{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:H6EQOXWPIXUARORGHDWBQLFUOG","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":"a9025b5a1b32be071ab16fe1643f37755526803b26c1f4b5b56e0cf3922d5e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-06-13T02:10:16Z","title_canon_sha256":"a44929d85c601a5c0fed2b03702198b5a9415147f3256530cf6ad14af41fc1a4"},"schema_version":"1.0","source":{"id":"1506.04211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04211","created_at":"2026-05-18T01:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04211v1","created_at":"2026-05-18T01:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04211","created_at":"2026-05-18T01:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"H6EQOXWPIXUA","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H6EQOXWPIXUARORG","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H6EQOXWP","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:0499fb27ead0dda586c88701a007dd792dc07e78ed7f8df56db0451dc3edf817","target":"graph","created_at":"2026-05-18T01:49:55Z","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 $A$ be an Artinian Gorenstein algebra over an infinite field $k$ with either $\\hbox{char}(k)=0$ or $\\hbox{char}(k)>\\nu$, where $\\nu$ is the socle degree of $A$. To every such algebra and a linear projection $\\pi$ on its maximal ideal ${\\mathfrak m}$ with range equal to the socle $\\hbox {Soc}(A)$ of $A$, one can associate a certain algebraic hypersurface $S_{\\pi}\\subset{\\mathfrak m}$, which is the graph of a polynomial map $P_{\\pi}:\\hbox{ker}\\,\\pi\\to \\hbox{Soc}(A)\\simeq k$. Recently, the author and his collaborators have obtained the following surprising criterion: two Artinian Gorenstein a","authors_text":"A. V. Isaev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-06-13T02:10:16Z","title":"A Criterion for Isomorphism of Artinian Gorenstein Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04211","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:de0de2f9b2528ba968d5698f23dc6bdaa3b04035cd5ebe50d31918130eaaf91d","target":"record","created_at":"2026-05-18T01:49:55Z","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":"a9025b5a1b32be071ab16fe1643f37755526803b26c1f4b5b56e0cf3922d5e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-06-13T02:10:16Z","title_canon_sha256":"a44929d85c601a5c0fed2b03702198b5a9415147f3256530cf6ad14af41fc1a4"},"schema_version":"1.0","source":{"id":"1506.04211","kind":"arxiv","version":1}},"canonical_sha256":"3f89075ecf45e808ba2638ec182cb471a34f386748de27f4dd3b8763bf8a278a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f89075ecf45e808ba2638ec182cb471a34f386748de27f4dd3b8763bf8a278a","first_computed_at":"2026-05-18T01:49:55.271849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:55.271849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q6BueXrf89AGtc4l1E27JybCm8SnbyGhGsG6AgTB+yG1mGiWoCfq8TcDU7aeZtvraSu6IX3BqujWqokeLvdFDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:55.272307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de0de2f9b2528ba968d5698f23dc6bdaa3b04035cd5ebe50d31918130eaaf91d","sha256:0499fb27ead0dda586c88701a007dd792dc07e78ed7f8df56db0451dc3edf817"],"state_sha256":"c373c0c9958c0705f8a7ed7a7af63e028d6ecd81399e2a85d2f979f955772954"}