{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:F5NVFWFZ3BXB2MPZWOE2C46C4J","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":"f8d19bd303cf82021c10a9d7b75d6f19a244874f46442790bf744c169f0967e0","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2004-11-03T19:20:11Z","title_canon_sha256":"2f31260efe1100a13e3f6d2f7c058259ffd47d7396164a1a1317d6b03596ec10"},"schema_version":"1.0","source":{"id":"cs/0411006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0411006","created_at":"2026-05-18T00:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0411006v1","created_at":"2026-05-18T00:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0411006","created_at":"2026-05-18T00:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"F5NVFWFZ3BXB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"F5NVFWFZ3BXB2MPZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"F5NVFWFZ","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:720d70623671ac2603c319ec3946a697e77d9e7dd68a976577239074e1f5d904","target":"graph","created_at":"2026-05-18T00:57:45Z","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":"In this paper, we present two low complexity algorithms that achieve capacity for the noiseless (d,k) constrained channel when k=2d+1, or when k-d+1 is not prime. The first algorithm, called symbol sliding, is a generalized version of the bit flipping algorithm introduced by Aviran et al. [1]. In addition to achieving capacity for (d,2d+1) constraints, it comes close to capacity in other cases. The second algorithm is based on interleaving, and is a generalized version of the bit stuffing algorithm introduced by Bender and Wolf [2]. This method uses fewer than k-d biased bit streams to achieve","authors_text":"Steven W. McLaughlin, Yogesh Sankarasubramaniam","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2004-11-03T19:20:11Z","title":"Capacity Achieving Code Constructions for Two Classes of (d,k) Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0411006","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":"sha256:79e5f7ba9ba04fc83b017492acf80dd9c899ece708494b87fc84cdea8e6c36a7","target":"record","created_at":"2026-05-18T00:57:45Z","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":"f8d19bd303cf82021c10a9d7b75d6f19a244874f46442790bf744c169f0967e0","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2004-11-03T19:20:11Z","title_canon_sha256":"2f31260efe1100a13e3f6d2f7c058259ffd47d7396164a1a1317d6b03596ec10"},"schema_version":"1.0","source":{"id":"cs/0411006","kind":"arxiv","version":1}},"canonical_sha256":"2f5b52d8b9d86e1d31f9b389a173c2e257aafba6aa84a101d7c62da6ab934ae5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f5b52d8b9d86e1d31f9b389a173c2e257aafba6aa84a101d7c62da6ab934ae5","first_computed_at":"2026-05-18T00:57:45.183521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:45.183521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Y4kYbVBnzJFLkhNyWjNNq1lxjPB4Lzy+yVra0WajvNZAn8ZS72DEeMVb2fmOQpD9SkdMuDngT06F/VOQpH9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:45.184025Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0411006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79e5f7ba9ba04fc83b017492acf80dd9c899ece708494b87fc84cdea8e6c36a7","sha256:720d70623671ac2603c319ec3946a697e77d9e7dd68a976577239074e1f5d904"],"state_sha256":"f00baa3097f31fd7723cef205ee9e588eb92d644d7452fd6dd16c0e1ecd85673"}