{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:MZRFINTHOJSIN77LUPINAEADCT","short_pith_number":"pith:MZRFINTH","canonical_record":{"source":{"id":"cond-mat/0211166","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-11-08T14:47:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"39cf444796c3c99cfed6f3d61a07e319c5dd5a503638c5569ea2bd0823c6d21e","abstract_canon_sha256":"55d4eb28a97d1e61e3c5a24f677c298d0c304d8fce756f60729f6687c8e5d561"},"schema_version":"1.0"},"canonical_sha256":"6662543667726486ffeba3d0d0100314f3c5e421c4e732165df8667015f9faa4","source":{"kind":"arxiv","id":"cond-mat/0211166","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0211166","created_at":"2026-05-18T01:06:58Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0211166v1","created_at":"2026-05-18T01:06:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0211166","created_at":"2026-05-18T01:06:58Z"},{"alias_kind":"pith_short_12","alias_value":"MZRFINTHOJSI","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"MZRFINTHOJSIN77L","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"MZRFINTH","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:MZRFINTHOJSIN77LUPINAEADCT","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0211166","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-11-08T14:47:00Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"39cf444796c3c99cfed6f3d61a07e319c5dd5a503638c5569ea2bd0823c6d21e","abstract_canon_sha256":"55d4eb28a97d1e61e3c5a24f677c298d0c304d8fce756f60729f6687c8e5d561"},"schema_version":"1.0"},"canonical_sha256":"6662543667726486ffeba3d0d0100314f3c5e421c4e732165df8667015f9faa4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:58.631812Z","signature_b64":"J0BEt8yYQsYI9OJxxa+5ZHdNphXMiq3ydZAYSwArY6hYbvTB1BlSEWN0Rjg10K9WcRbJj1WGl8HD1XoADlb5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6662543667726486ffeba3d0d0100314f3c5e421c4e732165df8667015f9faa4","last_reissued_at":"2026-05-18T01:06:58.631025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:58.631025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0211166","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":"2026-05-18T01:06:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KvI/CdzYZEHxUPBFgi0c1b6r+gjIrAZWst06Ce/MCqv4gxxhPyToWyaNxRmd0GIuQHDStSRgFSeF1TgXJi+YDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:29:51.882160Z"},"content_sha256":"763eb10245c4cc323216470b7fa11a1310e2f5cda712b3a9b3e85b1cb080fc3c","schema_version":"1.0","event_id":"sha256:763eb10245c4cc323216470b7fa11a1310e2f5cda712b3a9b3e85b1cb080fc3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:MZRFINTHOJSIN77LUPINAEADCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"N. Destainville","submitted_at":"2002-11-08T14:47:00Z","abstract_excerpt":"We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the ``absorption time'' of the ``Backgammon model'', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the ``Contingency table problem'', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0211166","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":"2026-05-18T01:06:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/c3GhMBOQAJ3NrYrwntLcfiE6YwiHyxCAg+qLTjJrkJvvsLz2LEz+99eoEVsg5jZkWp3gsh3TFYJQH3hdVRqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:29:51.882780Z"},"content_sha256":"4d78ab99b187859097f39963325938c534297cfee88af81a565ddf3da0cc3b81","schema_version":"1.0","event_id":"sha256:4d78ab99b187859097f39963325938c534297cfee88af81a565ddf3da0cc3b81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZRFINTHOJSIN77LUPINAEADCT/bundle.json","state_url":"https://pith.science/pith/MZRFINTHOJSIN77LUPINAEADCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZRFINTHOJSIN77LUPINAEADCT/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":"2026-06-04T23:29:51Z","links":{"resolver":"https://pith.science/pith/MZRFINTHOJSIN77LUPINAEADCT","bundle":"https://pith.science/pith/MZRFINTHOJSIN77LUPINAEADCT/bundle.json","state":"https://pith.science/pith/MZRFINTHOJSIN77LUPINAEADCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZRFINTHOJSIN77LUPINAEADCT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:MZRFINTHOJSIN77LUPINAEADCT","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":"55d4eb28a97d1e61e3c5a24f677c298d0c304d8fce756f60729f6687c8e5d561","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-11-08T14:47:00Z","title_canon_sha256":"39cf444796c3c99cfed6f3d61a07e319c5dd5a503638c5569ea2bd0823c6d21e"},"schema_version":"1.0","source":{"id":"cond-mat/0211166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0211166","created_at":"2026-05-18T01:06:58Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0211166v1","created_at":"2026-05-18T01:06:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0211166","created_at":"2026-05-18T01:06:58Z"},{"alias_kind":"pith_short_12","alias_value":"MZRFINTHOJSI","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"MZRFINTHOJSIN77L","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"MZRFINTH","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:4d78ab99b187859097f39963325938c534297cfee88af81a565ddf3da0cc3b81","target":"graph","created_at":"2026-05-18T01:06:58Z","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 propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the ``absorption time'' of the ``Backgammon model'', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the ``Contingency table problem'', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which a","authors_text":"N. Destainville","cross_cats":["math.PR"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-11-08T14:47:00Z","title":"Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0211166","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":"sha256:763eb10245c4cc323216470b7fa11a1310e2f5cda712b3a9b3e85b1cb080fc3c","target":"record","created_at":"2026-05-18T01:06:58Z","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":"55d4eb28a97d1e61e3c5a24f677c298d0c304d8fce756f60729f6687c8e5d561","cross_cats_sorted":["math.PR"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2002-11-08T14:47:00Z","title_canon_sha256":"39cf444796c3c99cfed6f3d61a07e319c5dd5a503638c5569ea2bd0823c6d21e"},"schema_version":"1.0","source":{"id":"cond-mat/0211166","kind":"arxiv","version":1}},"canonical_sha256":"6662543667726486ffeba3d0d0100314f3c5e421c4e732165df8667015f9faa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6662543667726486ffeba3d0d0100314f3c5e421c4e732165df8667015f9faa4","first_computed_at":"2026-05-18T01:06:58.631025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:58.631025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J0BEt8yYQsYI9OJxxa+5ZHdNphXMiq3ydZAYSwArY6hYbvTB1BlSEWN0Rjg10K9WcRbJj1WGl8HD1XoADlb5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:58.631812Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0211166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:763eb10245c4cc323216470b7fa11a1310e2f5cda712b3a9b3e85b1cb080fc3c","sha256:4d78ab99b187859097f39963325938c534297cfee88af81a565ddf3da0cc3b81"],"state_sha256":"ad2807c1fd97a1c3c27eaa1e3b4d4ba53754f300fba052a90c8f9bb84913084c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ycy0uGVfuC5yFnmpAQtVxzcg7WNZxJhY2j4QIXGS5m2ai/vge/3yF4M9DqB1xmucx0ff+62SBw5A8ScwCaYcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:29:51.886017Z","bundle_sha256":"9cb6d04c9a72b542413e7a5c85ab152ca23d59317432f1f0a2d8fcd70179a470"}}