{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LWMMUZV6NDAIOUJICG3YMCQ27X","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":"a6c78ec6d213a9132aba9bdc029e1a428bdc3eb51c09b10a8edfafac7616611e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-13T10:38:31Z","title_canon_sha256":"b6d6dec1ddd4eb2e37ba1f5039a24511fd6c81417563ddb5d9b7d817fdd72ab4"},"schema_version":"1.0","source":{"id":"1611.04109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04109","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04109v1","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04109","created_at":"2026-05-18T00:59:17Z"},{"alias_kind":"pith_short_12","alias_value":"LWMMUZV6NDAI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LWMMUZV6NDAIOUJI","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LWMMUZV6","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:afbed33950e99f3349495be42abf9f0693d51558f415a99517364d21251b46f3","target":"graph","created_at":"2026-05-18T00:59:17Z","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 import a duality notion coming from polymatroids to define duality for information inequalities. We show that the entropy region for $n\\ge 5$ is not closed under duality. Our result answers an open question of Mat\\`u\\v{s} (1992).","authors_text":"Tarik Kaced","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-13T10:38:31Z","title":"The Entropy Region is not Closed Under Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04109","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:adc17c069560ec7c3c73d1881c62646de4c7a60a78562fa83e18416ce18dc7b5","target":"record","created_at":"2026-05-18T00:59:17Z","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":"a6c78ec6d213a9132aba9bdc029e1a428bdc3eb51c09b10a8edfafac7616611e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-13T10:38:31Z","title_canon_sha256":"b6d6dec1ddd4eb2e37ba1f5039a24511fd6c81417563ddb5d9b7d817fdd72ab4"},"schema_version":"1.0","source":{"id":"1611.04109","kind":"arxiv","version":1}},"canonical_sha256":"5d98ca66be68c087512811b7860a1afdd20c978f6dbfdeac2be978956ea0adbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d98ca66be68c087512811b7860a1afdd20c978f6dbfdeac2be978956ea0adbb","first_computed_at":"2026-05-18T00:59:17.511053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:17.511053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClmnWeRe67NCjSYAbEiOLCALoPa/uK0zyT2vRKR6TTdmovw02vIxbykaqsV9dRpGWsVcItjaanqi2N686GdlCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:17.511634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adc17c069560ec7c3c73d1881c62646de4c7a60a78562fa83e18416ce18dc7b5","sha256:afbed33950e99f3349495be42abf9f0693d51558f415a99517364d21251b46f3"],"state_sha256":"f28f7c54a3a887f076fb07e823f034571d43ae00ec3d0837b5977fee0e4eb2d8"}