{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GQU7FQYDJKUNV6CPKCQC4AMAEY","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":"11aed708ba14751bf6317cf9de5bfb0bb0d961df31e5d75e846d2f59bdbb2575","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-16T06:03:22Z","title_canon_sha256":"91d157b2b3b47e72d9ca233c6f6a0651be474aa8a63214f82f3802eb4963dac6"},"schema_version":"1.0","source":{"id":"1804.05509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05509","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05509v1","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05509","created_at":"2026-05-18T00:18:27Z"},{"alias_kind":"pith_short_12","alias_value":"GQU7FQYDJKUN","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GQU7FQYDJKUNV6CP","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GQU7FQYD","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:1acb367f57355aebab5666634f15496fa4cf0c462269e3c4f5b02c5f6721dbc6","target":"graph","created_at":"2026-05-18T00:18:27Z","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 extend a functional limit theorem for symmetric $U$-statistics [Miller and Sen, 1972] to asymmetric $U$-statistics, and use this to show some renewal theory results for asymmetric $U$-statistics.\n  Some applications are given.","authors_text":"Svante Janson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-16T06:03:22Z","title":"Renewal theory for asymmetric $U$-statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05509","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":"sha256:7d2424a24cb788b444eec424b3b9052d54ce33b1a6aafbfdb3e1b7137a9f7958","target":"record","created_at":"2026-05-18T00:18:27Z","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":"11aed708ba14751bf6317cf9de5bfb0bb0d961df31e5d75e846d2f59bdbb2575","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-16T06:03:22Z","title_canon_sha256":"91d157b2b3b47e72d9ca233c6f6a0651be474aa8a63214f82f3802eb4963dac6"},"schema_version":"1.0","source":{"id":"1804.05509","kind":"arxiv","version":1}},"canonical_sha256":"3429f2c3034aa8daf84f50a02e01802628767f91e1dcaa02b711c3393f43c463","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3429f2c3034aa8daf84f50a02e01802628767f91e1dcaa02b711c3393f43c463","first_computed_at":"2026-05-18T00:18:27.990623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:27.990623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6sAHByaYPKyXAvFBl4CHrD+CrigOTfHAE4XQG/K8KC66i0GOVW7HuD5pfTd44yy2MHmXigDrWPWGfA9aGso0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:27.991051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d2424a24cb788b444eec424b3b9052d54ce33b1a6aafbfdb3e1b7137a9f7958","sha256:1acb367f57355aebab5666634f15496fa4cf0c462269e3c4f5b02c5f6721dbc6"],"state_sha256":"c30f38b1d349d4de0112650cb12ab9fd4ca3f978c7e74cbfd379a178dce6dd0d"}