{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:POP7NTREJLT4GQENQXYQWONY5U","short_pith_number":"pith:POP7NTRE","schema_version":"1.0","canonical_sha256":"7b9ff6ce244ae7c3408d85f10b39b8ed3f43daeabb2cfbc96d0eabc6a4f87956","source":{"kind":"arxiv","id":"1706.01074","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic Goodness-of-Fit Tests for Point Processes Based on Scaled Empirical K-Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lothar Heinrich","submitted_at":"2017-06-04T13:44:55Z","abstract_excerpt":"We study sequences of scaled edge-corrected empirical (generalized) K-functions (modifying Ripley's K-function) each of them constructed from a single observation of a $d$-dimensional fourth-order stationary point process in a sampling window W_n which grows together with some scaling rate unboundedly as n --> infty. Under some natural assumptions it is shown that the normalized difference between scaled empirical and scaled theoretical K-function converges weakly to a mean zero Gaussian process with simple covariance function. This result suggests discrepancy measures between empirical and th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.01074","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-06-04T13:44:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5809c74643ba91c5def504168f870f834b45bfd203c846bcb7e3a5ed8f326829","abstract_canon_sha256":"a2a2fab311b4c14dabae49d9ae64b265d2e68aa748dee804e6c4e941e87449b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:04.609355Z","signature_b64":"cxfrVvug6T6KcRpUJTpxd3hOcDX71v9Ax3JcGIkKGLLLXn5Bbbxi5hmtukVIUbWlvmdL/9uRWKA3CqMxyW1mBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b9ff6ce244ae7c3408d85f10b39b8ed3f43daeabb2cfbc96d0eabc6a4f87956","last_reissued_at":"2026-05-18T00:43:04.608569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:04.608569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Goodness-of-Fit Tests for Point Processes Based on Scaled Empirical K-Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Lothar Heinrich","submitted_at":"2017-06-04T13:44:55Z","abstract_excerpt":"We study sequences of scaled edge-corrected empirical (generalized) K-functions (modifying Ripley's K-function) each of them constructed from a single observation of a $d$-dimensional fourth-order stationary point process in a sampling window W_n which grows together with some scaling rate unboundedly as n --> infty. Under some natural assumptions it is shown that the normalized difference between scaled empirical and scaled theoretical K-function converges weakly to a mean zero Gaussian process with simple covariance function. This result suggests discrepancy measures between empirical and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01074","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.01074","created_at":"2026-05-18T00:43:04.608680+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.01074v1","created_at":"2026-05-18T00:43:04.608680+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01074","created_at":"2026-05-18T00:43:04.608680+00:00"},{"alias_kind":"pith_short_12","alias_value":"POP7NTREJLT4","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"POP7NTREJLT4GQEN","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"POP7NTRE","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U","json":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U.json","graph_json":"https://pith.science/api/pith-number/POP7NTREJLT4GQENQXYQWONY5U/graph.json","events_json":"https://pith.science/api/pith-number/POP7NTREJLT4GQENQXYQWONY5U/events.json","paper":"https://pith.science/paper/POP7NTRE"},"agent_actions":{"view_html":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U","download_json":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U.json","view_paper":"https://pith.science/paper/POP7NTRE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.01074&json=true","fetch_graph":"https://pith.science/api/pith-number/POP7NTREJLT4GQENQXYQWONY5U/graph.json","fetch_events":"https://pith.science/api/pith-number/POP7NTREJLT4GQENQXYQWONY5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U/action/storage_attestation","attest_author":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U/action/author_attestation","sign_citation":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U/action/citation_signature","submit_replication":"https://pith.science/pith/POP7NTREJLT4GQENQXYQWONY5U/action/replication_record"}},"created_at":"2026-05-18T00:43:04.608680+00:00","updated_at":"2026-05-18T00:43:04.608680+00:00"}