{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:HCW3CMOHIEYRLU2533DBDVLESS","short_pith_number":"pith:HCW3CMOH","canonical_record":{"source":{"id":"2208.06791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-08-14T06:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"672e18f4cecdd6a3bf44c78deb301ea238868e10233a76ef7d97f398fc55fd11","abstract_canon_sha256":"bb304f036ea98c522047199871981b30ae161b64867f4b428d46d3e3f6eef18c"},"schema_version":"1.0"},"canonical_sha256":"38adb131c7413115d35ddec611d56494b029d6a7d78dbcdc58b5a6f231c8aa1b","source":{"kind":"arxiv","id":"2208.06791","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.06791","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"2208.06791v1","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.06791","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"HCW3CMOHIEYR","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"pith_short_16","alias_value":"HCW3CMOHIEYRLU25","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"pith_short_8","alias_value":"HCW3CMOH","created_at":"2026-07-05T04:48:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:HCW3CMOHIEYRLU2533DBDVLESS","target":"record","payload":{"canonical_record":{"source":{"id":"2208.06791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-08-14T06:29:09Z","cross_cats_sorted":[],"title_canon_sha256":"672e18f4cecdd6a3bf44c78deb301ea238868e10233a76ef7d97f398fc55fd11","abstract_canon_sha256":"bb304f036ea98c522047199871981b30ae161b64867f4b428d46d3e3f6eef18c"},"schema_version":"1.0"},"canonical_sha256":"38adb131c7413115d35ddec611d56494b029d6a7d78dbcdc58b5a6f231c8aa1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:48:20.757307Z","signature_b64":"KhM8ZWsGJ6o8vjT9/27FPJuQ7VMdlEUSK9mls7qZ1dGemTHSiAbcM1dtJcPqNhlmTedoWRmA/O4Q1mNwXLpOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38adb131c7413115d35ddec611d56494b029d6a7d78dbcdc58b5a6f231c8aa1b","last_reissued_at":"2026-07-05T04:48:20.756960Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:48:20.756960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.06791","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":"2026-07-05T04:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2Jycwwog5cU/jqvE7c77qzAr3xKDRmtiBCdkihOT4NE8PxIwm4pe5x000b4RE8lfTCLrEOSTo5c+FzoScbICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T23:37:34.646220Z"},"content_sha256":"a0bf6e61a44885df20444bf3d393d8bb3b1d9094aa8f6a7ff90769bb7a8b866a","schema_version":"1.0","event_id":"sha256:a0bf6e61a44885df20444bf3d393d8bb3b1d9094aa8f6a7ff90769bb7a8b866a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:HCW3CMOHIEYRLU2533DBDVLESS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the recent-$k$-record of discrete random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anshui Li","submitted_at":"2022-08-14T06:29:09Z","abstract_excerpt":"Let $X_1,~X_2,\\cdots$ be a sequence of i.i.d random variables which are supposed to be observed in sequence. The $n$th value in the sequence is a $k-record~value$ if exactly $k$ of the first $n$ values (including $X_n$) are at least as large as it. Let ${\\bf R}_k$ denote the ordered set of $k$-record values. The famous Ignatov's Theorem states that the random sets ${\\bf R}_k(k=1,2,\\cdots)$ are independent with common distribution. We introduce one new record named $recent-k-record$ (RkR in short) in this paper: $X_n$ is a $j$-RkR if there are exactly $j$ values at least as large as $X_n$ in $X"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.06791","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.06791/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpIYH8Tj7R3VsGAM4+DIWzf4jLrIIvipsi+GTRwu5CRAEQhR5bqAIecqwD9NS36XDW/CVYcihGVxofc8/N2wBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T23:37:34.646712Z"},"content_sha256":"6dfaa820c8599cb0e33b83e5f2cb9ac521948f5f0cddbc7e91d220411346a4df","schema_version":"1.0","event_id":"sha256:6dfaa820c8599cb0e33b83e5f2cb9ac521948f5f0cddbc7e91d220411346a4df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCW3CMOHIEYRLU2533DBDVLESS/bundle.json","state_url":"https://pith.science/pith/HCW3CMOHIEYRLU2533DBDVLESS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCW3CMOHIEYRLU2533DBDVLESS/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":"2026-08-17T23:37:34Z","links":{"resolver":"https://pith.science/pith/HCW3CMOHIEYRLU2533DBDVLESS","bundle":"https://pith.science/pith/HCW3CMOHIEYRLU2533DBDVLESS/bundle.json","state":"https://pith.science/pith/HCW3CMOHIEYRLU2533DBDVLESS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCW3CMOHIEYRLU2533DBDVLESS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HCW3CMOHIEYRLU2533DBDVLESS","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":"bb304f036ea98c522047199871981b30ae161b64867f4b428d46d3e3f6eef18c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-08-14T06:29:09Z","title_canon_sha256":"672e18f4cecdd6a3bf44c78deb301ea238868e10233a76ef7d97f398fc55fd11"},"schema_version":"1.0","source":{"id":"2208.06791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.06791","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"2208.06791v1","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.06791","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"HCW3CMOHIEYR","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"pith_short_16","alias_value":"HCW3CMOHIEYRLU25","created_at":"2026-07-05T04:48:20Z"},{"alias_kind":"pith_short_8","alias_value":"HCW3CMOH","created_at":"2026-07-05T04:48:20Z"}],"graph_snapshots":[{"event_id":"sha256:6dfaa820c8599cb0e33b83e5f2cb9ac521948f5f0cddbc7e91d220411346a4df","target":"graph","created_at":"2026-07-05T04:48:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.06791/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X_1,~X_2,\\cdots$ be a sequence of i.i.d random variables which are supposed to be observed in sequence. The $n$th value in the sequence is a $k-record~value$ if exactly $k$ of the first $n$ values (including $X_n$) are at least as large as it. Let ${\\bf R}_k$ denote the ordered set of $k$-record values. The famous Ignatov's Theorem states that the random sets ${\\bf R}_k(k=1,2,\\cdots)$ are independent with common distribution. We introduce one new record named $recent-k-record$ (RkR in short) in this paper: $X_n$ is a $j$-RkR if there are exactly $j$ values at least as large as $X_n$ in $X","authors_text":"Anshui Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-08-14T06:29:09Z","title":"On the recent-$k$-record of discrete random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.06791","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:a0bf6e61a44885df20444bf3d393d8bb3b1d9094aa8f6a7ff90769bb7a8b866a","target":"record","created_at":"2026-07-05T04:48:20Z","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":"bb304f036ea98c522047199871981b30ae161b64867f4b428d46d3e3f6eef18c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-08-14T06:29:09Z","title_canon_sha256":"672e18f4cecdd6a3bf44c78deb301ea238868e10233a76ef7d97f398fc55fd11"},"schema_version":"1.0","source":{"id":"2208.06791","kind":"arxiv","version":1}},"canonical_sha256":"38adb131c7413115d35ddec611d56494b029d6a7d78dbcdc58b5a6f231c8aa1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38adb131c7413115d35ddec611d56494b029d6a7d78dbcdc58b5a6f231c8aa1b","first_computed_at":"2026-07-05T04:48:20.756960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:48:20.756960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KhM8ZWsGJ6o8vjT9/27FPJuQ7VMdlEUSK9mls7qZ1dGemTHSiAbcM1dtJcPqNhlmTedoWRmA/O4Q1mNwXLpOCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:48:20.757307Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.06791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0bf6e61a44885df20444bf3d393d8bb3b1d9094aa8f6a7ff90769bb7a8b866a","sha256:6dfaa820c8599cb0e33b83e5f2cb9ac521948f5f0cddbc7e91d220411346a4df"],"state_sha256":"617d677e9f53b6fad069e41e9357fbafbdc6ac081af61ce963839f597f180522"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XuasqBJffWCdtPVDrwCMSUL2yiNrzpXDM/cYksgXM95Zqi7Gy+PG6P2tiP/VA4mtM1BWSiDXkiwB/TnA9+3ZAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T23:37:34.650422Z","bundle_sha256":"1d7a93a2512c23ba4a9ce9419d7caa66fb3482de68e4e2966adfec82e4086cea"}}