{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2YDZD2SLQEDFQG7UE24BECTABN","short_pith_number":"pith:2YDZD2SL","canonical_record":{"source":{"id":"1606.01577","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-05T22:48:14Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"8c987d1d9f4c4c8fac79f588cd7f917b02a880add6f31df8e6d302c898808d45","abstract_canon_sha256":"c69b38188fc311ec49f5ebe45e6140e43dba467fc947ed70e00fde06c45f98d3"},"schema_version":"1.0"},"canonical_sha256":"d60791ea4b8106581bf426b8120a600b5973fab994116dbc437230708a094a86","source":{"kind":"arxiv","id":"1606.01577","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01577","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01577v4","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01577","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"2YDZD2SLQEDF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YDZD2SLQEDFQG7U","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YDZD2SL","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2YDZD2SLQEDFQG7UE24BECTABN","target":"record","payload":{"canonical_record":{"source":{"id":"1606.01577","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-05T22:48:14Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"8c987d1d9f4c4c8fac79f588cd7f917b02a880add6f31df8e6d302c898808d45","abstract_canon_sha256":"c69b38188fc311ec49f5ebe45e6140e43dba467fc947ed70e00fde06c45f98d3"},"schema_version":"1.0"},"canonical_sha256":"d60791ea4b8106581bf426b8120a600b5973fab994116dbc437230708a094a86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:59.954999Z","signature_b64":"zQs+fgKSsmbjlUqLGcbfDSl5cBiWTKd4QuNsPYIvMzED4JRs8wxhOv3xmsbqUo2XNTJ8w0lTV7nTKzFYC2XVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d60791ea4b8106581bf426b8120a600b5973fab994116dbc437230708a094a86","last_reissued_at":"2026-05-18T00:33:59.954341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:59.954341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.01577","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LpijiYEKue0DBLLvXqBtHaTY0SNk7YeOxZ8/TmlDKVKmozDstRaCiy0i8yfnhr8cgJsUuaGfX7afmIQkv8C+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:54:31.921622Z"},"content_sha256":"2f8d8e0c21323476acbcecb0339e5a13d0d75a97fba7d60295870acc533189eb","schema_version":"1.0","event_id":"sha256:2f8d8e0c21323476acbcecb0339e5a13d0d75a97fba7d60295870acc533189eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2YDZD2SLQEDFQG7UE24BECTABN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The moving particle lemma for the exclusion process on a weighted graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Joe P. Chen","submitted_at":"2016-06-05T22:48:14Z","abstract_excerpt":"We prove a version of the moving particle lemma for the exclusion process on any finite weighted graph, based on the octopus inequality of Caputo, Liggett, and Richthammer. In light of their proof of Aldous' spectral gap conjecture, we conjecture that our moving particle lemma is optimal in general. Our result can be applied to graphs which lack translational invariance, including, but not limited to, fractal graphs. An application of our result is the proof of local ergodicity for the exclusion process on a class of weighted graphs, the details of which are reported in a follow-up paper [arXi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01577","kind":"arxiv","version":4},"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":"2026-05-18T00:33:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hVUs6qkWUuOxg5l66jvGeAtTdeN4+qp4b2onqjCjX/qz35UyegUxB1c/kV1jstGvmSom7cOkWVyRpVayLHR5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:54:31.921975Z"},"content_sha256":"0838ef616a980c5272c329702f0a244ff6c7eef64299e3b9cc8caa501e82d667","schema_version":"1.0","event_id":"sha256:0838ef616a980c5272c329702f0a244ff6c7eef64299e3b9cc8caa501e82d667"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YDZD2SLQEDFQG7UE24BECTABN/bundle.json","state_url":"https://pith.science/pith/2YDZD2SLQEDFQG7UE24BECTABN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YDZD2SLQEDFQG7UE24BECTABN/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":"2026-06-02T07:54:31Z","links":{"resolver":"https://pith.science/pith/2YDZD2SLQEDFQG7UE24BECTABN","bundle":"https://pith.science/pith/2YDZD2SLQEDFQG7UE24BECTABN/bundle.json","state":"https://pith.science/pith/2YDZD2SLQEDFQG7UE24BECTABN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YDZD2SLQEDFQG7UE24BECTABN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2YDZD2SLQEDFQG7UE24BECTABN","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":"c69b38188fc311ec49f5ebe45e6140e43dba467fc947ed70e00fde06c45f98d3","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-05T22:48:14Z","title_canon_sha256":"8c987d1d9f4c4c8fac79f588cd7f917b02a880add6f31df8e6d302c898808d45"},"schema_version":"1.0","source":{"id":"1606.01577","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01577","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01577v4","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01577","created_at":"2026-05-18T00:33:59Z"},{"alias_kind":"pith_short_12","alias_value":"2YDZD2SLQEDF","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YDZD2SLQEDFQG7U","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YDZD2SL","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:0838ef616a980c5272c329702f0a244ff6c7eef64299e3b9cc8caa501e82d667","target":"graph","created_at":"2026-05-18T00:33:59Z","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 prove a version of the moving particle lemma for the exclusion process on any finite weighted graph, based on the octopus inequality of Caputo, Liggett, and Richthammer. In light of their proof of Aldous' spectral gap conjecture, we conjecture that our moving particle lemma is optimal in general. Our result can be applied to graphs which lack translational invariance, including, but not limited to, fractal graphs. An application of our result is the proof of local ergodicity for the exclusion process on a class of weighted graphs, the details of which are reported in a follow-up paper [arXi","authors_text":"Joe P. Chen","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-05T22:48:14Z","title":"The moving particle lemma for the exclusion process on a weighted graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01577","kind":"arxiv","version":4},"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":"sha256:2f8d8e0c21323476acbcecb0339e5a13d0d75a97fba7d60295870acc533189eb","target":"record","created_at":"2026-05-18T00:33:59Z","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":"c69b38188fc311ec49f5ebe45e6140e43dba467fc947ed70e00fde06c45f98d3","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-05T22:48:14Z","title_canon_sha256":"8c987d1d9f4c4c8fac79f588cd7f917b02a880add6f31df8e6d302c898808d45"},"schema_version":"1.0","source":{"id":"1606.01577","kind":"arxiv","version":4}},"canonical_sha256":"d60791ea4b8106581bf426b8120a600b5973fab994116dbc437230708a094a86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d60791ea4b8106581bf426b8120a600b5973fab994116dbc437230708a094a86","first_computed_at":"2026-05-18T00:33:59.954341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:59.954341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zQs+fgKSsmbjlUqLGcbfDSl5cBiWTKd4QuNsPYIvMzED4JRs8wxhOv3xmsbqUo2XNTJ8w0lTV7nTKzFYC2XVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:59.954999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01577","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f8d8e0c21323476acbcecb0339e5a13d0d75a97fba7d60295870acc533189eb","sha256:0838ef616a980c5272c329702f0a244ff6c7eef64299e3b9cc8caa501e82d667"],"state_sha256":"33f2ec741dc6d06d2d8629897bde8dcbfc9f8c575f798cc7782315bd8d06bf4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CIQ319Fc3XslV3oekqr7uZF4tHg2L+5411QcNoS68EQPQ71MmJVvWixLDH6SQjlImc/FtUR4+1YN+ujjBIgNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:54:31.923990Z","bundle_sha256":"79ff7364eacfffb3e8786c2351ed9c94e64234a98284563e842b08483791d4fe"}}