{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HE3C7JKPERXDKPTFUCXV6GV5A4","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":"571295b67dcfc6a60d727ecf15e7513b519c69007c2e7d4eeda00d031dcd8478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-31T01:42:29Z","title_canon_sha256":"7732b83d66fa1c7f91acae9b986022c25ac4d7541bb4727c0aeda7a5c1bbaa8a"},"schema_version":"1.0","source":{"id":"2308.16388","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.16388","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"arxiv_version","alias_value":"2308.16388v2","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.16388","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_12","alias_value":"HE3C7JKPERXD","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"HE3C7JKPERXDKPTF","created_at":"2026-07-05T11:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"HE3C7JKP","created_at":"2026-07-05T11:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:8175d7e148aed550bc118b5615cc39e1536c1d0ef2c6c1cfe16dc930714b463a","target":"graph","created_at":"2026-07-05T11:25:58Z","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/2308.16388/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Assign independent weights to the edges of the square lattice, from the uniform distribution on $\\{a,b\\}$ for some $0<a<b<\\infty$. The weighted graph induces a random metric on $\\mathbb{Z}^2$. Let $T_n$ denote the distance between $(0,0)$ and $(n,0)$ in this metric. The distribution of $T_n$ has a well-defined median. Itai Benjamini asked in 2011 if the sequence of Boolean functions encoding whether $T_n$ exceeds its median is noise sensitive? In this paper we present the first progress on Benjamini's problem. More precisely, we study the minimal weight along any path crossing an $n\\times n$-s","authors_text":"Daniel Ahlberg, Daniel de la Riva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-31T01:42:29Z","title":"Is 'being above the median' a noise sensitive property?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.16388","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":"sha256:4f1a9468d0dc1ae09d445477962efaa4d2854c36a47ce703e88aeeaa65e52892","target":"record","created_at":"2026-07-05T11:25:58Z","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":"571295b67dcfc6a60d727ecf15e7513b519c69007c2e7d4eeda00d031dcd8478","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-08-31T01:42:29Z","title_canon_sha256":"7732b83d66fa1c7f91acae9b986022c25ac4d7541bb4727c0aeda7a5c1bbaa8a"},"schema_version":"1.0","source":{"id":"2308.16388","kind":"arxiv","version":2}},"canonical_sha256":"39362fa54f246e353e65a0af5f1abd072a179fda893a860357d6d4f1660abd0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39362fa54f246e353e65a0af5f1abd072a179fda893a860357d6d4f1660abd0b","first_computed_at":"2026-07-05T11:25:58.735404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:58.735404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"clTWzBfhJomilYalwNtIfUeKEtameb0RKPyPSyJr7iGLmLQKfjIY7tTI4/vvta6a568pDNbWIdGtSen3/KX1Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:58.735876Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.16388","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f1a9468d0dc1ae09d445477962efaa4d2854c36a47ce703e88aeeaa65e52892","sha256:8175d7e148aed550bc118b5615cc39e1536c1d0ef2c6c1cfe16dc930714b463a"],"state_sha256":"65f429affadf52bb07511b6a3b169e1b7862f56645f5aabbc9ac8b62ba72faf5"}