{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QI5JFTMKE6DAH63YYP4RF5PV7O","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":"07b4e4bea7403b3d8e022d7432cd92d7bfe0efe20174106e91b954ee9efcd2d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-01-13T05:38:13Z","title_canon_sha256":"26e7a7883cf4b5225af70287c5b9b2c85be45f932754ff7d3c12ace66897397d"},"schema_version":"1.0","source":{"id":"2201.04799","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.04799","created_at":"2026-07-05T03:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"2201.04799v2","created_at":"2026-07-05T03:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.04799","created_at":"2026-07-05T03:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"QI5JFTMKE6DA","created_at":"2026-07-05T03:48:20Z"},{"alias_kind":"pith_short_16","alias_value":"QI5JFTMKE6DAH63Y","created_at":"2026-07-05T03:48:20Z"},{"alias_kind":"pith_short_8","alias_value":"QI5JFTMK","created_at":"2026-07-05T03:48:20Z"}],"graph_snapshots":[{"event_id":"sha256:0e42bd4068707447c47b65a75438a3a26d48ac33972ac09a9c003799edec3e1c","target":"graph","created_at":"2026-07-05T03:48:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.04799/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of computing an $(s,d)$-hypernetwork in an acyclic F-hypergraph. This is a fundamental computational problem arising in directed hypergraphs, and is a foundational step in tackling problems of reachability and redundancy. This problem was previously explored in the context of general directed hypergraphs (containing cycles), where it is NP-hard, and acyclic B-hypergraphs, where a linear time algorithm can be achieved. In a surprising contrast, we find that for acyclic F-hypergraphs the problem is NP-hard, which also implies the problem is hard in BF-hypergraphs. This is","authors_text":"Lo\\\"ic Miller, Max Ward, Reynaldo Gil-Pons","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-01-13T05:38:13Z","title":"Finding $(s,d)$-Hypernetworks in F-Hypergraphs is NP-Hard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.04799","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:a813cc7eb68b08bebd7116f6627e5d89052898e1b6b25d5da7c16f67e13112ae","target":"record","created_at":"2026-07-05T03:48:20Z","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":"07b4e4bea7403b3d8e022d7432cd92d7bfe0efe20174106e91b954ee9efcd2d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-01-13T05:38:13Z","title_canon_sha256":"26e7a7883cf4b5225af70287c5b9b2c85be45f932754ff7d3c12ace66897397d"},"schema_version":"1.0","source":{"id":"2201.04799","kind":"arxiv","version":2}},"canonical_sha256":"823a92cd8a278603fb78c3f912f5f5fb9f5e10a9bc2ad2143a971c7aba8296c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823a92cd8a278603fb78c3f912f5f5fb9f5e10a9bc2ad2143a971c7aba8296c3","first_computed_at":"2026-07-05T03:48:20.513617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:48:20.513617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ObKI3bQNXxtYmokqsOW2ASFq5D9kgCJ0nqyMAtTnWvj/PpHlzUZQRzmxBlV6QHe1CvlhVXZybeTkEkgfkYKsDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:48:20.514015Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.04799","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a813cc7eb68b08bebd7116f6627e5d89052898e1b6b25d5da7c16f67e13112ae","sha256:0e42bd4068707447c47b65a75438a3a26d48ac33972ac09a9c003799edec3e1c"],"state_sha256":"13fa4ac9201a3e525f781b761de5c3477b07a65fe483356aee479cadacd6764e"}