{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:HPME2B227XEJCIX7ZW62TM6ZZA","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":"f19c60ae78e767460bfcb164eb628d55d9f9a215e0131babaf15a9f37f63652f","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-01T18:25:57Z","title_canon_sha256":"173ba17bf96b89efd1f448b89e219d3bdfd727f862da6016c428e8964c55b5a7"},"schema_version":"1.0","source":{"id":"1907.01006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01006","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01006v1","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01006","created_at":"2026-05-17T23:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"HPME2B227XEJ","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"HPME2B227XEJCIX7","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"HPME2B22","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:f333b2126d7fe6a272ced2f061d31a24df461cea372b56a5ed83150ea4eec412","target":"graph","created_at":"2026-05-17T23:41:41Z","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":"In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on $n$ vertices, all preferred extensions can be enumerated in $O^*(3^{n/3})$ time and there are directed graphs with $\\Omega(3^{n/3})$ preferred extensions. We give faster enumeration algorithms for directed graphs with at most $0.8004\\cdot n$ vertices occurring in $2$-cycles. In particular, for oriented graphs (digraphs with no 2-cycles) one of our algorithms runs in time $O(1.2","authors_text":"Ray Li, Serge Gaspers","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-01T18:25:57Z","title":"Enumeration of Preferred Extensions in Almost Oriented Digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01006","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:e1de2cc777fa0f3903bc3ee8f56b1d99522d8a9bfb93c6cac7296a9fb6b45b1b","target":"record","created_at":"2026-05-17T23:41:41Z","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":"f19c60ae78e767460bfcb164eb628d55d9f9a215e0131babaf15a9f37f63652f","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-01T18:25:57Z","title_canon_sha256":"173ba17bf96b89efd1f448b89e219d3bdfd727f862da6016c428e8964c55b5a7"},"schema_version":"1.0","source":{"id":"1907.01006","kind":"arxiv","version":1}},"canonical_sha256":"3bd84d075afdc89122ffcdbda9b3d9c8000810259eb48076947366eafa4baaab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bd84d075afdc89122ffcdbda9b3d9c8000810259eb48076947366eafa4baaab","first_computed_at":"2026-05-17T23:41:41.474036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:41.474036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j/3FEOQwd1w9oYnGFFqwPldBoo2+BgQfZsR7EjU0dVpUKJykCpBdtavLnDUHNdEXgdLAmlH4E4GR1Vnt5cZ1Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:41.474542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.01006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1de2cc777fa0f3903bc3ee8f56b1d99522d8a9bfb93c6cac7296a9fb6b45b1b","sha256:f333b2126d7fe6a272ced2f061d31a24df461cea372b56a5ed83150ea4eec412"],"state_sha256":"006d04dbd34371abdeb85d3982f5f8512f224f7e5f91b0f56b4ef25312bc9df2"}