{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RKN2BPXK7TLC4OBYUKQFDFVMRZ","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":"bfac420d9c9e68b8b091ebe16131af3a5e7f7a836082aa3775f1540d164ab24d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-27T22:53:13Z","title_canon_sha256":"2fda69b25908de506a17e4a0109aba69d99eb7ddb5a8f8f12c9a62b5be75c320"},"schema_version":"1.0","source":{"id":"1303.7000","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7000","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7000v1","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7000","created_at":"2026-05-18T03:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"RKN2BPXK7TLC","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RKN2BPXK7TLC4OBY","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RKN2BPXK","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:9c0857fe4fd598bda2991afcbbb87042c1381b406c8cdd5fd9934fcdcd4a8ee0","target":"graph","created_at":"2026-05-18T03:29:38Z","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":"An interference alignment perspective is used to identify the simplest instances (minimum possible number of edges in the alignment graph, no more than 2 interfering messages at any destination) of index coding problems where non-Shannon information inequalities are necessary for capacity characterization. In particular, this includes the first known example of a multiple unicast (one destination per message) index coding problem where non-Shannon information inequalities are shown to be necessary. The simplest multiple unicast example has 7 edges in the alignment graph and 11 messages. The si","authors_text":"Hua Sun, Syed A. Jafar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-27T22:53:13Z","title":"Index Coding Capacity: How far can one go with only Shannon Inequalities?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7000","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":"sha256:27a2ba73924232b66bcced99eda3b3656066748df393f1ce2e38e93217a418d8","target":"record","created_at":"2026-05-18T03:29:38Z","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":"bfac420d9c9e68b8b091ebe16131af3a5e7f7a836082aa3775f1540d164ab24d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-03-27T22:53:13Z","title_canon_sha256":"2fda69b25908de506a17e4a0109aba69d99eb7ddb5a8f8f12c9a62b5be75c320"},"schema_version":"1.0","source":{"id":"1303.7000","kind":"arxiv","version":1}},"canonical_sha256":"8a9ba0beeafcd62e3838a2a05196ac8e791b6669195fd5cc7e85abca7fb76df5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a9ba0beeafcd62e3838a2a05196ac8e791b6669195fd5cc7e85abca7fb76df5","first_computed_at":"2026-05-18T03:29:38.893823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:38.893823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W8JP5j56IjdeAuJm5ILZQLd2lprrdE8tdKW2yg/JSXR7UxaO9jpVPp+fFgVzYD/V1jvGkhYRecxf4wV5e6znDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:38.894671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.7000","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27a2ba73924232b66bcced99eda3b3656066748df393f1ce2e38e93217a418d8","sha256:9c0857fe4fd598bda2991afcbbb87042c1381b406c8cdd5fd9934fcdcd4a8ee0"],"state_sha256":"1a2ab9ac294821369d518d9faf156a9a3a02676285976f00a03c69e274c24783"}