95294550d200fac3dacb2fc36f3821ec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-14T08:11:27Z","title_canon_sha256":"7465b49da3f401bbabb4334364747e8f422341f4a311d45d6dbd0a295d6b064c"},"schema_version":"1.0","source":{"id":"1308.3055","kind":"arxiv","version":1}},"canonical_sha256":"ed4c72f608eaaa20ae66defb060a9d04d5e835250e7066a15f7b0f8724774576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed4c72f608eaaa20ae66defb060a9d04d5e835250e7066a15f7b0f8724774576","first_computed_at":"2026-05-18T00:29:06.094160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:06.094160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Os6Hs9/mjRyOxPD/dhqSQAWS+rI/vyUX8rZlWMs1Yd37o73hS2Ztb6/o8m0OpyFOYxaGlWVrTt46Swaqf1OMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:06.094715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:985d9f5feac33d9fbb47b3c0901415897bb00fa7c629d8e5cd98967f42e0733c","sha256:45ab13433f38aea63b138ffc385c2dd54ac7ffa2962b933af6250f26f7c6fd3b"],"state_sha256":"82b085f050a6ee9bd0f47c10baff8ba1834d075d89969e20648e36deaf340275"}