{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QOFXSWF2XJU34ITHJMK3ROMRF6","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":"81b3b8eaabc19aa4e787761370a1317ab496f796706d664ee2bfa41829d2026e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-08T20:01:04Z","title_canon_sha256":"1e3619be9476385f8aeca347a6843304e97ead73c8e782cffd06ac8621b9b4a2"},"schema_version":"1.0","source":{"id":"1310.2252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2252","created_at":"2026-05-18T03:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2252v1","created_at":"2026-05-18T03:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2252","created_at":"2026-05-18T03:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"QOFXSWF2XJU3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QOFXSWF2XJU34ITH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QOFXSWF2","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:317834c6811f684fab54d319fa9efe2fdc45f0cee75f4184f5bd3f6eca2518b7","target":"graph","created_at":"2026-05-18T03:10:57Z","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 present a novel application of the Kramers-Wannier duality on one of the most important problems of computer science, the Boolean satisfiability problem (SAT). More specifically, we focus on sharp-SAT or equivalently #SAT - the problem of counting the number of solutions to a Boolean satisfaction formula. #SAT can be cast into a statistical-mechanical language, where it reduces to calculating the partition function of an Ising spin Hamiltonian with multi-spin interactions. We show that Kramers-Wannier duality can be generalized to apply to such multi-connected spin networks. We present an e","authors_text":"Benjamin Hsu, Joe Mitchell, Victor Galitski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-08T20:01:04Z","title":"Kramers-Wannier Duality of Statistical Mechanics Applied to the Boolean Satisfiability Problem of Computer Science"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2252","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":"sha256:5bee0ed9d7b905366b328cf22208060d0989b3f1e46330061bafd6d7a36976ce","target":"record","created_at":"2026-05-18T03:10:57Z","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":"81b3b8eaabc19aa4e787761370a1317ab496f796706d664ee2bfa41829d2026e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-10-08T20:01:04Z","title_canon_sha256":"1e3619be9476385f8aeca347a6843304e97ead73c8e782cffd06ac8621b9b4a2"},"schema_version":"1.0","source":{"id":"1310.2252","kind":"arxiv","version":1}},"canonical_sha256":"838b7958baba69be22674b15b8b9912f97cae7b8a3e30dadfdd40d115d58ac1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"838b7958baba69be22674b15b8b9912f97cae7b8a3e30dadfdd40d115d58ac1f","first_computed_at":"2026-05-18T03:10:57.503010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:57.503010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wj+Llml7VKqP1x5Oxc3SwIh9vJXa4r+R+P0iJpIqwtsrurvSqlmThQoFyM4DECvoN3O8fvaxMgYZcPLb9G2vCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:57.503794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bee0ed9d7b905366b328cf22208060d0989b3f1e46330061bafd6d7a36976ce","sha256:317834c6811f684fab54d319fa9efe2fdc45f0cee75f4184f5bd3f6eca2518b7"],"state_sha256":"d9edf7f2fbb7c573042a3817864c3a700a7129fc7dcd4496b3c11e40c09f9591"}