{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q3JVUQTKASM5ZNWXLH373RRY42","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":"f7ae0d0a6301983e4faebd8f5a3cc89a657cfa3023ef8a51ea98df8bce79a067","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-07T10:31:55Z","title_canon_sha256":"df3c8ad4092b6889e6982894360e0e53b66c4c11b2c9f4da40bb1ba8b0041b91"},"schema_version":"1.0","source":{"id":"1809.02392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02392","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02392v1","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02392","created_at":"2026-05-18T00:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"Q3JVUQTKASM5","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q3JVUQTKASM5ZNWX","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q3JVUQTK","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:09b7232282efb0c71dea39cedb8a643689eb4b8a3bdeb62a8b2b0b3f759b1dbc","target":"graph","created_at":"2026-05-18T00:06:17Z","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 consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant $\\gamma > 0$ such that if $n=2^k$ and $A$ is $3$-dimensional $n\\times n\\times n$ array where every cell contains at most $\\gamma n$ symbols, and every symbol occurs at most $\\gamma n$ times in every line of $A$, then $A$ is {\\em avoidable}; that is, there is a Latin cube $L$ of order $n$ such that for every $1\\leq i,j,k\\leq n$, the symbol in position $(i,j,k)$ of $L$ does not appear in the corresponding cell of $A$.","authors_text":"Carl Johan Casselgren, Klas Markstr\\\"om, Lan Anh Pham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-07T10:31:55Z","title":"Latin Cubes with Forbidden Entries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02392","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":"sha256:78f7af7844a6abdbb28447eb03707852f7e5b63dce6d2b6b4f586aa0b1c2ec58","target":"record","created_at":"2026-05-18T00:06:17Z","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":"f7ae0d0a6301983e4faebd8f5a3cc89a657cfa3023ef8a51ea98df8bce79a067","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-07T10:31:55Z","title_canon_sha256":"df3c8ad4092b6889e6982894360e0e53b66c4c11b2c9f4da40bb1ba8b0041b91"},"schema_version":"1.0","source":{"id":"1809.02392","kind":"arxiv","version":1}},"canonical_sha256":"86d35a426a0499dcb6d759f7fdc638e6aadbe0a89969fe8c9521f1c610b953a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86d35a426a0499dcb6d759f7fdc638e6aadbe0a89969fe8c9521f1c610b953a8","first_computed_at":"2026-05-18T00:06:17.244999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:17.244999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tpVMC2rDsrTxpIbk68oMG9J0bLWXiMKH3YFcPiP+nIYgJNABrmXBNzRV1YxtDjOhOibtv/ZMiDH9KxqNBitmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:17.245533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78f7af7844a6abdbb28447eb03707852f7e5b63dce6d2b6b4f586aa0b1c2ec58","sha256:09b7232282efb0c71dea39cedb8a643689eb4b8a3bdeb62a8b2b0b3f759b1dbc"],"state_sha256":"205ce84e4f4f74f602a271da93af4429c8ae8106272a465753516023b3d7157a"}