{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:G3FEKPNRSZVB5VUOW3OFXDKILT","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":"fddeda8918d106ebf031d71e89bd5994b89e156138c5188603ea47448ac51acd","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2006-08-09T09:46:06Z","title_canon_sha256":"0e09df92fabde8ac5e3172879b7639090b838acf35644fe823a7fa7ad9e93e9b"},"schema_version":"1.0","source":{"id":"math/0608216","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608216","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608216v1","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608216","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"G3FEKPNRSZVB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"G3FEKPNRSZVB5VUO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"G3FEKPNR","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:00ecae55a8ddd6896327c5ee949284851011a4efaf0f52f3fcfdbf908ecfd28b","target":"graph","created_at":"2026-05-18T01:08:49Z","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":"Consider the one-dimensional contact process. About ten years ago, N. Konno stated the conjecture that, for all positive integers $n,m$, the upper invariant measure has the following property: Conditioned on the event that $O$ is infected, the events $\\{$All sites $-n,...,-1$ are healthy$\\}$ and $\\{$All sites $1,...,m$ are healthy$\\}$ are negatively correlated. We prove (a stronger version of) this conjecture, and explain that in some sense it is a dual version of the planar case of one of our results in \\citeBHK.","authors_text":"J. Kahn, J. van den Berg, O. H\\\"aggstr\\\"om","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-08-09T09:46:06Z","title":"Proof of a conjecture of N. Konno for the 1D contact process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608216","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":"sha256:1ea25febad8b8cda0c3c7bce259e54108aa8e5de8c2604bac46fea79bf49ca54","target":"record","created_at":"2026-05-18T01:08:49Z","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":"fddeda8918d106ebf031d71e89bd5994b89e156138c5188603ea47448ac51acd","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2006-08-09T09:46:06Z","title_canon_sha256":"0e09df92fabde8ac5e3172879b7639090b838acf35644fe823a7fa7ad9e93e9b"},"schema_version":"1.0","source":{"id":"math/0608216","kind":"arxiv","version":1}},"canonical_sha256":"36ca453db1966a1ed68eb6dc5b8d485cec962fafe16b95c52d8c67c1ebd4fcff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36ca453db1966a1ed68eb6dc5b8d485cec962fafe16b95c52d8c67c1ebd4fcff","first_computed_at":"2026-05-18T01:08:49.820306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:49.820306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0l0eLzb8hnlRdcFf5EALUDYS5qkpc22SPKDchpa7J8XN8h60LLYbU0aKELzkeV0KuqZ0DkmTWPuoKHHz4qQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:49.820868Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608216","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ea25febad8b8cda0c3c7bce259e54108aa8e5de8c2604bac46fea79bf49ca54","sha256:00ecae55a8ddd6896327c5ee949284851011a4efaf0f52f3fcfdbf908ecfd28b"],"state_sha256":"8143fe47358456d8d9428278db6ddb198baf35c1a967d99b7c3ac92b186deb4c"}