{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QMHBI7FY5DHHOQ276Y2WSPJK2R","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":"3f2c8a3fb9144ab37b9c0d963f62f67c9c218938d920ea44ca109d69832f3944","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-01T13:32:15Z","title_canon_sha256":"1d2e5095651083357c7efad7206557bd18af1481a66a7d37a6f266f79d216412"},"schema_version":"1.0","source":{"id":"1108.0310","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0310","created_at":"2026-05-18T01:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0310v2","created_at":"2026-05-18T01:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0310","created_at":"2026-05-18T01:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"QMHBI7FY5DHH","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMHBI7FY5DHHOQ27","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMHBI7FY","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:aa018ad75738f84197265972b01cb6fccb94f64c28b3e78e37f7312ee8286392","target":"graph","created_at":"2026-05-18T01:37:21Z","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":"We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first for which the critical probability p_c \\ne 1/2. Our proof uses a version of the Benjamini-Kalai-Schramm Theorem for biased product measures. A quantitative version of this result was recently proved by Keller and Kindler. We give a simple deduction of the non-quantitative result from the unbiased version. We also develop a quite general method of approximating Continuum Percolation models by discrete mod","authors_text":"Daniel Ahlberg, Erik Broman, Robert Morris, Simon Griffiths","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-01T13:32:15Z","title":"Noise Sensitivity in Continuum Percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0310","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:a84c69e1be28da8114380eaddecb58d590d5e0976bb5d163eefb5c98b227541d","target":"record","created_at":"2026-05-18T01:37:21Z","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":"3f2c8a3fb9144ab37b9c0d963f62f67c9c218938d920ea44ca109d69832f3944","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-01T13:32:15Z","title_canon_sha256":"1d2e5095651083357c7efad7206557bd18af1481a66a7d37a6f266f79d216412"},"schema_version":"1.0","source":{"id":"1108.0310","kind":"arxiv","version":2}},"canonical_sha256":"830e147cb8e8ce77435ff635693d2ad47bf73f1e3c2b1344d65e80267a410161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"830e147cb8e8ce77435ff635693d2ad47bf73f1e3c2b1344d65e80267a410161","first_computed_at":"2026-05-18T01:37:21.965960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:21.965960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CIkzSLLBNMggyOyJeWX+7BN3WtvtPiLSW6Retea/RvZ3v96lpOgMcsDq0m6gH8+q3PrJds0SGd8rH57DjL0XAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:21.966672Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0310","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a84c69e1be28da8114380eaddecb58d590d5e0976bb5d163eefb5c98b227541d","sha256:aa018ad75738f84197265972b01cb6fccb94f64c28b3e78e37f7312ee8286392"],"state_sha256":"56b27d296c41f1e61d529c4ed88f15c387facf16d4178c971d8fbe40bf76239a"}