{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6WSXRFBHE46PNUBFM43AFSQ4PF","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":"b8291012a5094176e86b9aa068e8d8407f82c6ff3f6994126ca32377db42c133","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-14T08:58:35Z","title_canon_sha256":"4c49ee38db9552b4b7d0d5956bda4629be382c0b642617fb4fdeab82827d3945"},"schema_version":"1.0","source":{"id":"1102.2702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2702","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2702v2","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2702","created_at":"2026-05-18T04:12:54Z"},{"alias_kind":"pith_short_12","alias_value":"6WSXRFBHE46P","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6WSXRFBHE46PNUBF","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6WSXRFBH","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:56b3d19697782ffd4215b333a4ee708855e02275c60052d016801d93dfae1830","target":"graph","created_at":"2026-05-18T04:12:54Z","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":"Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which produces an isomorphic code, may drastically change the minimal distance of the code. Thus, we may choose a code structure for efficient encoding/decoding procedures, and then optimize the code's minimal distance via relabeling.\n  We formally define the relabeling problem, and show that all codes may be relabeled to get a minimal distance at most 2. The decision","authors_text":"Itzhak Tamo, Moshe Schwartz","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-14T08:58:35Z","title":"On the Labeling Problem of Permutation Group Codes under the Infinity Metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2702","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:bc21e27e8771a87ec86d8c2ace2845c9cbf81f82aec9f158c29e92c3c047dc8a","target":"record","created_at":"2026-05-18T04:12:54Z","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":"b8291012a5094176e86b9aa068e8d8407f82c6ff3f6994126ca32377db42c133","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-14T08:58:35Z","title_canon_sha256":"4c49ee38db9552b4b7d0d5956bda4629be382c0b642617fb4fdeab82827d3945"},"schema_version":"1.0","source":{"id":"1102.2702","kind":"arxiv","version":2}},"canonical_sha256":"f5a5789427273cf6d025673602ca1c797299b015e287da0108afd67c06ad5106","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5a5789427273cf6d025673602ca1c797299b015e287da0108afd67c06ad5106","first_computed_at":"2026-05-18T04:12:54.740078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:54.740078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"efZmoKjKd7q/SZpxOgvAVxeJrwXpEeSuvGaA1kv3Tk0/Etb8BrSJW4roQi1Ck86s8rSKm4ZIRdg+IqwGhucBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:54.740729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc21e27e8771a87ec86d8c2ace2845c9cbf81f82aec9f158c29e92c3c047dc8a","sha256:56b3d19697782ffd4215b333a4ee708855e02275c60052d016801d93dfae1830"],"state_sha256":"de588c7fa87eb64ce547e6bbedc8f8cdfbc8e855d7db330d4ec7b35559ede8e6"}