{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5QMNEWHVUHO7PI6B2QZVK4LBW2","short_pith_number":"pith:5QMNEWHV","canonical_record":{"source":{"id":"1605.06866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-23T00:24:24Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"9c56a30d3c97ecec3306ee6b96d8fd632021a521e23a604839d09085b256128e","abstract_canon_sha256":"324cba77dd3cd039652496351782aa42a5ec0162ba7779f12636f345ed65c698"},"schema_version":"1.0"},"canonical_sha256":"ec18d258f5a1ddf7a3c1d433557161b68369a6e3c5cd5b07811e4e1a53f73d1e","source":{"kind":"arxiv","id":"1605.06866","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06866","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06866v2","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06866","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"5QMNEWHVUHO7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5QMNEWHVUHO7PI6B","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5QMNEWHV","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5QMNEWHVUHO7PI6B2QZVK4LBW2","target":"record","payload":{"canonical_record":{"source":{"id":"1605.06866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-23T00:24:24Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"9c56a30d3c97ecec3306ee6b96d8fd632021a521e23a604839d09085b256128e","abstract_canon_sha256":"324cba77dd3cd039652496351782aa42a5ec0162ba7779f12636f345ed65c698"},"schema_version":"1.0"},"canonical_sha256":"ec18d258f5a1ddf7a3c1d433557161b68369a6e3c5cd5b07811e4e1a53f73d1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:37.407905Z","signature_b64":"H1iiirnqX3XfjUfe/LJpfpBamqR8JRlRYTHV793g0lXtgw9JT8PGP5f0q/Ps24AktNCM3vggtTAe531lHPDVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec18d258f5a1ddf7a3c1d433557161b68369a6e3c5cd5b07811e4e1a53f73d1e","last_reissued_at":"2026-05-18T01:13:37.407254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:37.407254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.06866","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5T8b1L6d/clJZUXs8T3/kmYhNaLG3NtATcrZtE50T/Nv5pBkYAU8Uy9mAMcd/SwpmqSWS16fbt5MqLefz0aPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:06:15.837947Z"},"content_sha256":"4bdbea5b04444d4cadf25f24a4f5e229e85f02f99d22cfb50c57244d49271348","schema_version":"1.0","event_id":"sha256:4bdbea5b04444d4cadf25f24a4f5e229e85f02f99d22cfb50c57244d49271348"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5QMNEWHVUHO7PI6B2QZVK4LBW2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularizing Random Points: Complementary Mat\\'ern Hard-Core Point Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Akram Al-Hourani, Bill Moran, Sithamparanathan Kandeepan","submitted_at":"2016-05-23T00:24:24Z","abstract_excerpt":"In this paper we present a tractable approach for regularizing randomly placed points, by splitting them into two subsets: the first is generated by means of the Mat\\'ern hard-core point process, while the remaining points constitute the complementary Mat\\'ern hard-core point process. We study the characteristics of these processes, deriving its pair-correlation functions, and the distribution of the distance to the nearest neighbour. The results have several applications in wireless communications, including the modeling of wireless sensor networks, where we investigate an example of regulari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06866","kind":"arxiv","version":2},"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":"2026-05-18T01:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZvO4KSttGx7WmSG8hXhxTGEzFeTz+mMkkRQu1unFlSf5HEXMar5mStirDbNp+WI8t0adRmYcVqGupCsaItYBAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:06:15.838291Z"},"content_sha256":"cb8fc454edf0cd7d2a2f5dff801d70f8bca77ab19f35b9985303939fdf406b6e","schema_version":"1.0","event_id":"sha256:cb8fc454edf0cd7d2a2f5dff801d70f8bca77ab19f35b9985303939fdf406b6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5QMNEWHVUHO7PI6B2QZVK4LBW2/bundle.json","state_url":"https://pith.science/pith/5QMNEWHVUHO7PI6B2QZVK4LBW2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5QMNEWHVUHO7PI6B2QZVK4LBW2/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":"2026-06-03T16:06:15Z","links":{"resolver":"https://pith.science/pith/5QMNEWHVUHO7PI6B2QZVK4LBW2","bundle":"https://pith.science/pith/5QMNEWHVUHO7PI6B2QZVK4LBW2/bundle.json","state":"https://pith.science/pith/5QMNEWHVUHO7PI6B2QZVK4LBW2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5QMNEWHVUHO7PI6B2QZVK4LBW2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5QMNEWHVUHO7PI6B2QZVK4LBW2","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":"324cba77dd3cd039652496351782aa42a5ec0162ba7779f12636f345ed65c698","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-23T00:24:24Z","title_canon_sha256":"9c56a30d3c97ecec3306ee6b96d8fd632021a521e23a604839d09085b256128e"},"schema_version":"1.0","source":{"id":"1605.06866","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06866","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06866v2","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06866","created_at":"2026-05-18T01:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"5QMNEWHVUHO7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5QMNEWHVUHO7PI6B","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5QMNEWHV","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:cb8fc454edf0cd7d2a2f5dff801d70f8bca77ab19f35b9985303939fdf406b6e","target":"graph","created_at":"2026-05-18T01:13:37Z","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":"In this paper we present a tractable approach for regularizing randomly placed points, by splitting them into two subsets: the first is generated by means of the Mat\\'ern hard-core point process, while the remaining points constitute the complementary Mat\\'ern hard-core point process. We study the characteristics of these processes, deriving its pair-correlation functions, and the distribution of the distance to the nearest neighbour. The results have several applications in wireless communications, including the modeling of wireless sensor networks, where we investigate an example of regulari","authors_text":"Akram Al-Hourani, Bill Moran, Sithamparanathan Kandeepan","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-23T00:24:24Z","title":"Regularizing Random Points: Complementary Mat\\'ern Hard-Core Point Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06866","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":"sha256:4bdbea5b04444d4cadf25f24a4f5e229e85f02f99d22cfb50c57244d49271348","target":"record","created_at":"2026-05-18T01:13:37Z","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":"324cba77dd3cd039652496351782aa42a5ec0162ba7779f12636f345ed65c698","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-05-23T00:24:24Z","title_canon_sha256":"9c56a30d3c97ecec3306ee6b96d8fd632021a521e23a604839d09085b256128e"},"schema_version":"1.0","source":{"id":"1605.06866","kind":"arxiv","version":2}},"canonical_sha256":"ec18d258f5a1ddf7a3c1d433557161b68369a6e3c5cd5b07811e4e1a53f73d1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec18d258f5a1ddf7a3c1d433557161b68369a6e3c5cd5b07811e4e1a53f73d1e","first_computed_at":"2026-05-18T01:13:37.407254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:37.407254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H1iiirnqX3XfjUfe/LJpfpBamqR8JRlRYTHV793g0lXtgw9JT8PGP5f0q/Ps24AktNCM3vggtTAe531lHPDVBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:37.407905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06866","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bdbea5b04444d4cadf25f24a4f5e229e85f02f99d22cfb50c57244d49271348","sha256:cb8fc454edf0cd7d2a2f5dff801d70f8bca77ab19f35b9985303939fdf406b6e"],"state_sha256":"e9b735dc63a58b53c5425ec932da7d7d2a299ad37fd3c9df22e5ae3c4722bb7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gq7aTz31YbXFAOjhyWVl8IWsPLI1hyOonDAMiQznkHTq25qHzAvRg+RW7yLNBgJMwXlEGPcbeomJloSXwcuGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:06:15.840239Z","bundle_sha256":"88819dbb92d99ed2320b9262c99fe189b4c540a2f0c4c5c2b4d1b319430a1fe9"}}