{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AUXQIAN6NIKERB4G25KYPJQOBM","short_pith_number":"pith:AUXQIAN6","canonical_record":{"source":{"id":"1606.03988","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-13T15:06:00Z","cross_cats_sorted":["cs.CG","math-ph","math.MP"],"title_canon_sha256":"47ce568e287219eece415486132e3f8bf9c7590b0863152ab9a24cfc8e512362","abstract_canon_sha256":"423893a83d452cb6059b95f33743264ebe1a88bbc72d8402a537f19bf9940693"},"schema_version":"1.0"},"canonical_sha256":"052f0401be6a14488786d75587a60e0b068dc4bcb16fd2bf230ab0fef96aaeba","source":{"kind":"arxiv","id":"1606.03988","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03988","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03988v3","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03988","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"AUXQIAN6NIKE","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AUXQIAN6NIKERB4G","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AUXQIAN6","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AUXQIAN6NIKERB4G25KYPJQOBM","target":"record","payload":{"canonical_record":{"source":{"id":"1606.03988","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-13T15:06:00Z","cross_cats_sorted":["cs.CG","math-ph","math.MP"],"title_canon_sha256":"47ce568e287219eece415486132e3f8bf9c7590b0863152ab9a24cfc8e512362","abstract_canon_sha256":"423893a83d452cb6059b95f33743264ebe1a88bbc72d8402a537f19bf9940693"},"schema_version":"1.0"},"canonical_sha256":"052f0401be6a14488786d75587a60e0b068dc4bcb16fd2bf230ab0fef96aaeba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:09.709304Z","signature_b64":"qxubrjwoeY6CD1mEsn8rcpN2JAjiqZAQukcVp4t96oZLNOjDlKDlhGj1ziWbXOwfPSJ7ho/NjFVemUJhoEecCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"052f0401be6a14488786d75587a60e0b068dc4bcb16fd2bf230ab0fef96aaeba","last_reissued_at":"2026-05-17T23:43:09.708814Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:09.708814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.03988","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7CRvg4BDpVe2WKGf52dIHxkye1x/nYxYBBYtNfaB5oci3oj+M2VMZfLlVn/Gspg8/iS/FTRFBfb8LZpMKUOODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:49:50.557241Z"},"content_sha256":"2e9a1781a4ce1cf2f4f9d4ecde7df3e20215940ec719e84984f37293280adcc3","schema_version":"1.0","event_id":"sha256:2e9a1781a4ce1cf2f4f9d4ecde7df3e20215940ec719e84984f37293280adcc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AUXQIAN6NIKERB4G25KYPJQOBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit theory for geometric statistics of point processes having fast decay of correlations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"B. Blaszczyszyn, D. Yogeshwaran, J. E. Yukich","submitted_at":"2016-06-13T15:06:00Z","abstract_excerpt":"Let $P$ be a simple,stationary point process having fast decay of correlations, i.e., its correlation functions factorize up to an additive error decaying faster than any power of the separation distance. Let $P_n:= P \\cap W_n$ be its restriction to windows $W_n:= [-{1 \\over 2}n^{1/d},{1 \\over 2}n^{1/d}]^d \\subset \\mathbb{R}^d$. We consider the statistic $H_n^\\xi:= \\sum_{x \\in P_n}\\xi(x,P_n)$ where $\\xi(x,P_n)$ denotes a score function representing the interaction of $x$ with respect to $P_n$. When $\\xi$ depends on local data in the sense that its radius of stabilization has an exponential tai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03988","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhQQtjkBdy9LPi37ilYh+sZOB0ZqV+XfsDZeVcba93TATAXy19iMm8T5uMafrDMAAo9pXOxn8t5NRuXflhxgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T00:49:50.557876Z"},"content_sha256":"aec6a24d29422ddd573c37bfcc58dc7631aef8647157082317d8039a8a1e6cf1","schema_version":"1.0","event_id":"sha256:aec6a24d29422ddd573c37bfcc58dc7631aef8647157082317d8039a8a1e6cf1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AUXQIAN6NIKERB4G25KYPJQOBM/bundle.json","state_url":"https://pith.science/pith/AUXQIAN6NIKERB4G25KYPJQOBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AUXQIAN6NIKERB4G25KYPJQOBM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T00:49:50Z","links":{"resolver":"https://pith.science/pith/AUXQIAN6NIKERB4G25KYPJQOBM","bundle":"https://pith.science/pith/AUXQIAN6NIKERB4G25KYPJQOBM/bundle.json","state":"https://pith.science/pith/AUXQIAN6NIKERB4G25KYPJQOBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AUXQIAN6NIKERB4G25KYPJQOBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AUXQIAN6NIKERB4G25KYPJQOBM","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":"423893a83d452cb6059b95f33743264ebe1a88bbc72d8402a537f19bf9940693","cross_cats_sorted":["cs.CG","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-13T15:06:00Z","title_canon_sha256":"47ce568e287219eece415486132e3f8bf9c7590b0863152ab9a24cfc8e512362"},"schema_version":"1.0","source":{"id":"1606.03988","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03988","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03988v3","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03988","created_at":"2026-05-17T23:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"AUXQIAN6NIKE","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AUXQIAN6NIKERB4G","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AUXQIAN6","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:aec6a24d29422ddd573c37bfcc58dc7631aef8647157082317d8039a8a1e6cf1","target":"graph","created_at":"2026-05-17T23:43:09Z","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 $P$ be a simple,stationary point process having fast decay of correlations, i.e., its correlation functions factorize up to an additive error decaying faster than any power of the separation distance. Let $P_n:= P \\cap W_n$ be its restriction to windows $W_n:= [-{1 \\over 2}n^{1/d},{1 \\over 2}n^{1/d}]^d \\subset \\mathbb{R}^d$. We consider the statistic $H_n^\\xi:= \\sum_{x \\in P_n}\\xi(x,P_n)$ where $\\xi(x,P_n)$ denotes a score function representing the interaction of $x$ with respect to $P_n$. When $\\xi$ depends on local data in the sense that its radius of stabilization has an exponential tai","authors_text":"B. Blaszczyszyn, D. Yogeshwaran, J. E. Yukich","cross_cats":["cs.CG","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-13T15:06:00Z","title":"Limit theory for geometric statistics of point processes having fast decay of correlations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03988","kind":"arxiv","version":3},"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":"sha256:2e9a1781a4ce1cf2f4f9d4ecde7df3e20215940ec719e84984f37293280adcc3","target":"record","created_at":"2026-05-17T23:43:09Z","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":"423893a83d452cb6059b95f33743264ebe1a88bbc72d8402a537f19bf9940693","cross_cats_sorted":["cs.CG","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-13T15:06:00Z","title_canon_sha256":"47ce568e287219eece415486132e3f8bf9c7590b0863152ab9a24cfc8e512362"},"schema_version":"1.0","source":{"id":"1606.03988","kind":"arxiv","version":3}},"canonical_sha256":"052f0401be6a14488786d75587a60e0b068dc4bcb16fd2bf230ab0fef96aaeba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"052f0401be6a14488786d75587a60e0b068dc4bcb16fd2bf230ab0fef96aaeba","first_computed_at":"2026-05-17T23:43:09.708814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:09.708814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qxubrjwoeY6CD1mEsn8rcpN2JAjiqZAQukcVp4t96oZLNOjDlKDlhGj1ziWbXOwfPSJ7ho/NjFVemUJhoEecCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:09.709304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03988","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e9a1781a4ce1cf2f4f9d4ecde7df3e20215940ec719e84984f37293280adcc3","sha256:aec6a24d29422ddd573c37bfcc58dc7631aef8647157082317d8039a8a1e6cf1"],"state_sha256":"733d8c923ac0fc2e2283d241dd73b24678a1c1391aa3ad02051d164a15864cc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCGanfvkmrnTQyYIHVhM0+axcsAzWapT/d0GFaoSc774U8hj9tl5TxqTA+ZKU1UgsVNlKK7eV3BfhuLc7fYfBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T00:49:50.561618Z","bundle_sha256":"71e9238c9d28581ba576a25c28c1697e4e4c3ffec5d96d5a953a0a19cdd90ddd"}}