{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4SRPWYHSVTKMYGMHUACK6QBI34","short_pith_number":"pith:4SRPWYHS","canonical_record":{"source":{"id":"1311.4451","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-18T17:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"b1fc7b2105d23b4c1e9ec3b9c18ed74dae09a955bf9ba5d163251b7723edf272","abstract_canon_sha256":"44b2b786841c0029c816772e26156c866b28312fbe3b4fca6ab3ccb05fe024e6"},"schema_version":"1.0"},"canonical_sha256":"e4a2fb60f2acd4cc1987a004af4028df2ce2bf623d81fbad8d94bb762ad3f490","source":{"kind":"arxiv","id":"1311.4451","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4451","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4451v4","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4451","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"pith_short_12","alias_value":"4SRPWYHSVTKM","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4SRPWYHSVTKMYGMH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4SRPWYHS","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4SRPWYHSVTKMYGMHUACK6QBI34","target":"record","payload":{"canonical_record":{"source":{"id":"1311.4451","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-18T17:03:51Z","cross_cats_sorted":[],"title_canon_sha256":"b1fc7b2105d23b4c1e9ec3b9c18ed74dae09a955bf9ba5d163251b7723edf272","abstract_canon_sha256":"44b2b786841c0029c816772e26156c866b28312fbe3b4fca6ab3ccb05fe024e6"},"schema_version":"1.0"},"canonical_sha256":"e4a2fb60f2acd4cc1987a004af4028df2ce2bf623d81fbad8d94bb762ad3f490","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:31.277006Z","signature_b64":"B7bb9h2wZM0sUASmO0jCc56whWfEJ9e0Tq8ioapU18iAY0IlJNciXfYmsgOFlRg1cfzGPPqA2yGxmLqEkFfdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4a2fb60f2acd4cc1987a004af4028df2ce2bf623d81fbad8d94bb762ad3f490","last_reissued_at":"2026-05-18T01:13:31.276234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:31.276234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.4451","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b3aDcA5kl1GN/W5NYjlyjc+Q8La7OnxbEaIl+bTxuW+HxsuQFXN9vTJsSzRc/oJlRdfeiIheNJXlXfBDu0h2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:53:29.723508Z"},"content_sha256":"f892ee9825520e82dc5c31519d713b22c46eb8fa41b20ec067ff4be633e6a9e7","schema_version":"1.0","event_id":"sha256:f892ee9825520e82dc5c31519d713b22c46eb8fa41b20ec067ff4be633e6a9e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4SRPWYHSVTKMYGMHUACK6QBI34","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andreas Galanis, Daniel Stefankovic, Eric Vigoda, Heng Guo, Jin-Yi Cai, Leslie Ann Goldberg, Mark Jerrum","submitted_at":"2013-11-18T17:03:51Z","abstract_excerpt":"Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS in the general framework of two-state spin systems on bipartite graphs. We define two notions, nearly-independent phase-correlated spins and unary symmetry breaking. We prove that it is #BIS-hard to approximate the partition function of any 2-spin system on bipartite graphs supporting these two notions. As a consequence, we classify the complexity of approxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4451","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNMD9bnBl1iXtEzK4vc1Tl9DSWqDF4V1uWrSdF55sm4Wew7JSOdX4zNJiwvpzuKppF17knxj7wVb6Uen2pYzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:53:29.723860Z"},"content_sha256":"9f870e802cc9cf6489738fe17815877f0930fe1ea7fb1969055a702bfa24726c","schema_version":"1.0","event_id":"sha256:9f870e802cc9cf6489738fe17815877f0930fe1ea7fb1969055a702bfa24726c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SRPWYHSVTKMYGMHUACK6QBI34/bundle.json","state_url":"https://pith.science/pith/4SRPWYHSVTKMYGMHUACK6QBI34/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SRPWYHSVTKMYGMHUACK6QBI34/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T06:53:29Z","links":{"resolver":"https://pith.science/pith/4SRPWYHSVTKMYGMHUACK6QBI34","bundle":"https://pith.science/pith/4SRPWYHSVTKMYGMHUACK6QBI34/bundle.json","state":"https://pith.science/pith/4SRPWYHSVTKMYGMHUACK6QBI34/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SRPWYHSVTKMYGMHUACK6QBI34/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4SRPWYHSVTKMYGMHUACK6QBI34","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":"44b2b786841c0029c816772e26156c866b28312fbe3b4fca6ab3ccb05fe024e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-18T17:03:51Z","title_canon_sha256":"b1fc7b2105d23b4c1e9ec3b9c18ed74dae09a955bf9ba5d163251b7723edf272"},"schema_version":"1.0","source":{"id":"1311.4451","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4451","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4451v4","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4451","created_at":"2026-05-18T01:13:31Z"},{"alias_kind":"pith_short_12","alias_value":"4SRPWYHSVTKM","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4SRPWYHSVTKMYGMH","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4SRPWYHS","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:9f870e802cc9cf6489738fe17815877f0930fe1ea7fb1969055a702bfa24726c","target":"graph","created_at":"2026-05-18T01:13:31Z","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":"Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS in the general framework of two-state spin systems on bipartite graphs. We define two notions, nearly-independent phase-correlated spins and unary symmetry breaking. We prove that it is #BIS-hard to approximate the partition function of any 2-spin system on bipartite graphs supporting these two notions. As a consequence, we classify the complexity of approxi","authors_text":"Andreas Galanis, Daniel Stefankovic, Eric Vigoda, Heng Guo, Jin-Yi Cai, Leslie Ann Goldberg, Mark Jerrum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-18T17:03:51Z","title":"#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4451","kind":"arxiv","version":4},"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:f892ee9825520e82dc5c31519d713b22c46eb8fa41b20ec067ff4be633e6a9e7","target":"record","created_at":"2026-05-18T01:13:31Z","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":"44b2b786841c0029c816772e26156c866b28312fbe3b4fca6ab3ccb05fe024e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-18T17:03:51Z","title_canon_sha256":"b1fc7b2105d23b4c1e9ec3b9c18ed74dae09a955bf9ba5d163251b7723edf272"},"schema_version":"1.0","source":{"id":"1311.4451","kind":"arxiv","version":4}},"canonical_sha256":"e4a2fb60f2acd4cc1987a004af4028df2ce2bf623d81fbad8d94bb762ad3f490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4a2fb60f2acd4cc1987a004af4028df2ce2bf623d81fbad8d94bb762ad3f490","first_computed_at":"2026-05-18T01:13:31.276234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:31.276234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B7bb9h2wZM0sUASmO0jCc56whWfEJ9e0Tq8ioapU18iAY0IlJNciXfYmsgOFlRg1cfzGPPqA2yGxmLqEkFfdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:31.277006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4451","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f892ee9825520e82dc5c31519d713b22c46eb8fa41b20ec067ff4be633e6a9e7","sha256:9f870e802cc9cf6489738fe17815877f0930fe1ea7fb1969055a702bfa24726c"],"state_sha256":"e2bd349c18b6661ed7f727569f9318866054fdc1806eff4c9687cfbf2cdc6f6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pbc3jKfXFmWcKI/cUDHdrQAyFAvKFtWzGwWkf1nWAJEh4ujYO9rhB78p0AuRsLHJYmlQTSeCoT7eR5/5zAmkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:53:29.725794Z","bundle_sha256":"a943eecdf083436461f184554ebf89395055efbbb5b04393bbe8e5fef7171642"}}