{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7AMJXQMCS43CFLNPBNRCRFIDYX","short_pith_number":"pith:7AMJXQMC","canonical_record":{"source":{"id":"1107.1794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-09T15:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"b9f28be606c73bd163c9a299f0ca247f78e40a3d3f821fef549b881bdc2bff1f","abstract_canon_sha256":"03a3ac05bcc91b3623cac5f0774c0c08fa1b6d970f237d6ca18fe3d456a1953d"},"schema_version":"1.0"},"canonical_sha256":"f8189bc182973622adaf0b62289503c5eec1e639716601971cd689c556e8cec4","source":{"kind":"arxiv","id":"1107.1794","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1794","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1794v2","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1794","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"7AMJXQMCS43C","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7AMJXQMCS43CFLNP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7AMJXQMC","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7AMJXQMCS43CFLNPBNRCRFIDYX","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-09T15:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"b9f28be606c73bd163c9a299f0ca247f78e40a3d3f821fef549b881bdc2bff1f","abstract_canon_sha256":"03a3ac05bcc91b3623cac5f0774c0c08fa1b6d970f237d6ca18fe3d456a1953d"},"schema_version":"1.0"},"canonical_sha256":"f8189bc182973622adaf0b62289503c5eec1e639716601971cd689c556e8cec4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:39.581932Z","signature_b64":"ZJQbKL0lDE5HsmqpftvwN6P/OQ/f0dc5AvpD5e/rCgDpiBnqJEqS8A1/YUBSIS1VZfAH5tEUQxQcBhz8MxHOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8189bc182973622adaf0b62289503c5eec1e639716601971cd689c556e8cec4","last_reissued_at":"2026-05-18T03:58:39.581367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:39.581367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1794","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hR/R0eKeqyvughw4J8MlQAhsyHZJovBDhpe7+b5L0V+YpRoaAf4IlcYz2sPYPqf7pvWYV9Cv92drpIggI4rKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:53:00.047078Z"},"content_sha256":"1fdfa2e7c24b1700eaa4d03ae29efc5d4caa405a6c213bb964cffe9249043620","schema_version":"1.0","event_id":"sha256:1fdfa2e7c24b1700eaa4d03ae29efc5d4caa405a6c213bb964cffe9249043620"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7AMJXQMCS43CFLNPBNRCRFIDYX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Aspects of Modeling Dependence in Copula-based Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Magda Peligrad, Martial Longla","submitted_at":"2011-07-09T15:54:30Z","abstract_excerpt":"Dependence coefficients have been widely studied for Markov processes defined by a set of transition probabilities and an initial distribution. This work clarifies some aspects of the theory of dependence structure of Markov chains generated by copulas that are useful in time series econometrics and other applied fields. The main aim of this paper is to clarify the relationship between the notions of geometric ergodicity and geometric {\\rho}-mixing; namely, to point out that for a large number of well known copulas, such as Clayton, Gumbel or Student, these notions are equivalent. Some of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1794","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":"2026-05-18T03:58:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SJn+JeCNWQF4teDj6Z6x79SlRTd+kjU8im0qT3Ti4fw+TPK6LkLcucVm2e4PShyLwaCg7R17RceuA6R1EfkpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:53:00.047444Z"},"content_sha256":"19257b706ec68a0d98d197e8cadb6b6a3bddba4158ef374408b69d059533bf40","schema_version":"1.0","event_id":"sha256:19257b706ec68a0d98d197e8cadb6b6a3bddba4158ef374408b69d059533bf40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AMJXQMCS43CFLNPBNRCRFIDYX/bundle.json","state_url":"https://pith.science/pith/7AMJXQMCS43CFLNPBNRCRFIDYX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AMJXQMCS43CFLNPBNRCRFIDYX/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":"2026-05-28T14:53:00Z","links":{"resolver":"https://pith.science/pith/7AMJXQMCS43CFLNPBNRCRFIDYX","bundle":"https://pith.science/pith/7AMJXQMCS43CFLNPBNRCRFIDYX/bundle.json","state":"https://pith.science/pith/7AMJXQMCS43CFLNPBNRCRFIDYX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AMJXQMCS43CFLNPBNRCRFIDYX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7AMJXQMCS43CFLNPBNRCRFIDYX","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":"03a3ac05bcc91b3623cac5f0774c0c08fa1b6d970f237d6ca18fe3d456a1953d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-09T15:54:30Z","title_canon_sha256":"b9f28be606c73bd163c9a299f0ca247f78e40a3d3f821fef549b881bdc2bff1f"},"schema_version":"1.0","source":{"id":"1107.1794","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1794","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1794v2","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1794","created_at":"2026-05-18T03:58:39Z"},{"alias_kind":"pith_short_12","alias_value":"7AMJXQMCS43C","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7AMJXQMCS43CFLNP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7AMJXQMC","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:19257b706ec68a0d98d197e8cadb6b6a3bddba4158ef374408b69d059533bf40","target":"graph","created_at":"2026-05-18T03:58:39Z","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":"Dependence coefficients have been widely studied for Markov processes defined by a set of transition probabilities and an initial distribution. This work clarifies some aspects of the theory of dependence structure of Markov chains generated by copulas that are useful in time series econometrics and other applied fields. The main aim of this paper is to clarify the relationship between the notions of geometric ergodicity and geometric {\\rho}-mixing; namely, to point out that for a large number of well known copulas, such as Clayton, Gumbel or Student, these notions are equivalent. Some of the ","authors_text":"Magda Peligrad, Martial Longla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-09T15:54:30Z","title":"Some Aspects of Modeling Dependence in Copula-based Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1794","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":"sha256:1fdfa2e7c24b1700eaa4d03ae29efc5d4caa405a6c213bb964cffe9249043620","target":"record","created_at":"2026-05-18T03:58:39Z","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":"03a3ac05bcc91b3623cac5f0774c0c08fa1b6d970f237d6ca18fe3d456a1953d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-09T15:54:30Z","title_canon_sha256":"b9f28be606c73bd163c9a299f0ca247f78e40a3d3f821fef549b881bdc2bff1f"},"schema_version":"1.0","source":{"id":"1107.1794","kind":"arxiv","version":2}},"canonical_sha256":"f8189bc182973622adaf0b62289503c5eec1e639716601971cd689c556e8cec4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8189bc182973622adaf0b62289503c5eec1e639716601971cd689c556e8cec4","first_computed_at":"2026-05-18T03:58:39.581367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:39.581367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZJQbKL0lDE5HsmqpftvwN6P/OQ/f0dc5AvpD5e/rCgDpiBnqJEqS8A1/YUBSIS1VZfAH5tEUQxQcBhz8MxHOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:39.581932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1794","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fdfa2e7c24b1700eaa4d03ae29efc5d4caa405a6c213bb964cffe9249043620","sha256:19257b706ec68a0d98d197e8cadb6b6a3bddba4158ef374408b69d059533bf40"],"state_sha256":"729b605c79ff6fb69a9c8ceb87a02aa79d06f4491490cd6cdd24c071bf960e46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SgwknyIMsEXIB1994liYypoknGT3lLjswhONMwksUKZy4Moe0wB5HPJSiJq+yyfgy6px2K6TC1TJs7lLVkwqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:53:00.049527Z","bundle_sha256":"c99212928a4259b0b640043d68096331fd274f7e16f8b77b6db1f59f0cd13801"}}