{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V42UHQAYMDADCPBN5ZNL2BIGLB","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":"bba03f6674db0311e0ee88750fd72196d602819f7eb447ae3d86303e03164ab6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-18T14:52:08Z","title_canon_sha256":"5c68ab87e45915057afbeeeb8e18bae4851a11dac0d2e92ed5cfe10ec2abed83"},"schema_version":"1.0","source":{"id":"1804.06770","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.06770","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1804.06770v2","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.06770","created_at":"2026-05-18T00:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"V42UHQAYMDAD","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V42UHQAYMDADCPBN","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V42UHQAY","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:4fa641005f656073b1747a2041166e72a2b465dfba0e89bf4eae086523134f02","target":"graph","created_at":"2026-05-18T00:04:30Z","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":"Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The $\\ell$-th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping sets of size up to $\\ell$. In this work, a notion of coverable stopping sets is defined. In order to achieve maximum-likelihood performance under iterative decoding over the BEC, the parity-check matrix should contain no coverable stopping sets of size $\\ell$, for $1 \\le \\ell \\le n-k$, where $n$ is the code length, $k$ is the code dimension. By estimating th","authors_text":"Boris D. Kudryashov, Irina E. Bocharova, Vitaly Skachek, Yauhen Yakimenka","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-18T14:52:08Z","title":"Stopping Redundancy Hierarchy Beyond the Minimum Distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06770","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":"sha256:3bcd74ae01cd9a066200a1564a341fd64f2557aed462f4078369ef2f0e010dd0","target":"record","created_at":"2026-05-18T00:04:30Z","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":"bba03f6674db0311e0ee88750fd72196d602819f7eb447ae3d86303e03164ab6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-18T14:52:08Z","title_canon_sha256":"5c68ab87e45915057afbeeeb8e18bae4851a11dac0d2e92ed5cfe10ec2abed83"},"schema_version":"1.0","source":{"id":"1804.06770","kind":"arxiv","version":2}},"canonical_sha256":"af3543c01860c0313c2dee5abd05065870214d40a6a430e20c6a627344f5a952","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af3543c01860c0313c2dee5abd05065870214d40a6a430e20c6a627344f5a952","first_computed_at":"2026-05-18T00:04:30.070667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:30.070667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gPWZo6Qn9t8yWT1bW+SB4fRB3eLLvhMW6jFMnDkCUnQu6Z7+RCw9h81VCWG3MYAbRK+PvsytkOMfcuAqqrrHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:30.071063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.06770","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bcd74ae01cd9a066200a1564a341fd64f2557aed462f4078369ef2f0e010dd0","sha256:4fa641005f656073b1747a2041166e72a2b465dfba0e89bf4eae086523134f02"],"state_sha256":"4fcbe70ad70dc966e76a0f01c70b20c809824830ad8ec4b86c0911eac05038c7"}