{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:57QCINWSI3QNZM2NJUNU3FFOUO","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":"72339d28bcd3efc96c6bc19cca0f2c38cc08e396e6cc46355388b867a69cd518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-03-27T13:09:10Z","title_canon_sha256":"51de14f623f595530d2591c25e96ee2f9aef0ca586530dd65f2061cc9104452a"},"schema_version":"1.0","source":{"id":"2403.18532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.18532","created_at":"2026-07-05T08:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"2403.18532v2","created_at":"2026-07-05T08:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.18532","created_at":"2026-07-05T08:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"57QCINWSI3QN","created_at":"2026-07-05T08:25:02Z"},{"alias_kind":"pith_short_16","alias_value":"57QCINWSI3QNZM2N","created_at":"2026-07-05T08:25:02Z"},{"alias_kind":"pith_short_8","alias_value":"57QCINWS","created_at":"2026-07-05T08:25:02Z"}],"graph_snapshots":[{"event_id":"sha256:80c58de9ed26442019ac1bebf3735eb32ed112d6e6f37c974b3ad19aa3f78397","target":"graph","created_at":"2026-07-05T08:25:02Z","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/2403.18532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study limit laws for simple random walks on supercritical long-range percolation clusters on the integer lattice. For the long range percolation model, the probability that two vertices are connected behaves asymptotically as a negative power of distance between them. We prove that the scaling limit of simple random walk on the infinite component converges to an isotropic alpha-stable Levy process. This complements the work of Crawford and Sly, who proved the corresponding result for alpha between 0 and 1. The convergence holds in both the quenched and annealed senses.","authors_text":"Noam Berger, Yuki Tokushige","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-03-27T13:09:10Z","title":"Scaling limits for random walks on long range percolation clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.18532","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":"sha256:294d804bea06ff656f9ac981dc39f6f373f25ce36ad495c8b7121611c7258d2b","target":"record","created_at":"2026-07-05T08:25:02Z","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":"72339d28bcd3efc96c6bc19cca0f2c38cc08e396e6cc46355388b867a69cd518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-03-27T13:09:10Z","title_canon_sha256":"51de14f623f595530d2591c25e96ee2f9aef0ca586530dd65f2061cc9104452a"},"schema_version":"1.0","source":{"id":"2403.18532","kind":"arxiv","version":2}},"canonical_sha256":"efe02436d246e0dcb34d4d1b4d94aea3ba1b87d818fc22fa8d55f1b068c3301a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efe02436d246e0dcb34d4d1b4d94aea3ba1b87d818fc22fa8d55f1b068c3301a","first_computed_at":"2026-07-05T08:25:02.188683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:25:02.188683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p0QDaxV8b0iaaAUuXl4rUS/zK8tUogGDWgQEhy0AT0QsncplZLG/f/3artOfwDwD0dRgqDzhH11oq/GJWRb6Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:25:02.189183Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.18532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:294d804bea06ff656f9ac981dc39f6f373f25ce36ad495c8b7121611c7258d2b","sha256:80c58de9ed26442019ac1bebf3735eb32ed112d6e6f37c974b3ad19aa3f78397"],"state_sha256":"fdc61e5c25b04413599d0984fc41533ef26888ae9356a14787b81f3206381be5"}