{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:B3467CJTX34NAXDVAVEJWL6Q64","short_pith_number":"pith:B3467CJT","canonical_record":{"source":{"id":"1208.3629","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-08-17T16:11:27Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"9167a36ce0a020bb1c1ab1f1377352c6953d56e305ef57cffcc9858508617a7c","abstract_canon_sha256":"b3b12a79af69f4fe8769721e8d7fea387ecbf8a8c7f634d5799308824b429e0b"},"schema_version":"1.0"},"canonical_sha256":"0ef9ef8933bef8d05c7505489b2fd0f711c1d4bcd1b5e47241ae7a5308962ec8","source":{"kind":"arxiv","id":"1208.3629","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3629","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3629v5","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3629","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"B3467CJTX34N","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B3467CJTX34NAXDV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B3467CJT","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:B3467CJTX34NAXDVAVEJWL6Q64","target":"record","payload":{"canonical_record":{"source":{"id":"1208.3629","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-08-17T16:11:27Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"9167a36ce0a020bb1c1ab1f1377352c6953d56e305ef57cffcc9858508617a7c","abstract_canon_sha256":"b3b12a79af69f4fe8769721e8d7fea387ecbf8a8c7f634d5799308824b429e0b"},"schema_version":"1.0"},"canonical_sha256":"0ef9ef8933bef8d05c7505489b2fd0f711c1d4bcd1b5e47241ae7a5308962ec8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:17.540659Z","signature_b64":"LFuox6VlaGfyY2xUfqCYgwQPTU8j4G9RSug0WqUvN66aodt1hWbV38KzhpaJy6iEjIs0T9r4v/36Fc7gvSK+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ef9ef8933bef8d05c7505489b2fd0f711c1d4bcd1b5e47241ae7a5308962ec8","last_reissued_at":"2026-05-18T03:14:17.540087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:17.540087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.3629","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CnSSpN2WLIMs7jLQHuLVcV9im9E2wROKtbYHrik80Fpc6kmVMRUaFBGgXv2r8E2U/E3qFGw2aBWyNM9Zi665AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:09:37.250967Z"},"content_sha256":"f897f81c7c47a8beeae5ed946708b4a6f3c139966a86689c483633e2678754e6","schema_version":"1.0","event_id":"sha256:f897f81c7c47a8beeae5ed946708b4a6f3c139966a86689c483633e2678754e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:B3467CJTX34NAXDVAVEJWL6Q64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"cs.DS","authors_text":"Hang Zhou, Marc Lelarge","submitted_at":"2012-08-17T16:11:27Z","abstract_excerpt":"For a graph $G$, let $Z(G,\\lambda)$ be the partition function of the monomer-dimer system defined by $\\sum_k m_k(G)\\lambda^k$, where $m_k(G)$ is the number of matchings of size $k$ in $G$. We consider graphs of bounded degree and develop a sublinear-time algorithm for estimating $\\log Z(G,\\lambda)$ at an arbitrary value $\\lambda>0$ within additive error $\\epsilon n$ with high probability. The query complexity of our algorithm does not depend on the size of $G$ and is polynomial in $1/\\epsilon$, and we also provide a lower bound quadratic in $1/\\epsilon$ for this problem. This is the first anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3629","kind":"arxiv","version":5},"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":"2026-05-18T03:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nh2835YN1S6zKZ15j2WmWCLhQPkKwI1GWhZ9qM3eSJUJskjocBJ6O+kob30lnxMhX5Iq7aBda44LND0M+bxPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:09:37.251726Z"},"content_sha256":"34c80c4d7b5e039ff4fc7f2337c8d7f458236efd0a066a118d8f151903de364a","schema_version":"1.0","event_id":"sha256:34c80c4d7b5e039ff4fc7f2337c8d7f458236efd0a066a118d8f151903de364a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3467CJTX34NAXDVAVEJWL6Q64/bundle.json","state_url":"https://pith.science/pith/B3467CJTX34NAXDVAVEJWL6Q64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3467CJTX34NAXDVAVEJWL6Q64/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":"2026-06-09T05:09:37Z","links":{"resolver":"https://pith.science/pith/B3467CJTX34NAXDVAVEJWL6Q64","bundle":"https://pith.science/pith/B3467CJTX34NAXDVAVEJWL6Q64/bundle.json","state":"https://pith.science/pith/B3467CJTX34NAXDVAVEJWL6Q64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3467CJTX34NAXDVAVEJWL6Q64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:B3467CJTX34NAXDVAVEJWL6Q64","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":"b3b12a79af69f4fe8769721e8d7fea387ecbf8a8c7f634d5799308824b429e0b","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-08-17T16:11:27Z","title_canon_sha256":"9167a36ce0a020bb1c1ab1f1377352c6953d56e305ef57cffcc9858508617a7c"},"schema_version":"1.0","source":{"id":"1208.3629","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.3629","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1208.3629v5","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.3629","created_at":"2026-05-18T03:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"B3467CJTX34N","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"B3467CJTX34NAXDV","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"B3467CJT","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:34c80c4d7b5e039ff4fc7f2337c8d7f458236efd0a066a118d8f151903de364a","target":"graph","created_at":"2026-05-18T03:14:17Z","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":"For a graph $G$, let $Z(G,\\lambda)$ be the partition function of the monomer-dimer system defined by $\\sum_k m_k(G)\\lambda^k$, where $m_k(G)$ is the number of matchings of size $k$ in $G$. We consider graphs of bounded degree and develop a sublinear-time algorithm for estimating $\\log Z(G,\\lambda)$ at an arbitrary value $\\lambda>0$ within additive error $\\epsilon n$ with high probability. The query complexity of our algorithm does not depend on the size of $G$ and is polynomial in $1/\\epsilon$, and we also provide a lower bound quadratic in $1/\\epsilon$ for this problem. This is the first anal","authors_text":"Hang Zhou, Marc Lelarge","cross_cats":["cs.DM","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-08-17T16:11:27Z","title":"Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3629","kind":"arxiv","version":5},"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:f897f81c7c47a8beeae5ed946708b4a6f3c139966a86689c483633e2678754e6","target":"record","created_at":"2026-05-18T03:14:17Z","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":"b3b12a79af69f4fe8769721e8d7fea387ecbf8a8c7f634d5799308824b429e0b","cross_cats_sorted":["cs.DM","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2012-08-17T16:11:27Z","title_canon_sha256":"9167a36ce0a020bb1c1ab1f1377352c6953d56e305ef57cffcc9858508617a7c"},"schema_version":"1.0","source":{"id":"1208.3629","kind":"arxiv","version":5}},"canonical_sha256":"0ef9ef8933bef8d05c7505489b2fd0f711c1d4bcd1b5e47241ae7a5308962ec8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ef9ef8933bef8d05c7505489b2fd0f711c1d4bcd1b5e47241ae7a5308962ec8","first_computed_at":"2026-05-18T03:14:17.540087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:17.540087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LFuox6VlaGfyY2xUfqCYgwQPTU8j4G9RSug0WqUvN66aodt1hWbV38KzhpaJy6iEjIs0T9r4v/36Fc7gvSK+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:17.540659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.3629","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f897f81c7c47a8beeae5ed946708b4a6f3c139966a86689c483633e2678754e6","sha256:34c80c4d7b5e039ff4fc7f2337c8d7f458236efd0a066a118d8f151903de364a"],"state_sha256":"45dc3a0666bc6fc8fe83073c6ae59722c61b819dc9f06038ab27a19d837e5497"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrOZPTkJ8Sj4pm2tCNkWO6FmSlwiXH4+7mtrYgoWxvjNOx44B4s+LcZ0u/1lyuOf8XBmYIY6q5BJKRb116jSAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:09:37.255865Z","bundle_sha256":"a43f1092152922535103218d8299e8811dcfaf644379f0493812829bff12aff3"}}