{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B743PXCS2KXRAWCCJVTISIX2HI","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":"4ee66bb0182f4bea6b0db5c8f7c045c0378aa250e6ab0d8dda18cf6a2f34551b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-30T15:05:12Z","title_canon_sha256":"e6fc6d5eb59db807f427d7c2ad4d027fece089f22311654ac8a65bd99a47162c"},"schema_version":"1.0","source":{"id":"1410.8395","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8395","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8395v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8395","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"B743PXCS2KXR","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B743PXCS2KXRAWCC","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B743PXCS","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:f0187b99a374bea68c0b46f3ccc74b65185ca6589676f24e253463cd2897614a","target":"graph","created_at":"2026-05-18T01:11:55Z","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 give a necessary and sufficient condition for extremality of a supermodular function based on its min-representation by means of (vertices of) the corresponding core polytope. The condition leads to solving a certain simple linear equation system determined by the combinatorial core structure. Our result allows us to characterize indecomposability in the class of generalized permutohedra. We provide an in-depth comparison between our result and the description of extremality in the supermodular/submodular cone achieved by other researchers.","authors_text":"M. Studen\\'y, T. Kroupa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-30T15:05:12Z","title":"Core-based criterion for extreme supermodular functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8395","kind":"arxiv","version":2},"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:ffab70085597932df6013904f744dfcb59509f7ecd2e13fd8eec45fb1f5c91d6","target":"record","created_at":"2026-05-18T01:11:55Z","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":"4ee66bb0182f4bea6b0db5c8f7c045c0378aa250e6ab0d8dda18cf6a2f34551b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-30T15:05:12Z","title_canon_sha256":"e6fc6d5eb59db807f427d7c2ad4d027fece089f22311654ac8a65bd99a47162c"},"schema_version":"1.0","source":{"id":"1410.8395","kind":"arxiv","version":2}},"canonical_sha256":"0ff9b7dc52d2af1058424d668922fa3a1c3c26d32870a934fb86a06d65724eff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ff9b7dc52d2af1058424d668922fa3a1c3c26d32870a934fb86a06d65724eff","first_computed_at":"2026-05-18T01:11:55.329586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.329586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bhyefq7WyEazflZqMu/YrtfTfFQbpqilwsMIiuyDqJpVtQxsZPz8CGjKGFgXuiye64TmjuUigUvzccB7wtLlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.329914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8395","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffab70085597932df6013904f744dfcb59509f7ecd2e13fd8eec45fb1f5c91d6","sha256:f0187b99a374bea68c0b46f3ccc74b65185ca6589676f24e253463cd2897614a"],"state_sha256":"03fb4c5a3c840722c7df6b249aebe63f6fc93b848a828c894719b60164e1ef0e"}