{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Y2VKIDZ5H3MPJVX3ARCXODOBYW","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":"a0172df6cac72d40feadd873c40a1428d34f9cf049383fc3840ffefe85386126","cross_cats_sorted":["math.PR","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2025-07-21T10:27:49Z","title_canon_sha256":"72e6b5ec0c52394b2904d7de2285120dcef60f51306dbbeaa55f6d29e8f5232b"},"schema_version":"1.0","source":{"id":"2507.15475","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.15475","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"2507.15475v2","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.15475","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"Y2VKIDZ5H3MP","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_16","alias_value":"Y2VKIDZ5H3MPJVX3","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_8","alias_value":"Y2VKIDZ5","created_at":"2026-05-20T00:01:34Z"}],"graph_snapshots":[{"event_id":"sha256:e24dd67421870ac1c78c57edbdc1f91439917a508592008a16ab75d785cd6209","target":"graph","created_at":"2026-05-20T00:01:34Z","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/2507.15475/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in signal processing. In particular, we derive the exact joint and marginal distributions for two steps, numerical solutions for a general number of steps, and approximations for a large number of steps. Furthermore, we provide an exact characterization of the support for an arbitrary number of steps. The results in this work provide a reference for future work i","authors_text":"Karl-Ludwig Besser","cross_cats":["math.PR","stat.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2025-07-21T10:27:49Z","title":"On the Distribution of a Two-Dimensional Random Walk with Restricted Angles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.15475","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:f8ee3d10906d37bd31df4ae1be69fb2fc384661988a46cb896505a1953af1d06","target":"record","created_at":"2026-05-20T00:01:34Z","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":"a0172df6cac72d40feadd873c40a1428d34f9cf049383fc3840ffefe85386126","cross_cats_sorted":["math.PR","stat.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2025-07-21T10:27:49Z","title_canon_sha256":"72e6b5ec0c52394b2904d7de2285120dcef60f51306dbbeaa55f6d29e8f5232b"},"schema_version":"1.0","source":{"id":"2507.15475","kind":"arxiv","version":2}},"canonical_sha256":"c6aaa40f3d3ed8f4d6fb0445770dc1c5930055582e26b341abb5eb3e6cf1f7e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6aaa40f3d3ed8f4d6fb0445770dc1c5930055582e26b341abb5eb3e6cf1f7e6","first_computed_at":"2026-05-20T00:01:34.884370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:34.884370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+UZoNK8nOeGx3KHzBsZHZHyyfVMtlu4uqt064NqYtpziPz5oXG+aQp+MNzQWF3ULy3uNlWVipmFDInLQz515Cg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:34.885115Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.15475","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8ee3d10906d37bd31df4ae1be69fb2fc384661988a46cb896505a1953af1d06","sha256:e24dd67421870ac1c78c57edbdc1f91439917a508592008a16ab75d785cd6209"],"state_sha256":"59789395694ce4fbb14068e90ae31904bd6b550490dbd2fc59774cfe57b874ad"}