{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZE7ED6GUGAAGJWQCSVOFUU2MH2","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":"612147308b461afc2cfb8f4d61e10cf2a64056a62e948447bf4d49b1eff3dfa2","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T23:49:36Z","title_canon_sha256":"7ebd39366e8948ceacddc5faf657f9722826c71cf04ba87ed33ce615675f3fc6"},"schema_version":"1.0","source":{"id":"1206.2689","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2689","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2689v2","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2689","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"ZE7ED6GUGAAG","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZE7ED6GUGAAGJWQC","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZE7ED6GU","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:e70483383c0a3b6150023a3eb74263acae5a8340d06172445d3d73601028ed7f","target":"graph","created_at":"2026-05-18T02:21:52Z","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":"Consider a family of distributions $\\{\\pi_{\\beta}\\}$ where $X\\sim\\pi_{\\beta}$ means that $\\mathbb{P}(X=x)=\\exp(-\\beta H(x))/Z(\\beta)$. Here $Z(\\beta)$ is the proper normalizing constant, equal to $\\sum_x\\exp(-\\beta H(x))$. Then $\\{\\pi_{\\beta}\\}$ is known as a Gibbs distribution, and $Z(\\beta)$ is the partition function. This work presents a new method for approximating the partition function to a specified level of relative accuracy using only a number of samples, that is, $O(\\ln(Z(\\beta))\\ln(\\ln(Z(\\beta))))$ when $Z(0)\\geq1$. This is a sharp improvement over previous, similar approaches that ","authors_text":"Mark Huber","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T23:49:36Z","title":"Approximation algorithms for the normalizing constant of Gibbs distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2689","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":"sha256:2e90147290d4cef704ec8fe3f6308173dc43b71f7fcbf2f845e800494310d9bd","target":"record","created_at":"2026-05-18T02:21:52Z","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":"612147308b461afc2cfb8f4d61e10cf2a64056a62e948447bf4d49b1eff3dfa2","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T23:49:36Z","title_canon_sha256":"7ebd39366e8948ceacddc5faf657f9722826c71cf04ba87ed33ce615675f3fc6"},"schema_version":"1.0","source":{"id":"1206.2689","kind":"arxiv","version":2}},"canonical_sha256":"c93e41f8d4300064da02955c5a534c3ea1e22ee9b4c26e6f0f2eddb82b0da353","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c93e41f8d4300064da02955c5a534c3ea1e22ee9b4c26e6f0f2eddb82b0da353","first_computed_at":"2026-05-18T02:21:52.081973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:52.081973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+6IxE4HyoPIAN83o52wWJFCqg2HR7mCeRuJ5tJoUw5Z65wk4W80s0wRjjMBArE66RA1DgQ0saziGohNbx+J6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:52.082662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2689","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e90147290d4cef704ec8fe3f6308173dc43b71f7fcbf2f845e800494310d9bd","sha256:e70483383c0a3b6150023a3eb74263acae5a8340d06172445d3d73601028ed7f"],"state_sha256":"d00593e38864829e0ea3207efe1bf2fbe2173f604cf7c79ae814c5b36b91e7b4"}