{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F76WM5LMM7OVO4WC44O6HOMXJW","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":"df50e30373bb7fba0d1fde7f1e537cf8b2e6ada0e59401e759e1c3d9b55656c1","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-01-14T08:02:59Z","title_canon_sha256":"f843d963454d3514b4c30fa1ffc746d976697f6e8dcd653274269fca70278993"},"schema_version":"1.0","source":{"id":"1301.2880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2880","created_at":"2026-05-18T03:36:34Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2880v1","created_at":"2026-05-18T03:36:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2880","created_at":"2026-05-18T03:36:34Z"},{"alias_kind":"pith_short_12","alias_value":"F76WM5LMM7OV","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"F76WM5LMM7OVO4WC","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"F76WM5LM","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:a03fa087a2c73a341a1942ffcc23f0b6dfe8c34975fce3bf73b84844365efbdd","target":"graph","created_at":"2026-05-18T03:36:34Z","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 an FPRAS for Holant problems with parity constraints and not-all-equal constraints, a generalisation of the problem of counting sink-free-orientations. The approach combines a sampler for near-assignments of \"windable\" functions -- using the cycle-unwinding canonical paths technique of Jerrum and Sinclair -- with a bound on the weight of near-assignments. The proof generalises to a larger class of Holant problems; we characterise this class and show that it cannot be extended by expressibility reductions.\n  We then ask whether windability is equivalent to expressibility by matchings ci","authors_text":"Colin McQuillan","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-01-14T08:02:59Z","title":"Approximating Holant problems by winding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2880","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":"sha256:9d3898b14c358babac4b9340ce42428e54f925fba23ff847b12e797296f06d9e","target":"record","created_at":"2026-05-18T03:36:34Z","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":"df50e30373bb7fba0d1fde7f1e537cf8b2e6ada0e59401e759e1c3d9b55656c1","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-01-14T08:02:59Z","title_canon_sha256":"f843d963454d3514b4c30fa1ffc746d976697f6e8dcd653274269fca70278993"},"schema_version":"1.0","source":{"id":"1301.2880","kind":"arxiv","version":1}},"canonical_sha256":"2ffd66756c67dd5772c2e71de3b9974d8fcc4cb7fb4e593308cb16f63a97fa5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ffd66756c67dd5772c2e71de3b9974d8fcc4cb7fb4e593308cb16f63a97fa5a","first_computed_at":"2026-05-18T03:36:34.844335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:34.844335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PhJc3VGfMTnc89+2SLEXmjufpWKhBgovk5wDI9+of7VaXMulDAXoBswShlVob0zghRGPrRfq1dlBHqVx7C2ZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:34.845101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d3898b14c358babac4b9340ce42428e54f925fba23ff847b12e797296f06d9e","sha256:a03fa087a2c73a341a1942ffcc23f0b6dfe8c34975fce3bf73b84844365efbdd"],"state_sha256":"b673424a7991e96d6cbcbaef55a1f69f05e09e8133a7ad274b7260330f42989d"}