{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GPQICE6TQ2X7HCL7B75ZDYBHIM","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":"ae5260cd7da577948b8a95af0c67effc50d569f0b0fdda492613649903158ed2","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-04-19T16:13:05Z","title_canon_sha256":"4c718e711cd02e79680ac61b6207de6f422719648f11f2ea381d32d6a916acb9"},"schema_version":"1.0","source":{"id":"1704.05798","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05798","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05798v2","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05798","created_at":"2026-05-18T00:01:43Z"},{"alias_kind":"pith_short_12","alias_value":"GPQICE6TQ2X7","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GPQICE6TQ2X7HCL7","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GPQICE6T","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:7cabd7e36a85998103a7cb1fd1de8e64701560bda33f1df420c40b6362cc6ee5","target":"graph","created_at":"2026-05-18T00:01:43Z","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":"Holant problems are a family of counting problems on graphs, parametrised by sets of complex-valued functions of Boolean inputs. Holant^c denotes a subfamily of those problems, where any function set considered must contain the two unary functions pinning inputs to values 0 or 1. The complexity classification of Holant problems usually takes the form of dichotomy theorems, showing that for any set of functions in the family, the problem is either #P-hard or it can be solved in polynomial time. Previous such results include a dichotomy for real-valued Holant^c and one for Holant^c with complex ","authors_text":"Miriam Backens","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-04-19T16:13:05Z","title":"A complete dichotomy for complex-valued Holant^c"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05798","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":"sha256:400d9e2ea0deec6247198e7124c2eddae46df0afd75eecadbc6e033c0c5cb75f","target":"record","created_at":"2026-05-18T00:01:43Z","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":"ae5260cd7da577948b8a95af0c67effc50d569f0b0fdda492613649903158ed2","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-04-19T16:13:05Z","title_canon_sha256":"4c718e711cd02e79680ac61b6207de6f422719648f11f2ea381d32d6a916acb9"},"schema_version":"1.0","source":{"id":"1704.05798","kind":"arxiv","version":2}},"canonical_sha256":"33e08113d386aff3897f0ffb91e027432d2613860bb1fce590aeea6ac258d5da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33e08113d386aff3897f0ffb91e027432d2613860bb1fce590aeea6ac258d5da","first_computed_at":"2026-05-18T00:01:43.922306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:43.922306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gU/TCWwUp06mcl5SKQmXv0Zt2hxY9IZcRv3d08VaruNoKHsp9xJONbEq1S9CFgKqYt2lKMWZFSYO4PeRR58BCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:43.922854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05798","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:400d9e2ea0deec6247198e7124c2eddae46df0afd75eecadbc6e033c0c5cb75f","sha256:7cabd7e36a85998103a7cb1fd1de8e64701560bda33f1df420c40b6362cc6ee5"],"state_sha256":"c9fbfedc5f20f0d80eabd8bf8c4a49a7f441a8070c72dd05d67b14c456d22465"}