{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:L2PPC2RWGBNV2GX6JZCTMFRDWY","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":"2dd16b7781c1cc23bfaee4bd54dd7eee8183bbd5e969163e32c2d9ac1e067754","cross_cats_sorted":["cs.CC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-05T12:25:06Z","title_canon_sha256":"9f40dc506691af1b55020b16a3d6124aa31ca880a8bb93ee6074e9d7179e2c50"},"schema_version":"1.0","source":{"id":"1207.1238","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1238","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1238v1","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1238","created_at":"2026-05-18T03:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"L2PPC2RWGBNV","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"L2PPC2RWGBNV2GX6","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"L2PPC2RW","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:8fa70f7a89b8f16449120e2da557af9a06f151bb47277ceed6a9f282baa28a99","target":"graph","created_at":"2026-05-18T03:03:44Z","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":"We investigate certain optimization problems for Shannon information measures, namely, minimization of joint and conditional entropies $H(X,Y)$, $H(X|Y)$, $H(Y|X)$, and maximization of mutual information $I(X;Y)$, over convex regions. When restricted to the so-called transportation polytopes (sets of distributions with fixed marginals), very simple proofs of NP-hardness are obtained for these problems because in that case they are all equivalent, and their connection to the well-known \\textsc{Subset sum} and \\textsc{Partition} problems is revealed. The computational intractability of the more ","authors_text":"Ivan Stanojevi\\'c, Mladen Kova\\v{c}evi\\'c, Vojin \\v{S}enk","cross_cats":["cs.CC","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-05T12:25:06Z","title":"On the Hardness of Entropy Minimization and Related Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1238","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:ba71c4459b4d791e11961d7638968bf71de239d6102425985276a3a40ce299a1","target":"record","created_at":"2026-05-18T03:03:44Z","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":"2dd16b7781c1cc23bfaee4bd54dd7eee8183bbd5e969163e32c2d9ac1e067754","cross_cats_sorted":["cs.CC","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-05T12:25:06Z","title_canon_sha256":"9f40dc506691af1b55020b16a3d6124aa31ca880a8bb93ee6074e9d7179e2c50"},"schema_version":"1.0","source":{"id":"1207.1238","kind":"arxiv","version":1}},"canonical_sha256":"5e9ef16a36305b5d1afe4e45361623b635c9c73038bd5c1b003ca83dc0e46723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e9ef16a36305b5d1afe4e45361623b635c9c73038bd5c1b003ca83dc0e46723","first_computed_at":"2026-05-18T03:03:44.790605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:44.790605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vXXlw7d/kBnTKYBSCS0LYHKv7GEJDvkhLdGZ6h3ikYL7PIVYj2ubdVoX+GxiX3rH7zeVHZLc698qnmHBT+BWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:44.791328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1238","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba71c4459b4d791e11961d7638968bf71de239d6102425985276a3a40ce299a1","sha256:8fa70f7a89b8f16449120e2da557af9a06f151bb47277ceed6a9f282baa28a99"],"state_sha256":"3ac899817b5f21c62bfa4f5872069249cbeec8ea1f64bcf810a7bc78a96ea923"}