{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MTGACWLAY6PNJAWB6SSCI37ACU","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":"8f996e9cd8a628ebb82ea39a8938c8e896e0ee2044693b5c964324bddb3f199f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-13T19:03:25Z","title_canon_sha256":"937c72de6890ad2233018634d31af83f4179737de4777d4bb502152579e3dc61"},"schema_version":"1.0","source":{"id":"1507.03551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03551","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03551v1","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03551","created_at":"2026-05-18T01:36:58Z"},{"alias_kind":"pith_short_12","alias_value":"MTGACWLAY6PN","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTGACWLAY6PNJAWB","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTGACWLA","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:9fbaf4a2619e2bf1a87646defc6635c83187adf2558c1c7c0dce5ef4d42a8144","target":"graph","created_at":"2026-05-18T01:36:58Z","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":"Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|\\cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $\\mu$ such that, for any $\\epsilon>0$, $\\sum|\\cdot|^\\epsilon\\mu=\\infty$. In particular, we provide a sharp lower bound for the return probability in the case when $\\mu$ has a finite weak-logarithmic moment.","authors_text":"Laurent Saloff-Coste, Tianyi Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-13T19:03:25Z","title":"Random walks under slowly varying moment conditions on groups of polynomial volume growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03551","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":"sha256:1de13a7c79801deed7aac5bc817992e92cd188b660e28021e049d1ed9ebe1408","target":"record","created_at":"2026-05-18T01:36:58Z","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":"8f996e9cd8a628ebb82ea39a8938c8e896e0ee2044693b5c964324bddb3f199f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-13T19:03:25Z","title_canon_sha256":"937c72de6890ad2233018634d31af83f4179737de4777d4bb502152579e3dc61"},"schema_version":"1.0","source":{"id":"1507.03551","kind":"arxiv","version":1}},"canonical_sha256":"64cc015960c79ed482c1f4a4246fe01539dc47b7b09953a24f6e54cc8672b5e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64cc015960c79ed482c1f4a4246fe01539dc47b7b09953a24f6e54cc8672b5e1","first_computed_at":"2026-05-18T01:36:58.571616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:58.571616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6dNdQ2DNUmiiGe9fUQi55Rz+gy5d+vzHIoXkXH4SJbWDPRzwBrzmYJ9CxNZdt/nXYFiWl2LVxirIcm4ynseaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:58.572267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de13a7c79801deed7aac5bc817992e92cd188b660e28021e049d1ed9ebe1408","sha256:9fbaf4a2619e2bf1a87646defc6635c83187adf2558c1c7c0dce5ef4d42a8144"],"state_sha256":"059cec634eefc24be517a9aa89c9cf11b456baa8207115a1faff2593f936d0b4"}