{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IUCQWM6XX7QVLCANXVGA5C7QQF","short_pith_number":"pith:IUCQWM6X","canonical_record":{"source":{"id":"1303.5533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-03-22T07:21:30Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"709797fc742c4cd0372486cd9cbf047246dced0d9859f7e81ea2aba945a3cf93","abstract_canon_sha256":"9f43947b4ef34855f85d15abcd93c50a627a511ddd10a628e46d0754cc7d03a2"},"schema_version":"1.0"},"canonical_sha256":"45050b33d7bfe155880dbd4c0e8bf0815100d9759d7551091b0c19a328458b1d","source":{"kind":"arxiv","id":"1303.5533","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5533","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5533v1","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5533","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"IUCQWM6XX7QV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IUCQWM6XX7QVLCAN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IUCQWM6X","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IUCQWM6XX7QVLCANXVGA5C7QQF","target":"record","payload":{"canonical_record":{"source":{"id":"1303.5533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-03-22T07:21:30Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"709797fc742c4cd0372486cd9cbf047246dced0d9859f7e81ea2aba945a3cf93","abstract_canon_sha256":"9f43947b4ef34855f85d15abcd93c50a627a511ddd10a628e46d0754cc7d03a2"},"schema_version":"1.0"},"canonical_sha256":"45050b33d7bfe155880dbd4c0e8bf0815100d9759d7551091b0c19a328458b1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:50:59.620886Z","signature_b64":"uJ1Xjks5N0ZPtaHiscaOiHJRA0x0x0+iSzXfjjJUKhXxSInKVgkVtZKdQ0SqXX2yA1YRYMPOBQ5tFmO0tb3lAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45050b33d7bfe155880dbd4c0e8bf0815100d9759d7551091b0c19a328458b1d","last_reissued_at":"2026-05-18T01:50:59.620400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:50:59.620400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.5533","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":"2026-05-18T01:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RptfOpD+YTWH1Wvdw18Z6SXoH5LPfkjjqRbDyXIH2bdQX0KkTHJT9tjAyonPG+bHwHwJkzteyP8ikRFhLOSMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:20:54.007834Z"},"content_sha256":"7e599a9f966112b0c478bacb79809bc158bbf190805a2f26159394a484e013c3","schema_version":"1.0","event_id":"sha256:7e599a9f966112b0c478bacb79809bc158bbf190805a2f26159394a484e013c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IUCQWM6XX7QVLCANXVGA5C7QQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"cond-mat.stat-mech","authors_text":"Aleksei V. Chechkin, Andrey G. Cherstvy, Ralf Metzler","submitted_at":"2013-03-22T07:21:30Z","abstract_excerpt":"We demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \\simeq|x|^{\\alpha}$, this process yield anomalous diffusion of the form $\\ < x^2(t)\\ > \\simeq t^{2/(2-\\alpha)}$. Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time averaged mean squared displacement $\\{\\delta^2}$ remains \\emph{linear} and thus differs from the corresponding ensemble average $\\ <x^2(t)\\ >$. We analyze the non-ergodic behavior of this process in terms of the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5533","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":"2026-05-18T01:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YV5VkuFWE/kLvPnaKNcusTQhv0Zi/OtHqixXIS+Uc0FBEz6twS+4dVb/wuP3R/Vg2gUOFQLCpyJ2ue4j58TYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:20:54.008180Z"},"content_sha256":"0402e5b8594667c264cf7db8c0f5cb46d3449c523e471af97c0f2a8685270a5b","schema_version":"1.0","event_id":"sha256:0402e5b8594667c264cf7db8c0f5cb46d3449c523e471af97c0f2a8685270a5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUCQWM6XX7QVLCANXVGA5C7QQF/bundle.json","state_url":"https://pith.science/pith/IUCQWM6XX7QVLCANXVGA5C7QQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUCQWM6XX7QVLCANXVGA5C7QQF/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":"2026-06-01T20:20:54Z","links":{"resolver":"https://pith.science/pith/IUCQWM6XX7QVLCANXVGA5C7QQF","bundle":"https://pith.science/pith/IUCQWM6XX7QVLCANXVGA5C7QQF/bundle.json","state":"https://pith.science/pith/IUCQWM6XX7QVLCANXVGA5C7QQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUCQWM6XX7QVLCANXVGA5C7QQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IUCQWM6XX7QVLCANXVGA5C7QQF","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":"9f43947b4ef34855f85d15abcd93c50a627a511ddd10a628e46d0754cc7d03a2","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-03-22T07:21:30Z","title_canon_sha256":"709797fc742c4cd0372486cd9cbf047246dced0d9859f7e81ea2aba945a3cf93"},"schema_version":"1.0","source":{"id":"1303.5533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5533","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5533v1","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5533","created_at":"2026-05-18T01:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"IUCQWM6XX7QV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IUCQWM6XX7QVLCAN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IUCQWM6X","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:0402e5b8594667c264cf7db8c0f5cb46d3449c523e471af97c0f2a8685270a5b","target":"graph","created_at":"2026-05-18T01:50:59Z","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 demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \\simeq|x|^{\\alpha}$, this process yield anomalous diffusion of the form $\\ < x^2(t)\\ > \\simeq t^{2/(2-\\alpha)}$. Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time averaged mean squared displacement $\\{\\delta^2}$ remains \\emph{linear} and thus differs from the corresponding ensemble average $\\ <x^2(t)\\ >$. We analyze the non-ergodic behavior of this process in terms of the e","authors_text":"Aleksei V. Chechkin, Andrey G. Cherstvy, Ralf Metzler","cross_cats":["q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-03-22T07:21:30Z","title":"Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5533","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":"sha256:7e599a9f966112b0c478bacb79809bc158bbf190805a2f26159394a484e013c3","target":"record","created_at":"2026-05-18T01:50:59Z","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":"9f43947b4ef34855f85d15abcd93c50a627a511ddd10a628e46d0754cc7d03a2","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-03-22T07:21:30Z","title_canon_sha256":"709797fc742c4cd0372486cd9cbf047246dced0d9859f7e81ea2aba945a3cf93"},"schema_version":"1.0","source":{"id":"1303.5533","kind":"arxiv","version":1}},"canonical_sha256":"45050b33d7bfe155880dbd4c0e8bf0815100d9759d7551091b0c19a328458b1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45050b33d7bfe155880dbd4c0e8bf0815100d9759d7551091b0c19a328458b1d","first_computed_at":"2026-05-18T01:50:59.620400Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:59.620400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uJ1Xjks5N0ZPtaHiscaOiHJRA0x0x0+iSzXfjjJUKhXxSInKVgkVtZKdQ0SqXX2yA1YRYMPOBQ5tFmO0tb3lAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:59.620886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e599a9f966112b0c478bacb79809bc158bbf190805a2f26159394a484e013c3","sha256:0402e5b8594667c264cf7db8c0f5cb46d3449c523e471af97c0f2a8685270a5b"],"state_sha256":"300a78ce8c04742350af2b6d5cdcdc18568e589edce6bb8bd6f330e0dfcf8f28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DRk1iRsEequs7DHZfp5bzn2CNsIJndPBTPGurd+tZ/i9vHb/UqTAGQj/do3SJrbxE1awRSvu9QE1TbKE8ez+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:20:54.010064Z","bundle_sha256":"23caf7fd24542640d0f3f2ca53490dc62c0fd4f3f3d7cd638d0bff3cb7f171bf"}}