{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:NFZPQKW3U7HG7LQ53OZ6W3GBJD","short_pith_number":"pith:NFZPQKW3","canonical_record":{"source":{"id":"cond-mat/0402010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-01-31T17:31:22Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"4ae94f325a34db372f53226a19300df9a75b608c9996043b5bab64a691f6fc6d","abstract_canon_sha256":"234545aaed884e9c4e1eab17570beac6d071d992948b7344fab4f7980f89601d"},"schema_version":"1.0"},"canonical_sha256":"6972f82adba7ce6fae1ddbb3eb6cc148d3a740b8939065a5c0a02ac749377cdf","source":{"kind":"arxiv","id":"cond-mat/0402010","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0402010","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0402010v1","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0402010","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"NFZPQKW3U7HG","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"NFZPQKW3U7HG7LQ5","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"NFZPQKW3","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:NFZPQKW3U7HG7LQ53OZ6W3GBJD","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0402010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-01-31T17:31:22Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"4ae94f325a34db372f53226a19300df9a75b608c9996043b5bab64a691f6fc6d","abstract_canon_sha256":"234545aaed884e9c4e1eab17570beac6d071d992948b7344fab4f7980f89601d"},"schema_version":"1.0"},"canonical_sha256":"6972f82adba7ce6fae1ddbb3eb6cc148d3a740b8939065a5c0a02ac749377cdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:31.187213Z","signature_b64":"CCtKZ/BhkQwJj2NF3qGthHoZgegXZ1LXzAuVmtCbBK/DVLLSpGvgJ16Q6DxjW6Ou8SeJSRUdd8nlFQ95AWtTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6972f82adba7ce6fae1ddbb3eb6cc148d3a740b8939065a5c0a02ac749377cdf","last_reissued_at":"2026-05-18T01:08:31.186589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:31.186589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0402010","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gID+SKLzC+v8wNNH3vp4lZxv2i19/fuBC012evKouP87NyFVSrgTvhl4aE/QMM9fdgKUu1XTM17MvmnwI9R3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:05:58.657086Z"},"content_sha256":"dded85fa82399e9490e6997885fcc8ad0b776e89401166113b3a012cf294db25","schema_version":"1.0","event_id":"sha256:dded85fa82399e9490e6997885fcc8ad0b776e89401166113b3a012cf294db25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:NFZPQKW3U7HG7LQ53OZ6W3GBJD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Number partitioning as random energy model","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Heiko Bauke, Silvio Franz, Stephan Mertens","submitted_at":"2004-01-31T17:31:22Z","abstract_excerpt":"Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local rando"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0402010","kind":"arxiv","version":1},"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":"2026-05-18T01:08:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VtERt+YCOZPVXJF52BAOzCQlX4C9gI/FusWUbYFsrNGCM9R+R3RxyIAcoyWg9u3/qrKNINTL8hB6HK0ri7cOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:05:58.657448Z"},"content_sha256":"7d1ca3324730e4f1780986c9e406efd55eb5728425d5e970bb7acc3655b96f8a","schema_version":"1.0","event_id":"sha256:7d1ca3324730e4f1780986c9e406efd55eb5728425d5e970bb7acc3655b96f8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFZPQKW3U7HG7LQ53OZ6W3GBJD/bundle.json","state_url":"https://pith.science/pith/NFZPQKW3U7HG7LQ53OZ6W3GBJD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFZPQKW3U7HG7LQ53OZ6W3GBJD/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":"2026-06-01T10:05:58Z","links":{"resolver":"https://pith.science/pith/NFZPQKW3U7HG7LQ53OZ6W3GBJD","bundle":"https://pith.science/pith/NFZPQKW3U7HG7LQ53OZ6W3GBJD/bundle.json","state":"https://pith.science/pith/NFZPQKW3U7HG7LQ53OZ6W3GBJD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFZPQKW3U7HG7LQ53OZ6W3GBJD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:NFZPQKW3U7HG7LQ53OZ6W3GBJD","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":"234545aaed884e9c4e1eab17570beac6d071d992948b7344fab4f7980f89601d","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-01-31T17:31:22Z","title_canon_sha256":"4ae94f325a34db372f53226a19300df9a75b608c9996043b5bab64a691f6fc6d"},"schema_version":"1.0","source":{"id":"cond-mat/0402010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0402010","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0402010v1","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0402010","created_at":"2026-05-18T01:08:31Z"},{"alias_kind":"pith_short_12","alias_value":"NFZPQKW3U7HG","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"NFZPQKW3U7HG7LQ5","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"NFZPQKW3","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:7d1ca3324730e4f1780986c9e406efd55eb5728425d5e970bb7acc3655b96f8a","target":"graph","created_at":"2026-05-18T01:08:31Z","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":"Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local rando","authors_text":"Heiko Bauke, Silvio Franz, Stephan Mertens","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-01-31T17:31:22Z","title":"Number partitioning as random energy model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0402010","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:dded85fa82399e9490e6997885fcc8ad0b776e89401166113b3a012cf294db25","target":"record","created_at":"2026-05-18T01:08:31Z","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":"234545aaed884e9c4e1eab17570beac6d071d992948b7344fab4f7980f89601d","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.dis-nn","submitted_at":"2004-01-31T17:31:22Z","title_canon_sha256":"4ae94f325a34db372f53226a19300df9a75b608c9996043b5bab64a691f6fc6d"},"schema_version":"1.0","source":{"id":"cond-mat/0402010","kind":"arxiv","version":1}},"canonical_sha256":"6972f82adba7ce6fae1ddbb3eb6cc148d3a740b8939065a5c0a02ac749377cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6972f82adba7ce6fae1ddbb3eb6cc148d3a740b8939065a5c0a02ac749377cdf","first_computed_at":"2026-05-18T01:08:31.186589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:31.186589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CCtKZ/BhkQwJj2NF3qGthHoZgegXZ1LXzAuVmtCbBK/DVLLSpGvgJ16Q6DxjW6Ou8SeJSRUdd8nlFQ95AWtTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:31.187213Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0402010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dded85fa82399e9490e6997885fcc8ad0b776e89401166113b3a012cf294db25","sha256:7d1ca3324730e4f1780986c9e406efd55eb5728425d5e970bb7acc3655b96f8a"],"state_sha256":"ae421cf5bd594d0c43febcec34541b5840928c3ad794e5d9658c47f47ec1ebce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6gZf8O2y5jSLuqwpSxn2LgHhA0Uywd1HmpPv/TEvTcdSPy/x1uZPTyHeFZ2xSZBV7TyDcBxcCP7YA3gmmnsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:05:58.659451Z","bundle_sha256":"352f0bfdf051be9ebd87a8edf313b51ca230c9b23bd39e9a69c373a372f80bb4"}}