{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JCBUC25B64DYQIDXDBE4PXKPUA","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":"dea77ab780d8e2025872d2acb644aaa8c4da15199b880557bfbb6a9c6418ccac","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-18T20:45:11Z","title_canon_sha256":"4ca762b90169a932ecc76839519678bdd51f0a4e08ce253d4d302901ae83f5e9"},"schema_version":"1.0","source":{"id":"1204.4204","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4204","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4204v3","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4204","created_at":"2026-05-18T02:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"JCBUC25B64DY","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JCBUC25B64DYQIDX","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JCBUC25B","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:c2892529004a33489c27e8fe7c0750e5878645db38d606423acba69f801c3042","target":"graph","created_at":"2026-05-18T02:21:16Z","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":"An $n$-dimensional chair consists of an $n$-dimensional box from which a smaller $n$-dimensional box is removed. A tiling of an $n$-dimensional chair has two nice applications in coding for write-once memories. The first one is in the design of codes which correct asymmetric errors with limited-magnitude. The second one is in the design of $n$ cells $q$-ary write-once memory codes. We show an equivalence between the design of a tiling with an integer lattice and the design of a tiling from a generalization of splitting (or of Sidon sequences). A tiling of an $n$-dimensional chair can define a ","authors_text":"Sarit Buzaglo, Tuvi Etzion","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-18T20:45:11Z","title":"Tilings with $n$-Dimensional Chairs and their Applications to Asymmetric Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4204","kind":"arxiv","version":3},"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":"sha256:57a8510d158350d8dd7b20524c65cd0c7c253faee68035b29cb55dddb31d763c","target":"record","created_at":"2026-05-18T02:21:16Z","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":"dea77ab780d8e2025872d2acb644aaa8c4da15199b880557bfbb6a9c6418ccac","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-04-18T20:45:11Z","title_canon_sha256":"4ca762b90169a932ecc76839519678bdd51f0a4e08ce253d4d302901ae83f5e9"},"schema_version":"1.0","source":{"id":"1204.4204","kind":"arxiv","version":3}},"canonical_sha256":"4883416ba1f7078820771849c7dd4fa0086cfcb0e82c35f646dcf38edb0c8b3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4883416ba1f7078820771849c7dd4fa0086cfcb0e82c35f646dcf38edb0c8b3d","first_computed_at":"2026-05-18T02:21:16.181204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:16.181204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"++D1/VjwBWqyY56rmhIBi9DkkRVutcSXeRgaNlGvA3Gs77XhIL4vT7AAqDkFGdHz77TUnqzZxzv6P7lfqoGrAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:16.181863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4204","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57a8510d158350d8dd7b20524c65cd0c7c253faee68035b29cb55dddb31d763c","sha256:c2892529004a33489c27e8fe7c0750e5878645db38d606423acba69f801c3042"],"state_sha256":"0d3e60f4ca9483c1e157b4a1537d7918f993e422843e5f630d7305bde7ecd6d8"}