{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:O6HRAS55ZGIAY4KWIQPCYWNDIM","short_pith_number":"pith:O6HRAS55","canonical_record":{"source":{"id":"1011.1685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-07T23:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"98d1bb6b70ccd4c13f7b64c50835680d238eb36307ebddf5075abf1d0c4ef981","abstract_canon_sha256":"126e615433265271443d62a9cd86b5fb3d3b798b979a21ed4041f36d5c6ce700"},"schema_version":"1.0"},"canonical_sha256":"778f104bbdc9900c7156441e2c59a3431bd5e3c27e85f224d35ff203fcff04ac","source":{"kind":"arxiv","id":"1011.1685","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1685","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1685v2","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1685","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"O6HRAS55ZGIA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O6HRAS55ZGIAY4KW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O6HRAS55","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:O6HRAS55ZGIAY4KWIQPCYWNDIM","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-07T23:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"98d1bb6b70ccd4c13f7b64c50835680d238eb36307ebddf5075abf1d0c4ef981","abstract_canon_sha256":"126e615433265271443d62a9cd86b5fb3d3b798b979a21ed4041f36d5c6ce700"},"schema_version":"1.0"},"canonical_sha256":"778f104bbdc9900c7156441e2c59a3431bd5e3c27e85f224d35ff203fcff04ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:47.144338Z","signature_b64":"APtAi1rHYgwHUQ5mS8+91pIOnUtsbyGi8kHdTmTz6+Ep1vA5agVUkUB9rmVtIiW21MdF3ctzD7lkHBnkx//qBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"778f104bbdc9900c7156441e2c59a3431bd5e3c27e85f224d35ff203fcff04ac","last_reissued_at":"2026-05-18T04:10:47.143856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:47.143856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1685","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":"2026-05-18T04:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SjTnz81m0+qedi/MU7WOgy7cWCmm7P/glAPFrg1RH4CRfVTMZOBYp8GiTYUn10niaRADB2QC57ThgsnhsjP4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:38:02.847487Z"},"content_sha256":"bd771a7710522d8f08e69cd03faeebc9414f9f990db74aa93a6491b1a488ae56","schema_version":"1.0","event_id":"sha256:bd771a7710522d8f08e69cd03faeebc9414f9f990db74aa93a6491b1a488ae56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:O6HRAS55ZGIAY4KWIQPCYWNDIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dariusz Buraczewski, Ewa Damek, Mariusz Mirek","submitted_at":"2010-11-07T23:02:57Z","abstract_excerpt":"Let $\\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\\R^d$. We study the Markov chain $\\{X_n^x\\}_{n=0}^\\infty$ on $\\R^d$ defined by the recursion $X_n^x = \\Phi_n(X^x_{n-1})$, $n\\in\\N$, $X_0^x=x\\in\\R^d$. We assume that $\\Phi_n(x)=\\Phi(A_n x,B_n(x))$ for a fixed continuous function $\\Phi:\\R^d\\times \\R^d\\to\\R^d$, commuting with dilations and i.i.d random pairs $(A_n,B_n)$, where $A_n\\in {End}(\\R^d)$ and $B_n$ is a continuous mapping of $\\R^d$. Moreover, $B_n$ is $\\alpha$-regularly varying and $A_n$ has a faster decay at infinity than $B_n$. We prove that the stationary measure $\\nu$ of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1685","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":"2026-05-18T04:10:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/xW7sk+kNgWArodHZxmCicVBNFRdlfrBIyHJAMuyzzqs+/BwEGlhUy1uM03+ez5wygtOCnB191CKwZdJnzmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:38:02.847840Z"},"content_sha256":"01687852fc24a42edbf4d778326c78897073c915d50dccb7f6db30af9eb05912","schema_version":"1.0","event_id":"sha256:01687852fc24a42edbf4d778326c78897073c915d50dccb7f6db30af9eb05912"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6HRAS55ZGIAY4KWIQPCYWNDIM/bundle.json","state_url":"https://pith.science/pith/O6HRAS55ZGIAY4KWIQPCYWNDIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6HRAS55ZGIAY4KWIQPCYWNDIM/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":"2026-06-01T19:38:02Z","links":{"resolver":"https://pith.science/pith/O6HRAS55ZGIAY4KWIQPCYWNDIM","bundle":"https://pith.science/pith/O6HRAS55ZGIAY4KWIQPCYWNDIM/bundle.json","state":"https://pith.science/pith/O6HRAS55ZGIAY4KWIQPCYWNDIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6HRAS55ZGIAY4KWIQPCYWNDIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:O6HRAS55ZGIAY4KWIQPCYWNDIM","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":"126e615433265271443d62a9cd86b5fb3d3b798b979a21ed4041f36d5c6ce700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-07T23:02:57Z","title_canon_sha256":"98d1bb6b70ccd4c13f7b64c50835680d238eb36307ebddf5075abf1d0c4ef981"},"schema_version":"1.0","source":{"id":"1011.1685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1685","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1685v2","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1685","created_at":"2026-05-18T04:10:47Z"},{"alias_kind":"pith_short_12","alias_value":"O6HRAS55ZGIA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O6HRAS55ZGIAY4KW","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O6HRAS55","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:01687852fc24a42edbf4d778326c78897073c915d50dccb7f6db30af9eb05912","target":"graph","created_at":"2026-05-18T04:10:47Z","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 $\\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\\R^d$. We study the Markov chain $\\{X_n^x\\}_{n=0}^\\infty$ on $\\R^d$ defined by the recursion $X_n^x = \\Phi_n(X^x_{n-1})$, $n\\in\\N$, $X_0^x=x\\in\\R^d$. We assume that $\\Phi_n(x)=\\Phi(A_n x,B_n(x))$ for a fixed continuous function $\\Phi:\\R^d\\times \\R^d\\to\\R^d$, commuting with dilations and i.i.d random pairs $(A_n,B_n)$, where $A_n\\in {End}(\\R^d)$ and $B_n$ is a continuous mapping of $\\R^d$. Moreover, $B_n$ is $\\alpha$-regularly varying and $A_n$ has a faster decay at infinity than $B_n$. We prove that the stationary measure $\\nu$ of th","authors_text":"Dariusz Buraczewski, Ewa Damek, Mariusz Mirek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-07T23:02:57Z","title":"Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1685","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:bd771a7710522d8f08e69cd03faeebc9414f9f990db74aa93a6491b1a488ae56","target":"record","created_at":"2026-05-18T04:10:47Z","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":"126e615433265271443d62a9cd86b5fb3d3b798b979a21ed4041f36d5c6ce700","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-07T23:02:57Z","title_canon_sha256":"98d1bb6b70ccd4c13f7b64c50835680d238eb36307ebddf5075abf1d0c4ef981"},"schema_version":"1.0","source":{"id":"1011.1685","kind":"arxiv","version":2}},"canonical_sha256":"778f104bbdc9900c7156441e2c59a3431bd5e3c27e85f224d35ff203fcff04ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"778f104bbdc9900c7156441e2c59a3431bd5e3c27e85f224d35ff203fcff04ac","first_computed_at":"2026-05-18T04:10:47.143856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:47.143856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"APtAi1rHYgwHUQ5mS8+91pIOnUtsbyGi8kHdTmTz6+Ep1vA5agVUkUB9rmVtIiW21MdF3ctzD7lkHBnkx//qBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:47.144338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd771a7710522d8f08e69cd03faeebc9414f9f990db74aa93a6491b1a488ae56","sha256:01687852fc24a42edbf4d778326c78897073c915d50dccb7f6db30af9eb05912"],"state_sha256":"a3dbe5f7d30dcbd5f9f89e18e2642056152d8cfa31276cc75713acc4bf08f865"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fbxHPcyooTrXcEY5RRYWpdcYgsL/CzVezlyUhY76ICFuhvZGGQJ3HIHjf7oP/Q4eY5fxQxIo3bcc9/M7KTGwAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:38:02.849769Z","bundle_sha256":"5c20c91087a72d914f89f4d1fa520248f93975c9f769ff02a45db0326eeac900"}}