{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IDTWQ2FD5AFXVWIBU3X6BHQ3YH","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":"4dfc45987c7d69002867484ea92ae425f97212718203d4187bd57cce847576b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-02-09T18:01:09Z","title_canon_sha256":"c95026ab37d423ab68fde5ede702f4e2143f5884efb094ca25a1b40b2e59a683"},"schema_version":"1.0","source":{"id":"1702.02918","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02918","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02918v1","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02918","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"IDTWQ2FD5AFX","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IDTWQ2FD5AFXVWIB","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IDTWQ2FD","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:8667dfb176a46df9746804f18290079d9a14494282c52c32aeb1e15ae8e41c0d","target":"graph","created_at":"2026-05-18T00:51:02Z","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":"Koszul algebras with quadratic Groebner bases, called strong Koszul algebras, are studied. We introduce affine algebraic varieties whose points are in one-to-one correspondence with certain strong Koszul algebras and we investigate the connection between the varieties and the algebras.","authors_text":"Edward L. Green","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-02-09T18:01:09Z","title":"The Geometry of Strong Koszul Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02918","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:b44f3ff429133832c2f0823a7b77e586728b14a8122e6f0acf9e1037c4badf37","target":"record","created_at":"2026-05-18T00:51:02Z","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":"4dfc45987c7d69002867484ea92ae425f97212718203d4187bd57cce847576b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-02-09T18:01:09Z","title_canon_sha256":"c95026ab37d423ab68fde5ede702f4e2143f5884efb094ca25a1b40b2e59a683"},"schema_version":"1.0","source":{"id":"1702.02918","kind":"arxiv","version":1}},"canonical_sha256":"40e76868a3e80b7ad901a6efe09e1bc1f265b03e61dac16524741cf95d39bce8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40e76868a3e80b7ad901a6efe09e1bc1f265b03e61dac16524741cf95d39bce8","first_computed_at":"2026-05-18T00:51:02.054775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:02.054775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4CE6XGPECkgx3VLwNcaiptc/UyA/WA8TMrqJAf+51Gq+swqYXg0VU+/3LoUWobtse3DWvNSQeRNeH55RUOWKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:02.055219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02918","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b44f3ff429133832c2f0823a7b77e586728b14a8122e6f0acf9e1037c4badf37","sha256:8667dfb176a46df9746804f18290079d9a14494282c52c32aeb1e15ae8e41c0d"],"state_sha256":"5d4845be9ee1b98059668de9df7297e12a40195b02f97c98254c04622eb38bad"}