{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6SIRWZJZ7RJTUOTIBYWLJ4ZWWX","short_pith_number":"pith:6SIRWZJZ","canonical_record":{"source":{"id":"1201.4579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-22T17:31:11Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"9e8d3cdd77360def096313844a975801c6ca9fc1d72af4a4350a2ae4f820f0d5","abstract_canon_sha256":"ae7c590f086c6b58dacd7dcfd6e183a62b966512b0e7ecb65eb99de49b85ff0c"},"schema_version":"1.0"},"canonical_sha256":"f4911b6539fc533a3a680e2cb4f336b5ccfd6be9b694b9c43884fd0e725134bd","source":{"kind":"arxiv","id":"1201.4579","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4579","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4579v1","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4579","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"6SIRWZJZ7RJT","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6SIRWZJZ7RJTUOTI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6SIRWZJZ","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6SIRWZJZ7RJTUOTIBYWLJ4ZWWX","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-22T17:31:11Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"9e8d3cdd77360def096313844a975801c6ca9fc1d72af4a4350a2ae4f820f0d5","abstract_canon_sha256":"ae7c590f086c6b58dacd7dcfd6e183a62b966512b0e7ecb65eb99de49b85ff0c"},"schema_version":"1.0"},"canonical_sha256":"f4911b6539fc533a3a680e2cb4f336b5ccfd6be9b694b9c43884fd0e725134bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:09.128805Z","signature_b64":"pA+C9TXpseDRqskA0TTre0FFX+VBK9wjDwt5/G0kZkYZyoj3c4BQ0OOzmjvYJPmqS4fu3kx3cXHEkylSfbdqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4911b6539fc533a3a680e2cb4f336b5ccfd6be9b694b9c43884fd0e725134bd","last_reissued_at":"2026-05-18T03:50:09.127998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:09.127998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4579","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":"2026-05-18T03:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Eaxzq+ArzVGBzCHqU66jL/vz5i9gffY3uyBVQdwpO9x27v3+H/I/y6PyEj6x70N1pW8PS8Scsp97XTGhXiKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:28:01.598718Z"},"content_sha256":"6ce4ef84d5427a483ac22128424628edaa65902101b852bd2af75b198159e727","schema_version":"1.0","event_id":"sha256:6ce4ef84d5427a483ac22128424628edaa65902101b852bd2af75b198159e727"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6SIRWZJZ7RJTUOTIBYWLJ4ZWWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit theorems for stationary Markov processes with L2-spectral gap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Deborah Ferre (IRMAR), James Ledoux (IRMAR), Lo\\\"ic Herv\\'e (IRMAR)","submitted_at":"2012-01-22T17:31:11Z","abstract_excerpt":"Let $(X_t, Y_t)_{t\\in T}$ be a discrete or continuous-time Markov process with state space $X \\times R^d$ where $X$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. $(X_t, Y_t)_{t\\in T}$ is assumed to be a Markov additive process. In particular, this implies that the first component $(X_t)_{t\\in T}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process $(Y_t)_{t\\in T}$ is shown to satisfy the following cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4579","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":"2026-05-18T03:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1dlnDnu4tuz2jdozZUS+q6Sdv/VhgXOrfWJtHG7jzvpIkhwJhDZdc9h7l+n9B0SvJJ7YNw9l9Ou4ChNTfZB3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:28:01.599070Z"},"content_sha256":"39f48d1c9d40d801bd8db9779cbf71caeb4cdf9430edf69da19f5847241363a5","schema_version":"1.0","event_id":"sha256:39f48d1c9d40d801bd8db9779cbf71caeb4cdf9430edf69da19f5847241363a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SIRWZJZ7RJTUOTIBYWLJ4ZWWX/bundle.json","state_url":"https://pith.science/pith/6SIRWZJZ7RJTUOTIBYWLJ4ZWWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SIRWZJZ7RJTUOTIBYWLJ4ZWWX/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":"2026-05-28T09:28:01Z","links":{"resolver":"https://pith.science/pith/6SIRWZJZ7RJTUOTIBYWLJ4ZWWX","bundle":"https://pith.science/pith/6SIRWZJZ7RJTUOTIBYWLJ4ZWWX/bundle.json","state":"https://pith.science/pith/6SIRWZJZ7RJTUOTIBYWLJ4ZWWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SIRWZJZ7RJTUOTIBYWLJ4ZWWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6SIRWZJZ7RJTUOTIBYWLJ4ZWWX","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":"ae7c590f086c6b58dacd7dcfd6e183a62b966512b0e7ecb65eb99de49b85ff0c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-22T17:31:11Z","title_canon_sha256":"9e8d3cdd77360def096313844a975801c6ca9fc1d72af4a4350a2ae4f820f0d5"},"schema_version":"1.0","source":{"id":"1201.4579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4579","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4579v1","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4579","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"6SIRWZJZ7RJT","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6SIRWZJZ7RJTUOTI","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6SIRWZJZ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:39f48d1c9d40d801bd8db9779cbf71caeb4cdf9430edf69da19f5847241363a5","target":"graph","created_at":"2026-05-18T03:50:09Z","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":"Let $(X_t, Y_t)_{t\\in T}$ be a discrete or continuous-time Markov process with state space $X \\times R^d$ where $X$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. $(X_t, Y_t)_{t\\in T}$ is assumed to be a Markov additive process. In particular, this implies that the first component $(X_t)_{t\\in T}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process $(Y_t)_{t\\in T}$ is shown to satisfy the following cl","authors_text":"Deborah Ferre (IRMAR), James Ledoux (IRMAR), Lo\\\"ic Herv\\'e (IRMAR)","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-22T17:31:11Z","title":"Limit theorems for stationary Markov processes with L2-spectral gap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4579","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":"sha256:6ce4ef84d5427a483ac22128424628edaa65902101b852bd2af75b198159e727","target":"record","created_at":"2026-05-18T03:50:09Z","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":"ae7c590f086c6b58dacd7dcfd6e183a62b966512b0e7ecb65eb99de49b85ff0c","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-22T17:31:11Z","title_canon_sha256":"9e8d3cdd77360def096313844a975801c6ca9fc1d72af4a4350a2ae4f820f0d5"},"schema_version":"1.0","source":{"id":"1201.4579","kind":"arxiv","version":1}},"canonical_sha256":"f4911b6539fc533a3a680e2cb4f336b5ccfd6be9b694b9c43884fd0e725134bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4911b6539fc533a3a680e2cb4f336b5ccfd6be9b694b9c43884fd0e725134bd","first_computed_at":"2026-05-18T03:50:09.127998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:09.127998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pA+C9TXpseDRqskA0TTre0FFX+VBK9wjDwt5/G0kZkYZyoj3c4BQ0OOzmjvYJPmqS4fu3kx3cXHEkylSfbdqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:09.128805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ce4ef84d5427a483ac22128424628edaa65902101b852bd2af75b198159e727","sha256:39f48d1c9d40d801bd8db9779cbf71caeb4cdf9430edf69da19f5847241363a5"],"state_sha256":"08e72b4acfb152a111a6a4c6e81efef0df36a9e87cac6728bcb6ef9a274f7afa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vH1hV0FLbu/R6WYzKsQCK26JUunrPbMsgplaiuVqrhpqaLAUY9Lt4gd3q31XqJfiRlWBZPP3zPpnw/ciJ1ndDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:28:01.601349Z","bundle_sha256":"cfdfee4a75d695b5f3b6a27aab57a5f2d4ba14aeda18c71678514ba7a69772a6"}}