{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XIPSGZSWJHRIYYZINXEJBM25BL","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":"15dc91ab11ddb4a228200f426b5cce0d5f0a2c65a211ffa840c8fe1479d58022","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-04T19:49:01Z","title_canon_sha256":"8a96f98ba690842a9f61b7bf70eab9bcae251a864fb67bcb24bb66cf24e3d493"},"schema_version":"1.0","source":{"id":"1303.0807","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0807","created_at":"2026-05-18T03:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0807v1","created_at":"2026-05-18T03:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0807","created_at":"2026-05-18T03:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"XIPSGZSWJHRI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XIPSGZSWJHRIYYZI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XIPSGZSW","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:55c77944586106d0fbfdc2cb044d145254f3857c693b54d8909ccb4ce579ef67","target":"graph","created_at":"2026-05-18T03:31:54Z","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 Riesz Decomposition Property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed to a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.","authors_text":"A. Dvurecenskij, M. Kolarik","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-04T19:49:01Z","title":"Lexicographic Product vs $\\mathbb Q$-perfect and $\\mathbb H$-perfect Pseudo Effect Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0807","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":"sha256:23c76d662ee20107ed49dc4ef1152fa8f2c4fc538157f54b681bfec5d8fed9d5","target":"record","created_at":"2026-05-18T03:31:54Z","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":"15dc91ab11ddb4a228200f426b5cce0d5f0a2c65a211ffa840c8fe1479d58022","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-03-04T19:49:01Z","title_canon_sha256":"8a96f98ba690842a9f61b7bf70eab9bcae251a864fb67bcb24bb66cf24e3d493"},"schema_version":"1.0","source":{"id":"1303.0807","kind":"arxiv","version":1}},"canonical_sha256":"ba1f23665649e28c63286dc890b35d0acf288ff9a9a4b1d47420a33f852e3509","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba1f23665649e28c63286dc890b35d0acf288ff9a9a4b1d47420a33f852e3509","first_computed_at":"2026-05-18T03:31:54.845792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:54.845792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h3ab9YxXJi1NVufwpIRk6vOydcqTfprKOmJAb01O+2QUKyzgafLsotMABrLD77gbVw8Sw3Cxg5C3Fj0FlS5CCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:54.846516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0807","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23c76d662ee20107ed49dc4ef1152fa8f2c4fc538157f54b681bfec5d8fed9d5","sha256:55c77944586106d0fbfdc2cb044d145254f3857c693b54d8909ccb4ce579ef67"],"state_sha256":"f58a669fc12975d0c93ee4a105dbb6e83119bc2be1ad8be9e6c528254b53b7ab"}