{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6Z2RPPAZQBYKPRS6FUSXQFXHDP","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":"e1018b366a963e957f05c2f9463adb8797e00ceaedf0f2d3ec5b6732c041e698","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-11T12:43:02Z","title_canon_sha256":"71234116ceb8a937a21d4da2cc333ab5e20b8cc56f708ab681b74d16b8e47f0d"},"schema_version":"1.0","source":{"id":"1403.2557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2557","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2557v1","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2557","created_at":"2026-05-18T02:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"6Z2RPPAZQBYK","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6Z2RPPAZQBYKPRS6","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6Z2RPPAZ","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:aa7662240db2c5a8166f80ad1ea73c1da7d8d86c828458753a52f5592d6be225","target":"graph","created_at":"2026-05-18T02:56:43Z","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 this paper we answer two questions from [16], by showing that, over any algebraically closed field, $K$, there is a finitely generated, infinitely dimensional algebra $A$ such that algebras $A\\otimes_{K}A$ and $A\\otimes_{K} A^{op}$ are nil.","authors_text":"Agata Smoktunowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-11T12:43:02Z","title":"Infinitely dimensional, affine nil algebras $A\\otimes A^{op}$ and $A\\otimes A$ exist"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2557","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":"sha256:8de0b179b0a95b5ef4afbbea00053a9c2a835f9bb7f0c6f67f9530d2762ff37e","target":"record","created_at":"2026-05-18T02:56:43Z","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":"e1018b366a963e957f05c2f9463adb8797e00ceaedf0f2d3ec5b6732c041e698","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-03-11T12:43:02Z","title_canon_sha256":"71234116ceb8a937a21d4da2cc333ab5e20b8cc56f708ab681b74d16b8e47f0d"},"schema_version":"1.0","source":{"id":"1403.2557","kind":"arxiv","version":1}},"canonical_sha256":"f67517bc198070a7c65e2d257816e71bcdc8a5eb4d52c0dc3951fa1bb180d5f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f67517bc198070a7c65e2d257816e71bcdc8a5eb4d52c0dc3951fa1bb180d5f5","first_computed_at":"2026-05-18T02:56:43.069959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:43.069959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9giUOa82PEHZeAwnWexxv6aQnJl+GMs10D2UhmJF25zYZsZGSGvVmSKmztIAXyIbBYO1B0s8j4J0K6ZrhiktDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:43.073894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8de0b179b0a95b5ef4afbbea00053a9c2a835f9bb7f0c6f67f9530d2762ff37e","sha256:aa7662240db2c5a8166f80ad1ea73c1da7d8d86c828458753a52f5592d6be225"],"state_sha256":"ba9e54c23629b3fd1f9c14b077b1dffe04cbceb5fea57c93352cc6c1c04acba5"}