{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GBPSLMI4IRE6HFH5C4GVWLJQJL","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":"792abe267576fee5c55bd5bcab91c61e4fc509fef43499974c6b937f5bb0c23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-05T14:28:21Z","title_canon_sha256":"98efe69350604cb6e4241b986d8f9f190843931439057e04914ebcb48a06ce33"},"schema_version":"1.0","source":{"id":"1906.02048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.02048","created_at":"2026-05-17T23:39:43Z"},{"alias_kind":"arxiv_version","alias_value":"1906.02048v1","created_at":"2026-05-17T23:39:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02048","created_at":"2026-05-17T23:39:43Z"},{"alias_kind":"pith_short_12","alias_value":"GBPSLMI4IRE6","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GBPSLMI4IRE6HFH5","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GBPSLMI4","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:08476c562438f23b5e6ff55002599f08a402ed430ecf6018c3125e44e87aa5f7","target":"graph","created_at":"2026-05-17T23:39:43Z","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":"This paper considers a random structure on the lattice $\\mathbb{Z}^2$ of the following kind. To each edge $e$ a random variable $X_e$ is assigned, together with a random sign $Y_e \\in \\{-1,+1\\}$. For an infinite self-avoiding path on $\\mathbb{Z}^2$ starting at the origin consider the sequence of partial sums along the path. These are computed by summing the $X_e$'s for the edges $e$ crossed by the path, with a sign depending on the direction of the crossing. If the edge is crossed rightward or upward the sign is given by $Y_e$, otherwise by $-Y_e$. We assume that the sequence of $X_e$'s is i.i","authors_text":"Emilio De Santis, Mauro Piccioni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-05T14:28:21Z","title":"Infinite paths on a random environment of $\\mathbb{Z}^2$ with bounded and recurrent sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02048","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:d7d433e0c0c19db6b0c751f99594e20a72532df48853aa96522ff5975e0f1aa9","target":"record","created_at":"2026-05-17T23:39:43Z","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":"792abe267576fee5c55bd5bcab91c61e4fc509fef43499974c6b937f5bb0c23f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-05T14:28:21Z","title_canon_sha256":"98efe69350604cb6e4241b986d8f9f190843931439057e04914ebcb48a06ce33"},"schema_version":"1.0","source":{"id":"1906.02048","kind":"arxiv","version":1}},"canonical_sha256":"305f25b11c4449e394fd170d5b2d304ae62872ceb695ea1090ff9c3af06d42ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"305f25b11c4449e394fd170d5b2d304ae62872ceb695ea1090ff9c3af06d42ad","first_computed_at":"2026-05-17T23:39:43.293668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:43.293668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tKuTPkI47xFlMnPOoraGw//LjIpGbtw0nYaXrGTkgduMPpHaoB6/lZqbZxFuSXHTTdXpZoWoCrewYx5RcQquDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:43.294395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.02048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7d433e0c0c19db6b0c751f99594e20a72532df48853aa96522ff5975e0f1aa9","sha256:08476c562438f23b5e6ff55002599f08a402ed430ecf6018c3125e44e87aa5f7"],"state_sha256":"4aebd185267059ca0909ce8e09da63d192b8204d8e58ff514e29b004c7703095"}