{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PZFXV37ZM6J43VWH47LDUU227R","short_pith_number":"pith:PZFXV37Z","canonical_record":{"source":{"id":"1710.05352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T16:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"d036f5314539ef63e9e7e4b61a3baa5bda310af486d764740f6ce462014e16d7","abstract_canon_sha256":"ea14b525bd7b7649bc53e73feb3a1f6d1ff21303f20af100621bbdb6185e9ae8"},"schema_version":"1.0"},"canonical_sha256":"7e4b7aeff96793cdd6c7e7d63a535afc6510621aaf94e9773e6642d1d1de2d1a","source":{"kind":"arxiv","id":"1710.05352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05352","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05352v1","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05352","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"PZFXV37ZM6J4","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PZFXV37ZM6J43VWH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PZFXV37Z","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PZFXV37ZM6J43VWH47LDUU227R","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T16:04:00Z","cross_cats_sorted":[],"title_canon_sha256":"d036f5314539ef63e9e7e4b61a3baa5bda310af486d764740f6ce462014e16d7","abstract_canon_sha256":"ea14b525bd7b7649bc53e73feb3a1f6d1ff21303f20af100621bbdb6185e9ae8"},"schema_version":"1.0"},"canonical_sha256":"7e4b7aeff96793cdd6c7e7d63a535afc6510621aaf94e9773e6642d1d1de2d1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:19.212744Z","signature_b64":"0wl6l6YYE+HG83KNXHiKVoQSlw0ZV5J9GvncODyiVcfoQqX6+sgKRn6TX68Qg9mAc9g2SE2C6CEc50o5GbrwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e4b7aeff96793cdd6c7e7d63a535afc6510621aaf94e9773e6642d1d1de2d1a","last_reissued_at":"2026-05-18T00:12:19.212073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:19.212073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05352","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4iJMbRPce4cujAxBUG1YfK0CP5gq6nfSy2MZfhCj7ExPYEwzc/ePzSrsjA+79NwV2ZMW/F0TO0mQA0ts56n9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:38:34.657488Z"},"content_sha256":"e41178494dc7d0d2c6cbdaed9d91ff988e4ace33e4d35e39aeb08c20337a8adc","schema_version":"1.0","event_id":"sha256:e41178494dc7d0d2c6cbdaed9d91ff988e4ace33e4d35e39aeb08c20337a8adc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PZFXV37ZM6J43VWH47LDUU227R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some properties of stationary determinantal point processes on $\\mathbb{Z}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ai-Hua Fan, Shi-lei Fan, Yan-qi Qiu","submitted_at":"2017-10-15T16:04:00Z","abstract_excerpt":"We study properties of stationary determinantal point processes $\\X$ on $\\Z$ from different points of views. It is proved that $\\X\\cap \\N$ is almost surely Bohr-dense and good universal for almost everywhere convergence in $L^1$, and that $\\X$ is not syndetic but $\\X +\\X = \\mathbb{Z}$. For the associated centered random field, we obtain a sub-Gaussian property, a Salem-Littlewood inequality and a Khintchine-Kahane inequality. Results can be generalized to $\\Z^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05352","kind":"arxiv","version":1},"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":"2026-05-18T00:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3asXGjD3wmPBYJJq4RHZfkQfeLoLNmjICBCFV+WskaGEGmCv1z+XgHQCy+9gaf7G/9L4/AmUY53BIKAittDvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:38:34.657954Z"},"content_sha256":"7a6608ec1c0468c9ac5ed10a162a61a8f1de45041df8abdaababe2fc9df8156e","schema_version":"1.0","event_id":"sha256:7a6608ec1c0468c9ac5ed10a162a61a8f1de45041df8abdaababe2fc9df8156e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZFXV37ZM6J43VWH47LDUU227R/bundle.json","state_url":"https://pith.science/pith/PZFXV37ZM6J43VWH47LDUU227R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZFXV37ZM6J43VWH47LDUU227R/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":"2026-06-25T07:38:34Z","links":{"resolver":"https://pith.science/pith/PZFXV37ZM6J43VWH47LDUU227R","bundle":"https://pith.science/pith/PZFXV37ZM6J43VWH47LDUU227R/bundle.json","state":"https://pith.science/pith/PZFXV37ZM6J43VWH47LDUU227R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZFXV37ZM6J43VWH47LDUU227R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PZFXV37ZM6J43VWH47LDUU227R","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":"ea14b525bd7b7649bc53e73feb3a1f6d1ff21303f20af100621bbdb6185e9ae8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T16:04:00Z","title_canon_sha256":"d036f5314539ef63e9e7e4b61a3baa5bda310af486d764740f6ce462014e16d7"},"schema_version":"1.0","source":{"id":"1710.05352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05352","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05352v1","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05352","created_at":"2026-05-18T00:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"PZFXV37ZM6J4","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PZFXV37ZM6J43VWH","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PZFXV37Z","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:7a6608ec1c0468c9ac5ed10a162a61a8f1de45041df8abdaababe2fc9df8156e","target":"graph","created_at":"2026-05-18T00:12:19Z","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 study properties of stationary determinantal point processes $\\X$ on $\\Z$ from different points of views. It is proved that $\\X\\cap \\N$ is almost surely Bohr-dense and good universal for almost everywhere convergence in $L^1$, and that $\\X$ is not syndetic but $\\X +\\X = \\mathbb{Z}$. For the associated centered random field, we obtain a sub-Gaussian property, a Salem-Littlewood inequality and a Khintchine-Kahane inequality. Results can be generalized to $\\Z^d$.","authors_text":"Ai-Hua Fan, Shi-lei Fan, Yan-qi Qiu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T16:04:00Z","title":"Some properties of stationary determinantal point processes on $\\mathbb{Z}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05352","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:e41178494dc7d0d2c6cbdaed9d91ff988e4ace33e4d35e39aeb08c20337a8adc","target":"record","created_at":"2026-05-18T00:12:19Z","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":"ea14b525bd7b7649bc53e73feb3a1f6d1ff21303f20af100621bbdb6185e9ae8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T16:04:00Z","title_canon_sha256":"d036f5314539ef63e9e7e4b61a3baa5bda310af486d764740f6ce462014e16d7"},"schema_version":"1.0","source":{"id":"1710.05352","kind":"arxiv","version":1}},"canonical_sha256":"7e4b7aeff96793cdd6c7e7d63a535afc6510621aaf94e9773e6642d1d1de2d1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e4b7aeff96793cdd6c7e7d63a535afc6510621aaf94e9773e6642d1d1de2d1a","first_computed_at":"2026-05-18T00:12:19.212073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:19.212073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0wl6l6YYE+HG83KNXHiKVoQSlw0ZV5J9GvncODyiVcfoQqX6+sgKRn6TX68Qg9mAc9g2SE2C6CEc50o5GbrwBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:19.212744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e41178494dc7d0d2c6cbdaed9d91ff988e4ace33e4d35e39aeb08c20337a8adc","sha256:7a6608ec1c0468c9ac5ed10a162a61a8f1de45041df8abdaababe2fc9df8156e"],"state_sha256":"533f55cc8cd660f859c4f2e98a9c714ba06457e12328f58a99f56b5f3f65098c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZIJHV3ly1/OBeWLXE5JvRViQ5eB/AiUnlM8OWk3t0jZPVCw1N9Qr2tSMV1689LDkyXoh/0P6TRgxueVsVNWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T07:38:34.660556Z","bundle_sha256":"1b6b6c7a83c2a3af9c60866273bf6fa7014820d04c36313e5c7e8cc171e73827"}}