{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AG6KRGMLEB4RCVVFJP6H4XZIFZ","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":"649f9a90b4be5f2d8564651a823261fc37c924428255dd0e63c46dfe0ddb5b89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-29T08:17:01Z","title_canon_sha256":"a6979a0b06d07b274b89b78c70a650ad1773cd3ea7fc56251b28fb61ffe2144e"},"schema_version":"1.0","source":{"id":"1505.07956","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07956","created_at":"2026-05-18T01:58:26Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07956v2","created_at":"2026-05-18T01:58:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07956","created_at":"2026-05-18T01:58:26Z"},{"alias_kind":"pith_short_12","alias_value":"AG6KRGMLEB4R","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AG6KRGMLEB4RCVVF","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AG6KRGML","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:cce70370805647a9b0c3224ee4021fcba11b7cb310c8eb933fe358034da78a89","target":"graph","created_at":"2026-05-18T01:58:26Z","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":"For a random walk $S_n, n\\geq 0$ in $\\mathbb{Z}^d$, let $l(n,x)$ be its local time at the site $x\\in \\mathbb{Z}^d$. Define the $\\alpha$-fold self intersection local time $L_n(\\alpha) := \\sum_{x} l(n,x)^{\\alpha}$, and let $L_n(\\alpha|\\epsilon, d)$ the corresponding quantity for $d$-dimensional simple random walk. Without imposing any moment conditions, we show that the variances of the local times $\\mathop{var}(L_n(\\alpha))$ of any genuinely $d$-dimensional random walk are bounded above by the corresponding characteristics of the simple symmetric random walk in $\\mathbb{Z}^d$, i.e. $\\mathop{var","authors_text":"George Deligiannidis, Sergey Utev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-29T08:17:01Z","title":"Optimal bounds for self-intersection local times"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07956","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":"sha256:8ec6f033727fe71f97f7c9d11056481cc46c2edb79a6bca81b48650c42427e0f","target":"record","created_at":"2026-05-18T01:58:26Z","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":"649f9a90b4be5f2d8564651a823261fc37c924428255dd0e63c46dfe0ddb5b89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-29T08:17:01Z","title_canon_sha256":"a6979a0b06d07b274b89b78c70a650ad1773cd3ea7fc56251b28fb61ffe2144e"},"schema_version":"1.0","source":{"id":"1505.07956","kind":"arxiv","version":2}},"canonical_sha256":"01bca8998b20791156a54bfc7e5f282e6fb58fe4232d5e2a97e003905d511030","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01bca8998b20791156a54bfc7e5f282e6fb58fe4232d5e2a97e003905d511030","first_computed_at":"2026-05-18T01:58:26.592680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:26.592680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IBoWlraad822b1P4+YDZlYQ8uqomaBITDrs115ZlQBIJgyitgR14G+BW71NuFEtvCPpzQuV+d37vI+ekRL4ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:26.593141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07956","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ec6f033727fe71f97f7c9d11056481cc46c2edb79a6bca81b48650c42427e0f","sha256:cce70370805647a9b0c3224ee4021fcba11b7cb310c8eb933fe358034da78a89"],"state_sha256":"eba2fd0f02d59a117a0554286044c8dff87322d258a059d5b7a11a0b14efd58b"}