{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J7XKWFMKYDWNMEUZNQZ6WLR5FM","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":"5252d1cd3bef75a01f6b513cf81dd45eece2388fd1d35f8af54bf224d0aebb05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-26T15:33:48Z","title_canon_sha256":"781d26c5eb030e1c96928ef2350db5507a4e6db7736db96705b0e47fb916b36b"},"schema_version":"1.0","source":{"id":"1102.5424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5424","created_at":"2026-05-18T04:27:46Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5424v1","created_at":"2026-05-18T04:27:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5424","created_at":"2026-05-18T04:27:46Z"},{"alias_kind":"pith_short_12","alias_value":"J7XKWFMKYDWN","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J7XKWFMKYDWNMEUZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J7XKWFMK","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:9c5f23d6fc3b4c36de9509bc35f146318d8e16e8c9d238e36976f6f75f3866df","target":"graph","created_at":"2026-05-18T04:27:46Z","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 show that every pseudo hoop satisfies the Riesz Decomposition Property. We visualize basic pseudo hoops by functions on a linearly ordered set. Finally, we study normal-valued basic pseudo hoops giving a countable base of equations for them.","authors_text":"Anatolij Dvure\\v{c}enskij, Michal Botur, Tomasz Kowalski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-26T15:33:48Z","title":"On Normal-Valued Basic Pseudo Hoops"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5424","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":"sha256:6c6ac0956049208584768e22670354f35cb7956161fc962b2529519d34edfff7","target":"record","created_at":"2026-05-18T04:27:46Z","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":"5252d1cd3bef75a01f6b513cf81dd45eece2388fd1d35f8af54bf224d0aebb05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-02-26T15:33:48Z","title_canon_sha256":"781d26c5eb030e1c96928ef2350db5507a4e6db7736db96705b0e47fb916b36b"},"schema_version":"1.0","source":{"id":"1102.5424","kind":"arxiv","version":1}},"canonical_sha256":"4feeab158ac0ecd612996c33eb2e3d2b1b3e63e3ec4f80fe4ff9b34b4e372ec8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4feeab158ac0ecd612996c33eb2e3d2b1b3e63e3ec4f80fe4ff9b34b4e372ec8","first_computed_at":"2026-05-18T04:27:46.969299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:46.969299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n+XC+bNWN9KT4UC+Cpaxtbc/EfNG7LJMKkzXfKk6Rl5K9jZMu5C6IulKREAyyCGAQA5tkIzM6bQq5IEiQP6zCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:46.970018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c6ac0956049208584768e22670354f35cb7956161fc962b2529519d34edfff7","sha256:9c5f23d6fc3b4c36de9509bc35f146318d8e16e8c9d238e36976f6f75f3866df"],"state_sha256":"f293acdce74a9deb82a7660432dddd10df0b9141f01de676fbf5e869f333262c"}