{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FQW6QSZ66WPPZLCF6RWN4R4K3T","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":"584af98b2178ae2c9646d3c55068b4c1888c2e7948969194a56358d3285cf957","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T06:36:45Z","title_canon_sha256":"729fee1db5dd4651fa4d2dd1d10ca1a0e63fa8d37f210bdf41560a36abe49449"},"schema_version":"1.0","source":{"id":"1902.10354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10354","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10354v1","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10354","created_at":"2026-05-17T23:52:31Z"},{"alias_kind":"pith_short_12","alias_value":"FQW6QSZ66WPP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FQW6QSZ66WPPZLCF","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FQW6QSZ6","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:f915db17f49b0247abda6e71467a2626222925669706e84c82cf13c7f8793686","target":"graph","created_at":"2026-05-17T23:52:31Z","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 consider a direct conversion of the, classical, set splitting problem to the directed Hamiltonian cycle problem. A constructive procedure for such a conversion is given, and it is shown that the input size of the converted instance is a linear function of the input size of the original instance. A proof that the two instances are equivalent is given, and a procedure for identifying a solution to the original instance from a solution of the converted instance is also provided. We conclude with two examples of set splitting problem instances, one with solutions and one without, and display th","authors_text":"Jerzy Filar, Michael Haythorpe","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T06:36:45Z","title":"A Linearly-growing Conversion from the Set Splitting Problem to the Directed Hamiltonian Cycle Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10354","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":"sha256:0ecf41931357304ec66b2a9d3414b5a11734d2e3096d832f36dbebea5aeae5cf","target":"record","created_at":"2026-05-17T23:52:31Z","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":"584af98b2178ae2c9646d3c55068b4c1888c2e7948969194a56358d3285cf957","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T06:36:45Z","title_canon_sha256":"729fee1db5dd4651fa4d2dd1d10ca1a0e63fa8d37f210bdf41560a36abe49449"},"schema_version":"1.0","source":{"id":"1902.10354","kind":"arxiv","version":1}},"canonical_sha256":"2c2de84b3ef59efcac45f46cde478adcca2e0428bc699de809b48592ff85bf8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c2de84b3ef59efcac45f46cde478adcca2e0428bc699de809b48592ff85bf8b","first_computed_at":"2026-05-17T23:52:31.087922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:31.087922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NPKUGlakWBYy2zA83cQERnyMWWKz4cLvU+G8wjNT1gc3y9vfsrtStuNJw/ZwstD8ppOKXRdyoEz+IyT79631Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:31.088375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ecf41931357304ec66b2a9d3414b5a11734d2e3096d832f36dbebea5aeae5cf","sha256:f915db17f49b0247abda6e71467a2626222925669706e84c82cf13c7f8793686"],"state_sha256":"c4ab31cdfccf9807bb4637a612e63bf7787504f257d3939601505e3733275c4e"}