{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NO7XBGYF6AHFGBW74HAHKDX3UB","short_pith_number":"pith:NO7XBGYF","canonical_record":{"source":{"id":"1304.0552","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-02T07:55:10Z","cross_cats_sorted":["cond-mat.dis-nn","cs.DS"],"title_canon_sha256":"59acd52407be9c9363320d023b8ecd6095ffb08736172048ccdb24e51249d158","abstract_canon_sha256":"6d897d313cc22f3fec5a3b88b661e46335127c85361612773e9a5519b98d63e8"},"schema_version":"1.0"},"canonical_sha256":"6bbf709b05f00e5306dfe1c0750efba0638d36e45507e5931b469e9a36bac973","source":{"kind":"arxiv","id":"1304.0552","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0552","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0552v3","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0552","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"pith_short_12","alias_value":"NO7XBGYF6AHF","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NO7XBGYF6AHFGBW7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NO7XBGYF","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NO7XBGYF6AHFGBW74HAHKDX3UB","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0552","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-02T07:55:10Z","cross_cats_sorted":["cond-mat.dis-nn","cs.DS"],"title_canon_sha256":"59acd52407be9c9363320d023b8ecd6095ffb08736172048ccdb24e51249d158","abstract_canon_sha256":"6d897d313cc22f3fec5a3b88b661e46335127c85361612773e9a5519b98d63e8"},"schema_version":"1.0"},"canonical_sha256":"6bbf709b05f00e5306dfe1c0750efba0638d36e45507e5931b469e9a36bac973","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:27.407476Z","signature_b64":"CjmzDufYl8Lo/SwWVlWV2NpqEWmnQEiwZ8vB2me7Vo/WmbRyLTgZp/97Bogo+x2LyPa5sJavhDgrF2U8SWgjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bbf709b05f00e5306dfe1c0750efba0638d36e45507e5931b469e9a36bac973","last_reissued_at":"2026-05-18T02:48:27.406951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:27.406951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0552","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cYEUM1MlLnut6h7X02/Du5HrSJNCUubKJtJB2ysEXi+AOC2QO5ZRaMZmkmFVxaRFMWgAPaDQsNeqt/V+XzpTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:14:05.430283Z"},"content_sha256":"ae1ce8184ae9a01b539bebac46c8e87ef2525f45e776146dca991be070cb3686","schema_version":"1.0","event_id":"sha256:ae1ce8184ae9a01b539bebac46c8e87ef2525f45e776146dca991be070cb3686"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NO7XBGYF6AHFGBW74HAHKDX3UB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Performance of the Metropolis algorithm on a disordered tree: The Einstein relation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.DS"],"primary_cat":"math.PR","authors_text":"Ofer Zeitouni, Pascal Maillard","submitted_at":"2013-04-02T07:55:10Z","abstract_excerpt":"Consider a $d$-ary rooted tree ($d\\geq3$) where each edge $e$ is assigned an i.i.d. (bounded) random variable $X(e)$ of negative mean. Assign to each vertex $v$ the sum $S(v)$ of $X(e)$ over all edges connecting $v$ to the root, and assume that the maximum $S_n^*$ of $S(v)$ over all vertices $v$ at distance $n$ from the root tends to infinity (necessarily, linearly) as $n$ tends to infinity. We analyze the Metropolis algorithm on the tree and show that under these assumptions there always exists a temperature $1/\\beta$ of the algorithm so that it achieves a linear (positive) growth rate in lin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0552","kind":"arxiv","version":3},"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":"2026-05-18T02:48:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VI0dv/yVIfgXvakYx+1BexUJtejD3LcV3JUo/hl2UM+GSUsQxWZJbfZAuZc1W85g0UuO3s2rnqP+ZYkdPLJmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T20:14:05.430903Z"},"content_sha256":"a5dec138a93cf1e6c8f69ee204095b356be095d9fe89f7f44563ea41c5da330c","schema_version":"1.0","event_id":"sha256:a5dec138a93cf1e6c8f69ee204095b356be095d9fe89f7f44563ea41c5da330c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NO7XBGYF6AHFGBW74HAHKDX3UB/bundle.json","state_url":"https://pith.science/pith/NO7XBGYF6AHFGBW74HAHKDX3UB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NO7XBGYF6AHFGBW74HAHKDX3UB/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":"2026-06-27T20:14:05Z","links":{"resolver":"https://pith.science/pith/NO7XBGYF6AHFGBW74HAHKDX3UB","bundle":"https://pith.science/pith/NO7XBGYF6AHFGBW74HAHKDX3UB/bundle.json","state":"https://pith.science/pith/NO7XBGYF6AHFGBW74HAHKDX3UB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NO7XBGYF6AHFGBW74HAHKDX3UB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NO7XBGYF6AHFGBW74HAHKDX3UB","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":"6d897d313cc22f3fec5a3b88b661e46335127c85361612773e9a5519b98d63e8","cross_cats_sorted":["cond-mat.dis-nn","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-02T07:55:10Z","title_canon_sha256":"59acd52407be9c9363320d023b8ecd6095ffb08736172048ccdb24e51249d158"},"schema_version":"1.0","source":{"id":"1304.0552","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0552","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0552v3","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0552","created_at":"2026-05-18T02:48:27Z"},{"alias_kind":"pith_short_12","alias_value":"NO7XBGYF6AHF","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NO7XBGYF6AHFGBW7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NO7XBGYF","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:a5dec138a93cf1e6c8f69ee204095b356be095d9fe89f7f44563ea41c5da330c","target":"graph","created_at":"2026-05-18T02:48:27Z","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 $d$-ary rooted tree ($d\\geq3$) where each edge $e$ is assigned an i.i.d. (bounded) random variable $X(e)$ of negative mean. Assign to each vertex $v$ the sum $S(v)$ of $X(e)$ over all edges connecting $v$ to the root, and assume that the maximum $S_n^*$ of $S(v)$ over all vertices $v$ at distance $n$ from the root tends to infinity (necessarily, linearly) as $n$ tends to infinity. We analyze the Metropolis algorithm on the tree and show that under these assumptions there always exists a temperature $1/\\beta$ of the algorithm so that it achieves a linear (positive) growth rate in lin","authors_text":"Ofer Zeitouni, Pascal Maillard","cross_cats":["cond-mat.dis-nn","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-02T07:55:10Z","title":"Performance of the Metropolis algorithm on a disordered tree: The Einstein relation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0552","kind":"arxiv","version":3},"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:ae1ce8184ae9a01b539bebac46c8e87ef2525f45e776146dca991be070cb3686","target":"record","created_at":"2026-05-18T02:48:27Z","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":"6d897d313cc22f3fec5a3b88b661e46335127c85361612773e9a5519b98d63e8","cross_cats_sorted":["cond-mat.dis-nn","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-02T07:55:10Z","title_canon_sha256":"59acd52407be9c9363320d023b8ecd6095ffb08736172048ccdb24e51249d158"},"schema_version":"1.0","source":{"id":"1304.0552","kind":"arxiv","version":3}},"canonical_sha256":"6bbf709b05f00e5306dfe1c0750efba0638d36e45507e5931b469e9a36bac973","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bbf709b05f00e5306dfe1c0750efba0638d36e45507e5931b469e9a36bac973","first_computed_at":"2026-05-18T02:48:27.406951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:27.406951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CjmzDufYl8Lo/SwWVlWV2NpqEWmnQEiwZ8vB2me7Vo/WmbRyLTgZp/97Bogo+x2LyPa5sJavhDgrF2U8SWgjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:27.407476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0552","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1ce8184ae9a01b539bebac46c8e87ef2525f45e776146dca991be070cb3686","sha256:a5dec138a93cf1e6c8f69ee204095b356be095d9fe89f7f44563ea41c5da330c"],"state_sha256":"cd9b9f4864aebadfcd25141122a33801b0cc3d40a77e4a0826963d866ac74cb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XfZGbR+ktnQygDXgKQ7adBuxhAksLnnLNF4XvWC5ge5tPqRfu6A2rTzku5gTDto+kPIh18kYB/O7MPF6BvLjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T20:14:05.433657Z","bundle_sha256":"f161f58eeecb42aa5a1c78e0d45c5124ab1e890de1c06dde11747e019ed10606"}}