{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PUWVHWAJEGJXNJCAB7FBF3PNJB","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":"d44f2b8768c3ada066dc7ad2c725d93b6dde4e60a112fff511fd0b9f6f5b5de9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-29T20:29:12Z","title_canon_sha256":"71cd6ecdb77e5cf65cedc918094d721d7e7ae18429b52efef6e0340b047fe804"},"schema_version":"1.0","source":{"id":"1007.5327","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.5327","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"arxiv_version","alias_value":"1007.5327v2","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.5327","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"pith_short_12","alias_value":"PUWVHWAJEGJX","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PUWVHWAJEGJXNJCA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PUWVHWAJ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:7460d1fe316d76eae5d9c74006bef00acd54a389d0bdd6457def890ae3a7c38e","target":"graph","created_at":"2026-05-18T04:22:02Z","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 X be a countably infinite set of real numbers and let Y_x, x \\in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various \"regular\" functions f with the property that f(x) \\in Y_x for all x \\in X. Several open questions are posed.","authors_text":"Martin P. W. Zerner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-29T20:29:12Z","title":"Interpolation percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5327","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":"sha256:7c28e7fc9dfe2c76f7bf4539c3c306f1698862504ddaebba61869983ea008160","target":"record","created_at":"2026-05-18T04:22:02Z","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":"d44f2b8768c3ada066dc7ad2c725d93b6dde4e60a112fff511fd0b9f6f5b5de9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-29T20:29:12Z","title_canon_sha256":"71cd6ecdb77e5cf65cedc918094d721d7e7ae18429b52efef6e0340b047fe804"},"schema_version":"1.0","source":{"id":"1007.5327","kind":"arxiv","version":2}},"canonical_sha256":"7d2d53d809219376a4400fca12eded484e9343c265507bd8beec920b5cee2b4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d2d53d809219376a4400fca12eded484e9343c265507bd8beec920b5cee2b4b","first_computed_at":"2026-05-18T04:22:02.352990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:02.352990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Yv1m56+aEBgbimtnjO+HG9KjTa1d3zffmGOqFwzAgQkdw3c9jwYXl1N0hOl2t3Ht9+wgpOsa0D+GRoBGJb8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:02.353484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.5327","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c28e7fc9dfe2c76f7bf4539c3c306f1698862504ddaebba61869983ea008160","sha256:7460d1fe316d76eae5d9c74006bef00acd54a389d0bdd6457def890ae3a7c38e"],"state_sha256":"c8ca6d938f6ea9e3b9f5a7caf77571caf90dcf5c1c144b7d5acc46525c0850ce"}