{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DM4OAQKDOHUYRUFOL26RI6DG6F","short_pith_number":"pith:DM4OAQKD","canonical_record":{"source":{"id":"1812.11962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-31T18:55:54Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"ffb7c3368284cb4a5e5e2cfe71a24f7beffbda50d161b43bf142e5fa331bb12a","abstract_canon_sha256":"767dadc88d5bc5ddd6ebc9dd184e4884f60f797136f8cf5d80777468ca06aa9c"},"schema_version":"1.0"},"canonical_sha256":"1b38e0414371e988d0ae5ebd147866f17dcf0bc1fd5dcc94ceb07a7b09be61f0","source":{"kind":"arxiv","id":"1812.11962","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11962","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11962v2","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11962","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"DM4OAQKDOHUY","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DM4OAQKDOHUYRUFO","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DM4OAQKD","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DM4OAQKDOHUYRUFOL26RI6DG6F","target":"record","payload":{"canonical_record":{"source":{"id":"1812.11962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-31T18:55:54Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"ffb7c3368284cb4a5e5e2cfe71a24f7beffbda50d161b43bf142e5fa331bb12a","abstract_canon_sha256":"767dadc88d5bc5ddd6ebc9dd184e4884f60f797136f8cf5d80777468ca06aa9c"},"schema_version":"1.0"},"canonical_sha256":"1b38e0414371e988d0ae5ebd147866f17dcf0bc1fd5dcc94ceb07a7b09be61f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:38.905071Z","signature_b64":"TOqHPuVeyXYPrKjo1k7nGoSSlEMmWa0pA2ttKgWwtKr9dqgXj9vma6V90Gtbm1rtmdnVsEDKJfr7ZJrU/XuxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b38e0414371e988d0ae5ebd147866f17dcf0bc1fd5dcc94ceb07a7b09be61f0","last_reissued_at":"2026-05-17T23:54:38.904476Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:38.904476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.11962","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oA4jbZLnirKkKk3NFhB8bWgplw7i2hEdYFQZ7SErs1/FKj6h/Ajgf8/tlmMld90HC847tKbf9oE9ihwi/+emAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:58:46.256033Z"},"content_sha256":"7ccc7f0ca47defba67f76709d325fe1b2536b46bee890e81c67d729115c4c9b6","schema_version":"1.0","event_id":"sha256:7ccc7f0ca47defba67f76709d325fe1b2536b46bee890e81c67d729115c4c9b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DM4OAQKDOHUYRUFOL26RI6DG6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solution of the Metropolis dynamics on a complete graph with application to the Markov chain Mpemba effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Israel Klich, Marija Vucelja","submitted_at":"2018-12-31T18:55:54Z","abstract_excerpt":"We find analytically the complete set of eigenvalues and eigenvectors associated with Metropolis dynamics on a complete graph. As an application, we use this information to study a counter-intuitive relaxation phenomenon, called the Mpemba effect. This effect describes situations when upon performing a thermal quench, a system prepared in equilibrium at high temperatures relaxes faster to the bath temperature than a system prepared at a temperature closer to that of the bath. We show that Metropolis dynamics on a complete graph does not support weak nor strong Mpemba effect, however, when the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11962","kind":"arxiv","version":2},"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":"2026-05-17T23:54:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qgHRpI2QXcW6VBRBqary7p9YToDpicUCVu9e0bcR7G/MH459mRFFYjfomAexoIN5rVDlFrldofTrWrUzRSEqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:58:46.256759Z"},"content_sha256":"2d8ddaf3272d1802b41fd299b0d4bc13db068afdfd023cf9ee16f59a6a99889c","schema_version":"1.0","event_id":"sha256:2d8ddaf3272d1802b41fd299b0d4bc13db068afdfd023cf9ee16f59a6a99889c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DM4OAQKDOHUYRUFOL26RI6DG6F/bundle.json","state_url":"https://pith.science/pith/DM4OAQKDOHUYRUFOL26RI6DG6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DM4OAQKDOHUYRUFOL26RI6DG6F/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":"2026-06-08T17:58:46Z","links":{"resolver":"https://pith.science/pith/DM4OAQKDOHUYRUFOL26RI6DG6F","bundle":"https://pith.science/pith/DM4OAQKDOHUYRUFOL26RI6DG6F/bundle.json","state":"https://pith.science/pith/DM4OAQKDOHUYRUFOL26RI6DG6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DM4OAQKDOHUYRUFOL26RI6DG6F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DM4OAQKDOHUYRUFOL26RI6DG6F","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":"767dadc88d5bc5ddd6ebc9dd184e4884f60f797136f8cf5d80777468ca06aa9c","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-31T18:55:54Z","title_canon_sha256":"ffb7c3368284cb4a5e5e2cfe71a24f7beffbda50d161b43bf142e5fa331bb12a"},"schema_version":"1.0","source":{"id":"1812.11962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11962","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11962v2","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11962","created_at":"2026-05-17T23:54:38Z"},{"alias_kind":"pith_short_12","alias_value":"DM4OAQKDOHUY","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DM4OAQKDOHUYRUFO","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DM4OAQKD","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:2d8ddaf3272d1802b41fd299b0d4bc13db068afdfd023cf9ee16f59a6a99889c","target":"graph","created_at":"2026-05-17T23:54:38Z","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 find analytically the complete set of eigenvalues and eigenvectors associated with Metropolis dynamics on a complete graph. As an application, we use this information to study a counter-intuitive relaxation phenomenon, called the Mpemba effect. This effect describes situations when upon performing a thermal quench, a system prepared in equilibrium at high temperatures relaxes faster to the bath temperature than a system prepared at a temperature closer to that of the bath. We show that Metropolis dynamics on a complete graph does not support weak nor strong Mpemba effect, however, when the ","authors_text":"Israel Klich, Marija Vucelja","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-31T18:55:54Z","title":"Solution of the Metropolis dynamics on a complete graph with application to the Markov chain Mpemba effect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11962","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":"sha256:7ccc7f0ca47defba67f76709d325fe1b2536b46bee890e81c67d729115c4c9b6","target":"record","created_at":"2026-05-17T23:54:38Z","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":"767dadc88d5bc5ddd6ebc9dd184e4884f60f797136f8cf5d80777468ca06aa9c","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-31T18:55:54Z","title_canon_sha256":"ffb7c3368284cb4a5e5e2cfe71a24f7beffbda50d161b43bf142e5fa331bb12a"},"schema_version":"1.0","source":{"id":"1812.11962","kind":"arxiv","version":2}},"canonical_sha256":"1b38e0414371e988d0ae5ebd147866f17dcf0bc1fd5dcc94ceb07a7b09be61f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b38e0414371e988d0ae5ebd147866f17dcf0bc1fd5dcc94ceb07a7b09be61f0","first_computed_at":"2026-05-17T23:54:38.904476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:38.904476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TOqHPuVeyXYPrKjo1k7nGoSSlEMmWa0pA2ttKgWwtKr9dqgXj9vma6V90Gtbm1rtmdnVsEDKJfr7ZJrU/XuxBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:38.905071Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ccc7f0ca47defba67f76709d325fe1b2536b46bee890e81c67d729115c4c9b6","sha256:2d8ddaf3272d1802b41fd299b0d4bc13db068afdfd023cf9ee16f59a6a99889c"],"state_sha256":"f394a4c2f4eb704f1a64431e4e96f847113e093e2af764f5762875685c0b611c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lbBLk7Fw06Phvt60Jv8kV5YPM8WcsA9V4zKztj6wslhIufhgcC6UYCP+wNhxFU//6S2buLwvU19rX6iI8avBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:58:46.260797Z","bundle_sha256":"5acaeef1178350b8bb648253a2e11c40f86c9febe74dfcb4666942c37be01485"}}