{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CMGERR3WMDNWVJ6ULCC7ETII6S","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":"7b3a69902147b67116244e2f89f9fece7faa0ecf3007591df36a68609efa176f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-16T17:52:55Z","title_canon_sha256":"b8f38ba4437ec8357797b38fe7e0ae13cddab4093fa8625243d767678084795d"},"schema_version":"1.0","source":{"id":"1405.4255","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4255","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4255v2","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4255","created_at":"2026-05-18T01:36:36Z"},{"alias_kind":"pith_short_12","alias_value":"CMGERR3WMDNW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CMGERR3WMDNWVJ6U","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CMGERR3W","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:6ac215484a76c12c22e4de7f464c1f99ec63890c72856c9321e54315371098ad","target":"graph","created_at":"2026-05-18T01:36:36Z","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 discuss several examples of point processes (all taken from Hough, Krishnapur, Peres, Vir\\'ag (2009)) for which the autocorrelation and diffraction measures can be calculated explicitly. These include certain classes of determinantal and permanental point processes, as well as an isometry-invariant point process that arises as the zero set of a Gaussian random analytic function.","authors_text":"Holger K\\\"osters, Michael Baake, Robert V. Moody","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-16T17:52:55Z","title":"Diffraction Theory of Point Processes: Systems with Clumping and Repulsion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4255","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":"sha256:6537118b27e635db7a3eaaaa3dde8a2360095592539269480173bbc72f18265e","target":"record","created_at":"2026-05-18T01:36:36Z","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":"7b3a69902147b67116244e2f89f9fece7faa0ecf3007591df36a68609efa176f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-05-16T17:52:55Z","title_canon_sha256":"b8f38ba4437ec8357797b38fe7e0ae13cddab4093fa8625243d767678084795d"},"schema_version":"1.0","source":{"id":"1405.4255","kind":"arxiv","version":2}},"canonical_sha256":"130c48c77660db6aa7d45885f24d08f49dcee7b6808015010721b96a994ffcf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"130c48c77660db6aa7d45885f24d08f49dcee7b6808015010721b96a994ffcf0","first_computed_at":"2026-05-18T01:36:36.058814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:36.058814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u0oHKw4nmmGXbI9Lw9ulYbfC+oC/46q9iUleUsi32Vtjufife7FmEz57wFR1RJTzLSUbCDNBq3lJiA7VmdpJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:36.059351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4255","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6537118b27e635db7a3eaaaa3dde8a2360095592539269480173bbc72f18265e","sha256:6ac215484a76c12c22e4de7f464c1f99ec63890c72856c9321e54315371098ad"],"state_sha256":"53f39fa331053de360c179329f6d0beb148a25577c6e37fdbbc3e2748b42b6cd"}