{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5VYH46AVIYPRXDPBAVA7KWXHXB","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":"f0f65a66847dbbbf4f83ca5c50758168de998a9dfb0dc5d8f8e71f4169d6c178","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-08-02T18:00:56Z","title_canon_sha256":"a39763dd683c6f147db7eb81fecf11ffdffc3bb05cbcdf670672b1051f7ff36a"},"schema_version":"1.0","source":{"id":"1908.00990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00990","created_at":"2026-07-05T00:45:51Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00990v2","created_at":"2026-07-05T00:45:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00990","created_at":"2026-07-05T00:45:51Z"},{"alias_kind":"pith_short_12","alias_value":"5VYH46AVIYPR","created_at":"2026-07-05T00:45:51Z"},{"alias_kind":"pith_short_16","alias_value":"5VYH46AVIYPRXDPB","created_at":"2026-07-05T00:45:51Z"},{"alias_kind":"pith_short_8","alias_value":"5VYH46AV","created_at":"2026-07-05T00:45:51Z"}],"graph_snapshots":[{"event_id":"sha256:07b0aad581b1423d04eee2583da04293ddeb3d0d1f62afbde21b86275561f001","target":"graph","created_at":"2026-07-05T00:45:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.00990/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a connection between exclusion statistics with arbitrary integer exclusion parameter $g$ and a class of random walks on planar lattices. This connection maps the generating function for the number of closed walks of given length enclosing a given algebraic area on the lattice to the grand partition function of particles obeying exclusion statistics $g$ in a particular single-particle spectrum, determined by the properties of the random walk. Square lattice random walks, described in terms of the Hofstadter Hamiltonian, correspond to $g=2$. In the $g=3$ case we explicitly construct","authors_text":"Alexios P. Polychronakos, Stephane Ouvry","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-08-02T18:00:56Z","title":"Exclusion statistics and lattice random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00990","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":"sha256:1603038958156f9ffbf598558b7ee92b1b67b3ea9927a3459a3c4dc49c1a7087","target":"record","created_at":"2026-07-05T00:45:51Z","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":"f0f65a66847dbbbf4f83ca5c50758168de998a9dfb0dc5d8f8e71f4169d6c178","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2019-08-02T18:00:56Z","title_canon_sha256":"a39763dd683c6f147db7eb81fecf11ffdffc3bb05cbcdf670672b1051f7ff36a"},"schema_version":"1.0","source":{"id":"1908.00990","kind":"arxiv","version":2}},"canonical_sha256":"ed707e7815461f1b8de10541f55ae7b86d0e2cbe9572abc7e4fffee0a724c730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed707e7815461f1b8de10541f55ae7b86d0e2cbe9572abc7e4fffee0a724c730","first_computed_at":"2026-07-05T00:45:51.970218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:45:51.970218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0MxIuWYTDRCb1jLMrk5BJ1MJNwJXp2izCEYF8HccBkjPeLh5Vi3vlJbQV7rSks3mSQ6prG1lCQxbPcI9SwgCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:45:51.970691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1603038958156f9ffbf598558b7ee92b1b67b3ea9927a3459a3c4dc49c1a7087","sha256:07b0aad581b1423d04eee2583da04293ddeb3d0d1f62afbde21b86275561f001"],"state_sha256":"bcda4fd23dad20640883291134c1d1ec4cf5d229a8c9b95d434750e21ae9214b"}