{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A5RSBM7LBC3FWDTWCCM5ND257E","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":"5219559794691dbad5dc1829799bb124a60a87fe70cb80ac73e7f52af63104dd","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-07T16:11:06Z","title_canon_sha256":"d510feb62bbe1e8f8adb58f09aea537b7033ae5a8f8b60413297b12d4b132042"},"schema_version":"1.0","source":{"id":"1712.02690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02690","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02690v1","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02690","created_at":"2026-05-18T00:28:33Z"},{"alias_kind":"pith_short_12","alias_value":"A5RSBM7LBC3F","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A5RSBM7LBC3FWDTW","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A5RSBM7L","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:cf3a7e963142c723ac8918e0046848b45a641d631fff9be07e8b53bbf6f08a9f","target":"graph","created_at":"2026-05-18T00:28:33Z","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":"The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the $(0,k)$-runlength limited (RLL) constraint, i.e., no more than $k$ consecutive `$0$'s are allowed. The feedback capacity of this channel is derived for all $k\\geq 1$, and is given by $$C^\\mathrm{fb}_{(0,k)}(\\varepsilon) = \\max\\frac{\\overline{\\varepsilon}H_2(\\delta_0)+\\sum_{i=1}^{k-1}\\left(\\overline{\\varepsilon}^{i+1}H_2(\\delta_i)\\prod_{m=0}^{i-1}\\delta_m\\right)}{1+\\sum_{i=0}^{k-1}\\left(\\overline{\\varepsilon}^{i+1}\n  \\prod_{m=0}^{i}\\delta_m\\right)},$$ where $\\","authors_text":"Haim H. Permuter, Ori Peled, Oron Sabag","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-07T16:11:06Z","title":"Feedback Capacity and Coding for the $(0,k)$-RLL Input-Constrained BEC"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02690","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":"sha256:3fe81b51b6c422718badf78d1612a5f258eb4db3d1655b7150202b9eb19b3db6","target":"record","created_at":"2026-05-18T00:28:33Z","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":"5219559794691dbad5dc1829799bb124a60a87fe70cb80ac73e7f52af63104dd","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-07T16:11:06Z","title_canon_sha256":"d510feb62bbe1e8f8adb58f09aea537b7033ae5a8f8b60413297b12d4b132042"},"schema_version":"1.0","source":{"id":"1712.02690","kind":"arxiv","version":1}},"canonical_sha256":"076320b3eb08b65b0e761099d68f5df92375404bd2bf9360d681e2d20a963356","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"076320b3eb08b65b0e761099d68f5df92375404bd2bf9360d681e2d20a963356","first_computed_at":"2026-05-18T00:28:33.156509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:33.156509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jy3ZKFJ+F2hZg4h1/y3kCNs2OgQg7nV1V9uRKyjXrr8rOzT1RM94clS/g0nLC76XNkUb8eUKqpCscPUHwyKiBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:33.157268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fe81b51b6c422718badf78d1612a5f258eb4db3d1655b7150202b9eb19b3db6","sha256:cf3a7e963142c723ac8918e0046848b45a641d631fff9be07e8b53bbf6f08a9f"],"state_sha256":"4a5f1c6f0501733095a164aea510a15b939c6d6b8bd12c0f19f3de382d1c7691"}