{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ENOBWJK2OJ7D54FNBDWJYPN6OA","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":"9d467d40ce9bf1c3ef5536d5c4e30e76f26224b724fe9e5b28beb21da500db40","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-05T15:08:47Z","title_canon_sha256":"de9f7b4c66e5ca545b370f9638b7e4bc048a7eda5bced6160addb4e40ed3f33e"},"schema_version":"1.0","source":{"id":"2211.02925","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02925","created_at":"2026-07-05T05:13:42Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02925v1","created_at":"2026-07-05T05:13:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02925","created_at":"2026-07-05T05:13:42Z"},{"alias_kind":"pith_short_12","alias_value":"ENOBWJK2OJ7D","created_at":"2026-07-05T05:13:42Z"},{"alias_kind":"pith_short_16","alias_value":"ENOBWJK2OJ7D54FN","created_at":"2026-07-05T05:13:42Z"},{"alias_kind":"pith_short_8","alias_value":"ENOBWJK2","created_at":"2026-07-05T05:13:42Z"}],"graph_snapshots":[{"event_id":"sha256:7b3a8165f8e81a725bf35f75f18676a3e13f945c05b521e07966d030a1366b36","target":"graph","created_at":"2026-07-05T05:13:42Z","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/2211.02925/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Random walks in cones have the double interest of being at the heart of many probabilistic problems and of being related to many mathematical fields, such as spectral theory, combinatorics, or discrete complex analysis. In this article, we present some key ideas associated with these processes: we will discuss their definition, the link with Brownian motion in cones, as well as some recent research topics such as the construction of discrete harmonic functions.","authors_text":"Kilian Raschel, Pierre Tarrago","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-05T15:08:47Z","title":"Marches al\\'eatoires dans un c\\^one et fonctions discr\\`etes harmoniques"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02925","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:c03cf0c2a32fae83cdfa66ecfee056befdc7dae8228c9d9ce9df3040961f9e8c","target":"record","created_at":"2026-07-05T05:13:42Z","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":"9d467d40ce9bf1c3ef5536d5c4e30e76f26224b724fe9e5b28beb21da500db40","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-05T15:08:47Z","title_canon_sha256":"de9f7b4c66e5ca545b370f9638b7e4bc048a7eda5bced6160addb4e40ed3f33e"},"schema_version":"1.0","source":{"id":"2211.02925","kind":"arxiv","version":1}},"canonical_sha256":"235c1b255a727e3ef0ad08ec9c3dbe700b33320dbf35878036b706dfd53f4d19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"235c1b255a727e3ef0ad08ec9c3dbe700b33320dbf35878036b706dfd53f4d19","first_computed_at":"2026-07-05T05:13:42.340460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:42.340460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I9mRxfaaCVWZJqqht4IUqKjZHXR3MmANHk3CXsqn/y8jWjC6g48Z6PIouLJZZw+62Q2h3Ej+TE0oSbjVragGCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:42.340891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.02925","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c03cf0c2a32fae83cdfa66ecfee056befdc7dae8228c9d9ce9df3040961f9e8c","sha256:7b3a8165f8e81a725bf35f75f18676a3e13f945c05b521e07966d030a1366b36"],"state_sha256":"d105668c8727a84be205faa81d8420f66f9512a147985c7757335375c12f4214"}