{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NHTSPRDGUROIOAOIQCNSFSOD2V","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":"86b8963e1386976d42038c76142fb61a3d68e7ecc19c43d71c64ad7ae96c3651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-14T08:34:48Z","title_canon_sha256":"85904d55830e373e0f0b359c5b3c437cac085d545ad3c24028989fc68f52ce94"},"schema_version":"1.0","source":{"id":"1101.2737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2737","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2737v1","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2737","created_at":"2026-05-18T04:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"NHTSPRDGUROI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NHTSPRDGUROIOAOI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NHTSPRDG","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:dc90fd44d1ff41cbfcb892980644705fabf99b5af191c47659d16ebcbadc767a","target":"graph","created_at":"2026-05-18T04:30:25Z","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 the concept of extension of a Q-fuzzy ideal in semigroups has been introduced and some important properties have been studied.","authors_text":"Samit Kumar Majumder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-14T08:34:48Z","title":"On Q-Fuzzy Ideal Extensions in Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2737","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":"sha256:529f45eb382f5a46bcc67fa39dcf547fa431a3395b13ab60a73cdf6d1ed6df57","target":"record","created_at":"2026-05-18T04:30:25Z","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":"86b8963e1386976d42038c76142fb61a3d68e7ecc19c43d71c64ad7ae96c3651","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2011-01-14T08:34:48Z","title_canon_sha256":"85904d55830e373e0f0b359c5b3c437cac085d545ad3c24028989fc68f52ce94"},"schema_version":"1.0","source":{"id":"1101.2737","kind":"arxiv","version":1}},"canonical_sha256":"69e727c466a45c8701c8809b22c9c3d553a8d6cd8eb99eff0f0bafa9900359f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69e727c466a45c8701c8809b22c9c3d553a8d6cd8eb99eff0f0bafa9900359f8","first_computed_at":"2026-05-18T04:30:25.280130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:25.280130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WLqEVGMtzSzkXFNls/x07AphlOy9lsaAKHgyEpjNHCcN2EXfb8+XCL28VVR7TGXYBmPCDyGTKLQ4pYyA25jUBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:25.280727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:529f45eb382f5a46bcc67fa39dcf547fa431a3395b13ab60a73cdf6d1ed6df57","sha256:dc90fd44d1ff41cbfcb892980644705fabf99b5af191c47659d16ebcbadc767a"],"state_sha256":"2c8fb881f8ebd043d80b5037e58f67a66a1a4c5dd6bf4476c1efff505b03d160"}