{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NTDQIQMUTPG34IBJ6XPXHJK5BZ","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":"e8dc47394a31f2b677ecb135b63829500a1c4bad7c7845e40213dc5ce8cb0ed4","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-06T13:47:03Z","title_canon_sha256":"dad43a898dfa8a7d300b0ea36c152dd5977238405c5c3ea16f982270d9916f87"},"schema_version":"1.0","source":{"id":"1410.1371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1371","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1371v1","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1371","created_at":"2026-05-18T02:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"NTDQIQMUTPG3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NTDQIQMUTPG34IBJ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NTDQIQMU","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:f3a97013df39de11679f4db5fdf498d76e2d6bbb089605aa5893d3ef4b1d156b","target":"graph","created_at":"2026-05-18T02:41:02Z","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":"It is known that the minimum broadcast rate of a linear index code over $\\mathbb{F}_q$ is equal to the $minrank_q$ of the underlying digraph. In [3] it is proved that for $\\mathbb{F}_2$ and any positive integer $k$, $minrank_q(G)\\leq k$ iff there exists a homomorphism from the complement of the graph $G$ to the complement of a particular undirected graph family called \"graph family $\\{G_k\\}$\". As observed in [2], by combining these two results one can relate the linear index coding problem of undirected graphs to the graph homomorphism problem. In [4], a direct connection between linear index ","authors_text":"Javad B. Ebrahimi, Mahdi Jafari Siavoshani","cross_cats":["cs.DM","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-06T13:47:03Z","title":"Linear Index Coding via Graph Homomorphism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1371","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":"sha256:46a99788dc23aaed9e80eb6ad9e9d2ac955040bc0796316770ac545386056783","target":"record","created_at":"2026-05-18T02:41:02Z","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":"e8dc47394a31f2b677ecb135b63829500a1c4bad7c7845e40213dc5ce8cb0ed4","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-06T13:47:03Z","title_canon_sha256":"dad43a898dfa8a7d300b0ea36c152dd5977238405c5c3ea16f982270d9916f87"},"schema_version":"1.0","source":{"id":"1410.1371","kind":"arxiv","version":1}},"canonical_sha256":"6cc70441949bcdbe2029f5df73a55d0e6c6e9da8d61d96ce2d415481d6369aea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cc70441949bcdbe2029f5df73a55d0e6c6e9da8d61d96ce2d415481d6369aea","first_computed_at":"2026-05-18T02:41:02.229357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:02.229357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RjJNclA/I+pkuV9NqfXDlXsAoHMz39x5dKHCf3tOnRcT2BGulYFh+UiTTO93sLLt8ZLV8ZiJvPkxGhK+OTYoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:02.229830Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46a99788dc23aaed9e80eb6ad9e9d2ac955040bc0796316770ac545386056783","sha256:f3a97013df39de11679f4db5fdf498d76e2d6bbb089605aa5893d3ef4b1d156b"],"state_sha256":"c62df0a6da57acbecd6b8e883e25ac436baff4557492b1c9e23422139cbabe59"}