{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GQQKQC34VB66KGGO7KWEJ3F4BG","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":"8f2cb5a2ec9d531037e13a3bd119fbb3bde26e8936a5e4c98c8f0a0c4f9f2498","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-09-20T15:06:19Z","title_canon_sha256":"cc17570bdda9b2b2908ef1d8ac529a95fa5904439e83673a9b62f2c51b44c34b"},"schema_version":"1.0","source":{"id":"1309.5292","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5292","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5292v1","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5292","created_at":"2026-05-18T03:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"GQQKQC34VB66","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GQQKQC34VB66KGGO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GQQKQC34","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:6131f908cbdfd791d7755969c81e84920d801f386345ad8abcd843cb849a7f34","target":"graph","created_at":"2026-05-18T03:12:47Z","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 \"Gluing Algorithm\" of Semaev [Des.\\ Codes Cryptogr.\\ 49 (2008), 47--60] --- that finds all solutions of a sparse system of linear equations over the Galois field $GF(q)$ --- has average running time $O(mq^{\\max \\left\\vert \\cup_{1}^{k}X_{j}\\right\\vert -k}), $ where $m$ is the total number of equations, and $\\cup_{1}^{k}X_{j}$ is the set of all unknowns actively occurring in the first $k$ equations. Our goal here is to minimize the exponent of $q$ in the case where every equation contains at most three unknowns. %Applying hypergraph-theoretic methods we prove The main result states that if t","authors_text":"Peter Horak, Zsolt Tuza","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-09-20T15:06:19Z","title":"Speeding up Deciphering by Hypergraph Ordering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5292","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":"sha256:1a8c33e815df7ee8a681b84a9ebe14f3af2b089732aaaf0534ed5e2d97c9cec1","target":"record","created_at":"2026-05-18T03:12:47Z","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":"8f2cb5a2ec9d531037e13a3bd119fbb3bde26e8936a5e4c98c8f0a0c4f9f2498","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-09-20T15:06:19Z","title_canon_sha256":"cc17570bdda9b2b2908ef1d8ac529a95fa5904439e83673a9b62f2c51b44c34b"},"schema_version":"1.0","source":{"id":"1309.5292","kind":"arxiv","version":1}},"canonical_sha256":"3420a80b7ca87de518cefaac44ecbc09b9930926957249bc0b1aa5fe93fad3be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3420a80b7ca87de518cefaac44ecbc09b9930926957249bc0b1aa5fe93fad3be","first_computed_at":"2026-05-18T03:12:47.074868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:47.074868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8HrGnGXK/GtKrd2TpyEAM+IRYlJGJOd+FwHOOv+DZP/SuCqMtA0XZ8qGr+LKOYQc9ip0ZpA8Vo7cGlGeUqoKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:47.075477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5292","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a8c33e815df7ee8a681b84a9ebe14f3af2b089732aaaf0534ed5e2d97c9cec1","sha256:6131f908cbdfd791d7755969c81e84920d801f386345ad8abcd843cb849a7f34"],"state_sha256":"24bbd1d68873e85a76e670aa99b4222b2f2e3958c0cc48adfa4429454c1c4b79"}