{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q7EP6CZ74OZNE4MTLRSS7IX3H5","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":"9f46d93787c1e7770b22185414bab503b0c195e0f214b831b94a0a686126b9fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-23T08:41:46Z","title_canon_sha256":"6cf551268e9fc8548eb011d25d27bc27148ef3f2bd2686339438a7786a45e6a8"},"schema_version":"1.0","source":{"id":"1305.5345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5345","created_at":"2026-05-18T03:21:53Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5345v2","created_at":"2026-05-18T03:21:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5345","created_at":"2026-05-18T03:21:53Z"},{"alias_kind":"pith_short_12","alias_value":"Q7EP6CZ74OZN","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q7EP6CZ74OZNE4MT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q7EP6CZ7","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:4ad446886c428aa74d6ecebe94778c5d3b415b475f302c67934bb24bdd81637a","target":"graph","created_at":"2026-05-18T03:21:53Z","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":"A parallelohedron is called reducible, if it can be represented as a direct product of two parallelohedra of lower dimension. In his Ph.D. thesis (2005) the first author proved a criterion of reducibility of a parallelohedron in terms of the Venkov graph. In December 2011 the second author presented a slightly revised version of the original proof at the seminar \"Discrete Geometry and Geometry of Numbers\" (Moscow State University). The present paper follows that talk.","authors_text":"Alexander Magazinov, Andrei Ordine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-23T08:41:46Z","title":"A criterion of reducibility for a parallelohedron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5345","kind":"arxiv","version":2},"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":"sha256:554ab0083b6a117062b08ba45f5faccf2c5fd8d0825865f87f4e2ce0f2895cdd","target":"record","created_at":"2026-05-18T03:21:53Z","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":"9f46d93787c1e7770b22185414bab503b0c195e0f214b831b94a0a686126b9fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-23T08:41:46Z","title_canon_sha256":"6cf551268e9fc8548eb011d25d27bc27148ef3f2bd2686339438a7786a45e6a8"},"schema_version":"1.0","source":{"id":"1305.5345","kind":"arxiv","version":2}},"canonical_sha256":"87c8ff0b3fe3b2d271935c652fa2fb3f61951178d27dfd649569dd92b0f87208","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87c8ff0b3fe3b2d271935c652fa2fb3f61951178d27dfd649569dd92b0f87208","first_computed_at":"2026-05-18T03:21:53.472748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:53.472748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w9jdiLCX3KMmduGf/IAvUpnjjyajtT8b9nxHwPFr05NReRqgZq/HB0tAOdVbADTR6eub49SCXExN4hGT0yG9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:53.473251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:554ab0083b6a117062b08ba45f5faccf2c5fd8d0825865f87f4e2ce0f2895cdd","sha256:4ad446886c428aa74d6ecebe94778c5d3b415b475f302c67934bb24bdd81637a"],"state_sha256":"9ca1f59dded5efe71aa9b692ae7ae44ed27021f749d739db3adf2fd882669aac"}