{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NI6K5L7L3CCXWIIUJLSLHUE6U3","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":"7ef0fe38c679d486052aae35acb872debda836d38938b337633b00035b48a60c","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-07-22T17:15:33Z","title_canon_sha256":"c363b70ec76f83017d3f3c5db57810ffe4d0bdaca711d94b0077178e5188fe8a"},"schema_version":"1.0","source":{"id":"1007.3944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3944","created_at":"2026-05-18T04:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3944v1","created_at":"2026-05-18T04:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3944","created_at":"2026-05-18T04:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"NI6K5L7L3CCX","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NI6K5L7L3CCXWIIU","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NI6K5L7L","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:db1d3ad89878aa06ce53ec6785baf4d17d4bf2bc10352b4b11d5df61f281e3c5","target":"graph","created_at":"2026-05-18T04:16:13Z","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 study the question on whether the famous Golod-Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper 'Generic algebras and CW-complexes', Princeton Univ. Press., where he proved that the estimate is attained for the number of quadratic relations $d \\leq \\frac{n^2}{4}$ and $d \\geq \\frac{n^2}{2}$, and conjectured that this is the case for any number of quadratic relations. The particular point where the number of relations is equal to $ \\frac{n(n-1)}{2}$ was addressed by Vershi","authors_text":"Natalia Iyudu, Stanislav Shkarin","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-07-22T17:15:33Z","title":"The Golod-Shafarevich inequality for Hilbert series of quadratic algebras and the Anick conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3944","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:cda86be71fd935e3041fd14d0c4b7eaa405c40ad9c69a7af338679969f6635d4","target":"record","created_at":"2026-05-18T04:16:13Z","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":"7ef0fe38c679d486052aae35acb872debda836d38938b337633b00035b48a60c","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-07-22T17:15:33Z","title_canon_sha256":"c363b70ec76f83017d3f3c5db57810ffe4d0bdaca711d94b0077178e5188fe8a"},"schema_version":"1.0","source":{"id":"1007.3944","kind":"arxiv","version":1}},"canonical_sha256":"6a3caeafebd8857b21144ae4b3d09ea6e523f52ccd7d42cb01f80bfdd92b805f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a3caeafebd8857b21144ae4b3d09ea6e523f52ccd7d42cb01f80bfdd92b805f","first_computed_at":"2026-05-18T04:16:13.048139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:13.048139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zMbHpdas4Hb8LDC5/ee1teuZAhhW8OwrF16t8JzTuzH6jWkRwyf36irKOVC3PDvCqEIjS6rBdyWVg//J/zHwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:13.048741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cda86be71fd935e3041fd14d0c4b7eaa405c40ad9c69a7af338679969f6635d4","sha256:db1d3ad89878aa06ce53ec6785baf4d17d4bf2bc10352b4b11d5df61f281e3c5"],"state_sha256":"f112fbf1c0f2eb34049d6415bfced2344b5c3093a801330a944fcbe02284cdd3"}