{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OTL55HXFSOBFJPN4H6KHKBSMGV","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":"4833d1421b8f8c3cba927deec94b1859c79b5f1bda77d2e9f18c5f3c47d70453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-22T12:58:41Z","title_canon_sha256":"5de31417e136cfd57e2e651d2a8c3a381e06b9422d1b90838d05a6d3612bb558"},"schema_version":"1.0","source":{"id":"1302.5574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5574","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5574v2","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5574","created_at":"2026-05-18T03:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"OTL55HXFSOBF","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OTL55HXFSOBFJPN4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OTL55HXF","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:c4f2ee56895ba6ceae89130d6365f164d098b25d4631572a5a446ef645cdb945","target":"graph","created_at":"2026-05-18T03:13:00Z","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 present a Master Equation formulation based on a Markovian random walk model that exhibits sub-diffusion, classical diffusion and super-diffusion as a function of a single parameter. The non-classical diffusive behavior is generated by allowing for interactions between a population of walkers. At the macroscopic level, this gives rise to a nonlinear Fokker-Planck equation. The diffusive behavior is reflected not only in the mean-squared displacement ($<r^2(t)>\\sim t^{\\gamma}$ with $0 <\\gamma \\leq 1.5$) but also in the existence of self-similar scaling solutions of the Fokker-Planck equation","authors_text":"James F. Lutsko, Jean Pierre Boon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-22T12:58:41Z","title":"Molecular theory of anomalous diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5574","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:f39f0a2eebf61e8ff514f839e0e88786880dc385b2e996a2840d47e0ca4fb9ef","target":"record","created_at":"2026-05-18T03:13:00Z","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":"4833d1421b8f8c3cba927deec94b1859c79b5f1bda77d2e9f18c5f3c47d70453","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-02-22T12:58:41Z","title_canon_sha256":"5de31417e136cfd57e2e651d2a8c3a381e06b9422d1b90838d05a6d3612bb558"},"schema_version":"1.0","source":{"id":"1302.5574","kind":"arxiv","version":2}},"canonical_sha256":"74d7de9ee5938254bdbc3f9475064c356d7135b4835b897c311f4030eea472cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74d7de9ee5938254bdbc3f9475064c356d7135b4835b897c311f4030eea472cc","first_computed_at":"2026-05-18T03:13:00.003728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:00.003728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K26TBXL2UTFJEbIyN/s6okvb6XrkUzfBpq0CDxLR4terARqEFWMc0VykjCy+TkKUweXAEV3t9DvccOnKDawlAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:00.004485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f39f0a2eebf61e8ff514f839e0e88786880dc385b2e996a2840d47e0ca4fb9ef","sha256:c4f2ee56895ba6ceae89130d6365f164d098b25d4631572a5a446ef645cdb945"],"state_sha256":"ebf08932048358f85434cf042093de4cfdb01e28364516bd3a3ef236575ad7e4"}