{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DJPA7JG7UVYAOKBAI4C3L4UJML","short_pith_number":"pith:DJPA7JG7","canonical_record":{"source":{"id":"1311.3998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-15T23:12:55Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"d485ce9e63adcff500a4208f8eb0aa32d85cf2a1575445015f1f0563820eb01c","abstract_canon_sha256":"c05ec2e85b7a791702002722d9a83ab9499c3450618082c2690caa5803e5af06"},"schema_version":"1.0"},"canonical_sha256":"1a5e0fa4dfa5700728204705b5f28962fcd5b25b40bda75657939918d1a90055","source":{"kind":"arxiv","id":"1311.3998","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3998","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3998v1","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3998","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"DJPA7JG7UVYA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DJPA7JG7UVYAOKBA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DJPA7JG7","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DJPA7JG7UVYAOKBAI4C3L4UJML","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-15T23:12:55Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"d485ce9e63adcff500a4208f8eb0aa32d85cf2a1575445015f1f0563820eb01c","abstract_canon_sha256":"c05ec2e85b7a791702002722d9a83ab9499c3450618082c2690caa5803e5af06"},"schema_version":"1.0"},"canonical_sha256":"1a5e0fa4dfa5700728204705b5f28962fcd5b25b40bda75657939918d1a90055","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:53.973012Z","signature_b64":"v76pH0jmHZf2CRTTGhImHHjDAdTR1AMFHUvR8kSTbvrozavd9Qb0QLWt0wydmz3zUOqdOMUiCd946v+PpjEDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a5e0fa4dfa5700728204705b5f28962fcd5b25b40bda75657939918d1a90055","last_reissued_at":"2026-05-18T03:06:53.972311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:53.972311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3998","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":"2026-05-18T03:06:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DADvKCXObg6pY+2mzAOk43GF2XSSzXpvx+5LQyFG5EHr9D1wZih/dGN9OdEIu9j3SCTt0B2Alib+TN/tRvCABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:13:11.532499Z"},"content_sha256":"4cd478c9654b5395f5804a0a2d5d9f2d846c93514cf9198bb769eb385f966f76","schema_version":"1.0","event_id":"sha256:4cd478c9654b5395f5804a0a2d5d9f2d846c93514cf9198bb769eb385f966f76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DJPA7JG7UVYAOKBAI4C3L4UJML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a Clustering Criterion for Dependent Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Karthik Bharath","submitted_at":"2013-11-15T23:12:55Z","abstract_excerpt":"A univariate clustering criterion for stationary processes satisfying a $\\beta$-mixing condition is proposed extending the work of \\cite{KB2} to the dependent setup. The approach is characterized by an alternative sample criterion function based on truncated partial sums which renders the framework amenable to various interesting extensions for which limit results for partial sums are available. Techniques from empirical process theory for mixing sequences play a vital role in the arguments employed in the proofs of the limit theorems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3998","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":"2026-05-18T03:06:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eJLMtl2mjQ4yoXH38K37hmV/gGYIYktW0hnL9F1rgFTN3Hd3quCRes71ydgkdMWn4K9n418MCWELvc7jol5gDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:13:11.533258Z"},"content_sha256":"4d84901c7e9eabedde95b2cd148e6ce201f48e25a59e42e4aeac7ebe4324552b","schema_version":"1.0","event_id":"sha256:4d84901c7e9eabedde95b2cd148e6ce201f48e25a59e42e4aeac7ebe4324552b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DJPA7JG7UVYAOKBAI4C3L4UJML/bundle.json","state_url":"https://pith.science/pith/DJPA7JG7UVYAOKBAI4C3L4UJML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DJPA7JG7UVYAOKBAI4C3L4UJML/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":"2026-06-10T07:13:11Z","links":{"resolver":"https://pith.science/pith/DJPA7JG7UVYAOKBAI4C3L4UJML","bundle":"https://pith.science/pith/DJPA7JG7UVYAOKBAI4C3L4UJML/bundle.json","state":"https://pith.science/pith/DJPA7JG7UVYAOKBAI4C3L4UJML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DJPA7JG7UVYAOKBAI4C3L4UJML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DJPA7JG7UVYAOKBAI4C3L4UJML","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":"c05ec2e85b7a791702002722d9a83ab9499c3450618082c2690caa5803e5af06","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-15T23:12:55Z","title_canon_sha256":"d485ce9e63adcff500a4208f8eb0aa32d85cf2a1575445015f1f0563820eb01c"},"schema_version":"1.0","source":{"id":"1311.3998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3998","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3998v1","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3998","created_at":"2026-05-18T03:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"DJPA7JG7UVYA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DJPA7JG7UVYAOKBA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DJPA7JG7","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:4d84901c7e9eabedde95b2cd148e6ce201f48e25a59e42e4aeac7ebe4324552b","target":"graph","created_at":"2026-05-18T03:06:53Z","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":"A univariate clustering criterion for stationary processes satisfying a $\\beta$-mixing condition is proposed extending the work of \\cite{KB2} to the dependent setup. The approach is characterized by an alternative sample criterion function based on truncated partial sums which renders the framework amenable to various interesting extensions for which limit results for partial sums are available. Techniques from empirical process theory for mixing sequences play a vital role in the arguments employed in the proofs of the limit theorems.","authors_text":"Karthik Bharath","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-15T23:12:55Z","title":"On a Clustering Criterion for Dependent Observations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3998","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":"sha256:4cd478c9654b5395f5804a0a2d5d9f2d846c93514cf9198bb769eb385f966f76","target":"record","created_at":"2026-05-18T03:06:53Z","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":"c05ec2e85b7a791702002722d9a83ab9499c3450618082c2690caa5803e5af06","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-15T23:12:55Z","title_canon_sha256":"d485ce9e63adcff500a4208f8eb0aa32d85cf2a1575445015f1f0563820eb01c"},"schema_version":"1.0","source":{"id":"1311.3998","kind":"arxiv","version":1}},"canonical_sha256":"1a5e0fa4dfa5700728204705b5f28962fcd5b25b40bda75657939918d1a90055","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a5e0fa4dfa5700728204705b5f28962fcd5b25b40bda75657939918d1a90055","first_computed_at":"2026-05-18T03:06:53.972311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:53.972311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v76pH0jmHZf2CRTTGhImHHjDAdTR1AMFHUvR8kSTbvrozavd9Qb0QLWt0wydmz3zUOqdOMUiCd946v+PpjEDCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:53.973012Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cd478c9654b5395f5804a0a2d5d9f2d846c93514cf9198bb769eb385f966f76","sha256:4d84901c7e9eabedde95b2cd148e6ce201f48e25a59e42e4aeac7ebe4324552b"],"state_sha256":"0126aa0c7bb4f621475d41a8f5dec26d9fc8309e7c1bf1eaa30ba7a19e248df7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pe0YOz7putuPYcGw5/ihppKYTCO6VIcvyO0LazcoCCfydzD8Jcfr+dp6JKG53afu3SgxhwpIn9YzOT1I/rpACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:13:11.537147Z","bundle_sha256":"b920d544fcdb5260c2b2ad443500f59b23ffb4187631b228b2d1f36ce6671e93"}}