{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZCPBNZDLVATJUTSWUAKSI36TOW","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":"1ea51d49b2a2d959145647e2cdb4980c71b61f2fcdf5e7f53d68ac04a8254f25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-25T23:13:07Z","title_canon_sha256":"401bdfb26cb91166c379473e68ee1bac9e7832fbc79c44749ff73ff2de736e49"},"schema_version":"1.0","source":{"id":"1502.07399","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07399","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07399v2","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07399","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZCPBNZDLVATJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZCPBNZDLVATJUTSW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZCPBNZDL","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:a3e4782341338d4cf948e1b53aef24cf7e8aef9ab7eeae8df972e2466175e042","target":"graph","created_at":"2026-05-18T01:34:54Z","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":"The Lamperti--Kiu transformation for real-valued self-similar Markov processes (rssMp) states that, associated to each rssMp via a space-time transformation, there is a Markov additive process (MAP). In the case that the rssMp is taken to be an $\\alpha$-stable process with $\\alpha\\in(0,2)$, Chaumont et al. (2013) and Kuznetsov et al. (2014) have computed explicitly the characteristics of the matrix exponent of the semi-group of the embedded MAP, which we henceforth refer to as the {\\it Lamperti-stable MAP}. Specifically, the matrix exponent of the Lamperti-stable MAP's transition semi-group ca","authors_text":"Andreas E. Kyprianou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-25T23:13:07Z","title":"Deep factorisation of the stable process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07399","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":"sha256:45f35548a01a8ea29961df7cddea1a6f028123edde3172bb6150b3f9753cad68","target":"record","created_at":"2026-05-18T01:34:54Z","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":"1ea51d49b2a2d959145647e2cdb4980c71b61f2fcdf5e7f53d68ac04a8254f25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-25T23:13:07Z","title_canon_sha256":"401bdfb26cb91166c379473e68ee1bac9e7832fbc79c44749ff73ff2de736e49"},"schema_version":"1.0","source":{"id":"1502.07399","kind":"arxiv","version":2}},"canonical_sha256":"c89e16e46ba8269a4e56a015246fd37581c0cb6191c8a334185e28a31769d0ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c89e16e46ba8269a4e56a015246fd37581c0cb6191c8a334185e28a31769d0ef","first_computed_at":"2026-05-18T01:34:54.963731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:54.963731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7sHLdz4lAQ2FvEJNcd1M9z/woKLEnTfEtKxlfW/dQrXjLCJFrn9eUT85GgnWwIEb90+BGSHZMLzPhYRfsWTzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:54.964265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07399","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45f35548a01a8ea29961df7cddea1a6f028123edde3172bb6150b3f9753cad68","sha256:a3e4782341338d4cf948e1b53aef24cf7e8aef9ab7eeae8df972e2466175e042"],"state_sha256":"6a5c9d297a7fba3ed13d7637c1d746395caad0ac89e9e57a3e685ae5408386e5"}