{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JTMHVT2Z4FLGBXF676APOKAQVI","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":"5a8f39d79fe5c07ed37352f75f288cf3b748167798c267d56204466199a87b11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-27T16:10:18Z","title_canon_sha256":"85388f0813c30b2d2c402b357cbc57d320a40d809b3865ec4eadf7e147e7a879"},"schema_version":"1.0","source":{"id":"1004.4845","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.4845","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.4845v1","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4845","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"JTMHVT2Z4FLG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JTMHVT2Z4FLGBXF6","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JTMHVT2Z","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:a11fb7c5f0b80d91dd5b1768805dff42e02586ef399f499f1da68e5e90ea831f","target":"graph","created_at":"2026-05-18T02:24:15Z","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 Darboux-Wiener type lemma and apply it to obtain an exact asymptotic for the variance of the self-intersection of one and two-dimensional random walks. As a corollary, we obtain a central limit theorem for random walk in random scenery conjectured by Kesten and Spitzer in 1979.","authors_text":"George Deligiannidis, Sergey Utev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-27T16:10:18Z","title":"An asymptotic variance of the self-intersections of random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4845","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:a892d7a2de1da6a92fd7b7bc49d5145d493840ad2048b2fa00be6096636d6818","target":"record","created_at":"2026-05-18T02:24:15Z","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":"5a8f39d79fe5c07ed37352f75f288cf3b748167798c267d56204466199a87b11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-27T16:10:18Z","title_canon_sha256":"85388f0813c30b2d2c402b357cbc57d320a40d809b3865ec4eadf7e147e7a879"},"schema_version":"1.0","source":{"id":"1004.4845","kind":"arxiv","version":1}},"canonical_sha256":"4cd87acf59e15660dcbeff80f72810aa3ed97a8d1af950f51e7b7bd55ce421ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cd87acf59e15660dcbeff80f72810aa3ed97a8d1af950f51e7b7bd55ce421ab","first_computed_at":"2026-05-18T02:24:15.794251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:15.794251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h1yCHnFDUgVOfJQsniiGeKckg7WOCLehwm6YIE8mp4qbTMImJSe7+ITtK4T3bCirv39pRyaTgxYKyg+D5VAAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:15.794930Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.4845","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a892d7a2de1da6a92fd7b7bc49d5145d493840ad2048b2fa00be6096636d6818","sha256:a11fb7c5f0b80d91dd5b1768805dff42e02586ef399f499f1da68e5e90ea831f"],"state_sha256":"8fb61346afa59d5a0688465456a019b30dbb51bc121e0bfdc3b54e6555be6d6b"}