{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7KX5O263MPPWRIWBI7R5O3BXMI","short_pith_number":"pith:7KX5O263","schema_version":"1.0","canonical_sha256":"faafd76bdb63df68a2c147e3d76c376213b6260c6dc520935855d0d1f2540f18","source":{"kind":"arxiv","id":"1604.08909","version":1},"attestation_state":"computed","paper":{"title":"When Lexicographic Product of Two po-Groups has the Riesz Decomposition Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Anatolij Dvure\\v{c}enskij, Omid Zahiri","submitted_at":"2016-04-29T16:55:24Z","abstract_excerpt":"We study conditions when a certain type of the Riesz Decomposition Property (RDP for short) holds in the lexicographic product of two po-groups. Defining two important properties of po-groups, we extend known situations showing that the lexicographic product satisfies RDP or even RDP$_1$, a stronger type of RDP. We recall that a very strong type of RDP, RDP$_2$, entails that the group is lattice ordered. RDP's of the lexicographic products are important for the study of lexicographic pseudo effect algebras, or perfect types of pseudo MV-algebras and pseudo effect algebras, where infinitesimal "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1604.08909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-04-29T16:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"5adb4c5068cc5ae38ef61de15eb092fff42326c5e051244d77309b94c9540e36","abstract_canon_sha256":"cef24acc69d7b549823d260903b4fcf4e676bd9bcb3ce02f0ddfb7040caf2283"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:01.448510Z","signature_b64":"sAN2v11SmoUjsdHAXLorbbO+1NSWMnX9jarXfGQGb/MhzVyjiB5SsTLziMY1dWU4l8KUY/qKoqIE434U+284Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"faafd76bdb63df68a2c147e3d76c376213b6260c6dc520935855d0d1f2540f18","last_reissued_at":"2026-05-18T01:16:01.447817Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:01.447817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When Lexicographic Product of Two po-Groups has the Riesz Decomposition Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Anatolij Dvure\\v{c}enskij, Omid Zahiri","submitted_at":"2016-04-29T16:55:24Z","abstract_excerpt":"We study conditions when a certain type of the Riesz Decomposition Property (RDP for short) holds in the lexicographic product of two po-groups. Defining two important properties of po-groups, we extend known situations showing that the lexicographic product satisfies RDP or even RDP$_1$, a stronger type of RDP. We recall that a very strong type of RDP, RDP$_2$, entails that the group is lattice ordered. RDP's of the lexicographic products are important for the study of lexicographic pseudo effect algebras, or perfect types of pseudo MV-algebras and pseudo effect algebras, where infinitesimal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08909","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.08909","created_at":"2026-05-18T01:16:01.447934+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.08909v1","created_at":"2026-05-18T01:16:01.447934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08909","created_at":"2026-05-18T01:16:01.447934+00:00"},{"alias_kind":"pith_short_12","alias_value":"7KX5O263MPPW","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7KX5O263MPPWRIWB","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7KX5O263","created_at":"2026-05-18T12:30:04.600751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI","json":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI.json","graph_json":"https://pith.science/api/pith-number/7KX5O263MPPWRIWBI7R5O3BXMI/graph.json","events_json":"https://pith.science/api/pith-number/7KX5O263MPPWRIWBI7R5O3BXMI/events.json","paper":"https://pith.science/paper/7KX5O263"},"agent_actions":{"view_html":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI","download_json":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI.json","view_paper":"https://pith.science/paper/7KX5O263","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.08909&json=true","fetch_graph":"https://pith.science/api/pith-number/7KX5O263MPPWRIWBI7R5O3BXMI/graph.json","fetch_events":"https://pith.science/api/pith-number/7KX5O263MPPWRIWBI7R5O3BXMI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI/action/storage_attestation","attest_author":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI/action/author_attestation","sign_citation":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI/action/citation_signature","submit_replication":"https://pith.science/pith/7KX5O263MPPWRIWBI7R5O3BXMI/action/replication_record"}},"created_at":"2026-05-18T01:16:01.447934+00:00","updated_at":"2026-05-18T01:16:01.447934+00:00"}