{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7MB4OXP3QZJMJVLXNB37DL33AK","short_pith_number":"pith:7MB4OXP3","canonical_record":{"source":{"id":"1801.10424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-01-31T12:44:52Z","cross_cats_sorted":[],"title_canon_sha256":"a438c15874e994e5f42e784d5ec073637ccddf2f291aa77709c815930ff7a771","abstract_canon_sha256":"bb70bccd567231477c65baff17bdde4e289763257aa73ae6c66945d9d60f57b1"},"schema_version":"1.0"},"canonical_sha256":"fb03c75dfb8652c4d5776877f1af7b028c297cc557b0a02a51916cc512364bd2","source":{"kind":"arxiv","id":"1801.10424","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10424","created_at":"2026-05-18T00:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10424v2","created_at":"2026-05-18T00:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10424","created_at":"2026-05-18T00:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"7MB4OXP3QZJM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7MB4OXP3QZJMJVLX","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7MB4OXP3","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7MB4OXP3QZJMJVLXNB37DL33AK","target":"record","payload":{"canonical_record":{"source":{"id":"1801.10424","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-01-31T12:44:52Z","cross_cats_sorted":[],"title_canon_sha256":"a438c15874e994e5f42e784d5ec073637ccddf2f291aa77709c815930ff7a771","abstract_canon_sha256":"bb70bccd567231477c65baff17bdde4e289763257aa73ae6c66945d9d60f57b1"},"schema_version":"1.0"},"canonical_sha256":"fb03c75dfb8652c4d5776877f1af7b028c297cc557b0a02a51916cc512364bd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:22.110159Z","signature_b64":"FVDwUmRXJPJMaASRBsX7zSubs6rwwi8kyvtBfbm2NPL24ZtGrt4V8Nss9rtb9cZz5Gvj75SlQtDb4hwrgqLpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb03c75dfb8652c4d5776877f1af7b028c297cc557b0a02a51916cc512364bd2","last_reissued_at":"2026-05-18T00:10:22.109478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:22.109478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.10424","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":"2026-05-18T00:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKDoG4ZOkgGs18BpOekTtRi8JHPM3Sj/UavxH+9TJPn4WEWwGFOdGmzAuw2tYjuvdkxrBjyx8/L7LKciX9roCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:03:53.964747Z"},"content_sha256":"d3226a4f70f11594e43f5142cee3773ec4a0c5a2aa4e8cbe5b2e8ddb7b2f0b81","schema_version":"1.0","event_id":"sha256:d3226a4f70f11594e43f5142cee3773ec4a0c5a2aa4e8cbe5b2e8ddb7b2f0b81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7MB4OXP3QZJMJVLXNB37DL33AK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised Langevin Equation Formulation for Anomalous Diffusion in the Ising Model at the Critical Temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Debabrata Panja, Gerard T. Barkema, Robin C. Ball, Wei Zhong","submitted_at":"2018-01-31T12:44:52Z","abstract_excerpt":"We consider the two- (2D) and three-dimensional (3D) Ising model on a square lattice at the critical temperature $T_c$, under Monte-Carlo spin flip dynamics. The bulk magnetisation and the magnetisation of a tagged line in the 2D Ising model, and the bulk magnetisation and the magnetisation of a tagged plane in the 3D Ising model exhibit anomalous diffusion. Specifically, their mean-square displacement increases as power-laws in time, collectively denoted as $\\sim t^c$, where $c$ is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10424","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":"2026-05-18T00:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S32aTpKn+QsqcaGYfAVHIqgsNEBODFGBk4EC6tZD34BwUcYyVBSyAlf0ymoEaTOLbbKDdoCsvLYIoui++EqWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:03:53.965502Z"},"content_sha256":"b90120359005c3c901113463d49be9d90512cac9d7a653bff7b684e1d545404c","schema_version":"1.0","event_id":"sha256:b90120359005c3c901113463d49be9d90512cac9d7a653bff7b684e1d545404c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7MB4OXP3QZJMJVLXNB37DL33AK/bundle.json","state_url":"https://pith.science/pith/7MB4OXP3QZJMJVLXNB37DL33AK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7MB4OXP3QZJMJVLXNB37DL33AK/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":"2026-06-09T08:03:53Z","links":{"resolver":"https://pith.science/pith/7MB4OXP3QZJMJVLXNB37DL33AK","bundle":"https://pith.science/pith/7MB4OXP3QZJMJVLXNB37DL33AK/bundle.json","state":"https://pith.science/pith/7MB4OXP3QZJMJVLXNB37DL33AK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7MB4OXP3QZJMJVLXNB37DL33AK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7MB4OXP3QZJMJVLXNB37DL33AK","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":"bb70bccd567231477c65baff17bdde4e289763257aa73ae6c66945d9d60f57b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-01-31T12:44:52Z","title_canon_sha256":"a438c15874e994e5f42e784d5ec073637ccddf2f291aa77709c815930ff7a771"},"schema_version":"1.0","source":{"id":"1801.10424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10424","created_at":"2026-05-18T00:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10424v2","created_at":"2026-05-18T00:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10424","created_at":"2026-05-18T00:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"7MB4OXP3QZJM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7MB4OXP3QZJMJVLX","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7MB4OXP3","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:b90120359005c3c901113463d49be9d90512cac9d7a653bff7b684e1d545404c","target":"graph","created_at":"2026-05-18T00:10:22Z","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 consider the two- (2D) and three-dimensional (3D) Ising model on a square lattice at the critical temperature $T_c$, under Monte-Carlo spin flip dynamics. The bulk magnetisation and the magnetisation of a tagged line in the 2D Ising model, and the bulk magnetisation and the magnetisation of a tagged plane in the 3D Ising model exhibit anomalous diffusion. Specifically, their mean-square displacement increases as power-laws in time, collectively denoted as $\\sim t^c$, where $c$ is the anomalous exponent. We argue that the anomalous diffusion in all these quantities for the Ising model stems ","authors_text":"Debabrata Panja, Gerard T. Barkema, Robin C. Ball, Wei Zhong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-01-31T12:44:52Z","title":"Generalised Langevin Equation Formulation for Anomalous Diffusion in the Ising Model at the Critical Temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10424","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:d3226a4f70f11594e43f5142cee3773ec4a0c5a2aa4e8cbe5b2e8ddb7b2f0b81","target":"record","created_at":"2026-05-18T00:10:22Z","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":"bb70bccd567231477c65baff17bdde4e289763257aa73ae6c66945d9d60f57b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2018-01-31T12:44:52Z","title_canon_sha256":"a438c15874e994e5f42e784d5ec073637ccddf2f291aa77709c815930ff7a771"},"schema_version":"1.0","source":{"id":"1801.10424","kind":"arxiv","version":2}},"canonical_sha256":"fb03c75dfb8652c4d5776877f1af7b028c297cc557b0a02a51916cc512364bd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb03c75dfb8652c4d5776877f1af7b028c297cc557b0a02a51916cc512364bd2","first_computed_at":"2026-05-18T00:10:22.109478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:22.109478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FVDwUmRXJPJMaASRBsX7zSubs6rwwi8kyvtBfbm2NPL24ZtGrt4V8Nss9rtb9cZz5Gvj75SlQtDb4hwrgqLpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:22.110159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3226a4f70f11594e43f5142cee3773ec4a0c5a2aa4e8cbe5b2e8ddb7b2f0b81","sha256:b90120359005c3c901113463d49be9d90512cac9d7a653bff7b684e1d545404c"],"state_sha256":"876651bc3aff35adee212d12dd9204aeb54ffbe501b8989d0b96d2dbf12b50ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wp3fkzlF/H38Yoq2fjmTCCFVtgeWF0nvNI4BuD/s5LaY6RVrxRhPbiU1mEYq6Qi2AtEbJbTPdFUWfYGtoSyaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:03:53.969218Z","bundle_sha256":"f5f748feee83e6217c1fd3efbbac52d58d711ca698f84ce1a258b027d304d06c"}}