{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RCZRJYPMAKXN2QNNDBVZTR7XST","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":"f75d45d609a42f9793ca7c2b452e0696265732ec054280c83befa1fec00ace23","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-03T09:50:22Z","title_canon_sha256":"120a87ce19fb7235ea3f7723556960ece9bf1bbc7363db3b5806f21e38fe4e8f"},"schema_version":"1.0","source":{"id":"2504.02435","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.02435","created_at":"2026-07-05T10:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"2504.02435v1","created_at":"2026-07-05T10:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02435","created_at":"2026-07-05T10:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"RCZRJYPMAKXN","created_at":"2026-07-05T10:43:56Z"},{"alias_kind":"pith_short_16","alias_value":"RCZRJYPMAKXN2QNN","created_at":"2026-07-05T10:43:56Z"},{"alias_kind":"pith_short_8","alias_value":"RCZRJYPM","created_at":"2026-07-05T10:43:56Z"}],"graph_snapshots":[{"event_id":"sha256:6a04e59c657dfa1c62aef69d5351cb8510e4564f303dce71ec5f8ce61af5ba85","target":"graph","created_at":"2026-07-05T10:43:56Z","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/2504.02435/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the uniqueness thresholds for Poisson-Voronoi percolation in symmetric spaces of connected higher rank semisimple Lie groups with property (T) converge to zero in the low-intensity limit. This phenomenon is fundamentally different from situations in which Poisson-Voronoi percolation has previously been studied.\n  Our approach builds on a recent breakthrough of Fraczyk, Mellick and Wilkens (arXiv:2307.01194) and provides an alternative proof strategy for Gaboriau's fixed price problem. As a further application of our result, we give a new class of examples of non-amenable Cayley gr","authors_text":"Jan Greb\\'ik, Konstantin Recke","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-03T09:50:22Z","title":"Poisson-Voronoi percolation in higher rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02435","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:d56b37475d2367ad3a11e13510a2334797292a0589a214a5d29a41fcb7c05a0c","target":"record","created_at":"2026-07-05T10:43:56Z","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":"f75d45d609a42f9793ca7c2b452e0696265732ec054280c83befa1fec00ace23","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-03T09:50:22Z","title_canon_sha256":"120a87ce19fb7235ea3f7723556960ece9bf1bbc7363db3b5806f21e38fe4e8f"},"schema_version":"1.0","source":{"id":"2504.02435","kind":"arxiv","version":1}},"canonical_sha256":"88b314e1ec02aedd41ad186b99c7f794ed4010fff5167a640d3616758b705728","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b314e1ec02aedd41ad186b99c7f794ed4010fff5167a640d3616758b705728","first_computed_at":"2026-07-05T10:43:56.955078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:43:56.955078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u3dyEr5gvHerrFIooDi1F7nq8gnriLgVVs1gBcdtm//LOf6uoRchXmEy95SKGi9Ta0rGHF8S/87O7phOREh+Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:43:56.955598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.02435","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d56b37475d2367ad3a11e13510a2334797292a0589a214a5d29a41fcb7c05a0c","sha256:6a04e59c657dfa1c62aef69d5351cb8510e4564f303dce71ec5f8ce61af5ba85"],"state_sha256":"61e90ddee83a23d4e71165c9e028c309faa485a1bb129f05761cf8ecda1b4ad7"}