{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QGMIBJHSSP5YKODTGQKJRCGAW2","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":"8e096473d8fb85beac10c2e221fbd59e8a0ee3a1a7eb118751516bb1c96ee644","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-06T16:43:13Z","title_canon_sha256":"1b09074b2dd7b479af0c154b383a28b80ba472130d79fb22e1f338f61abae32a"},"schema_version":"1.0","source":{"id":"1809.02085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02085","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02085v1","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02085","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"QGMIBJHSSP5Y","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QGMIBJHSSP5YKODT","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QGMIBJHS","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:2bc713199d80484f6242714edc466f16fa14a38c9dcd3ec81cc8e05d946a1572","target":"graph","created_at":"2026-05-18T00:06:21Z","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":"An $\\mathbb{R}^d$-valued Markov process $X^{(x)}_t=(X^{1,x_1}_t,\\dots,X^{d,x_d}_t)$, $t\\ge0,x\\in\\mathbb{R}^d$ is said to be multi-self-similar with index $(\\alpha_1,\\dots,\\alpha_d)\\in[0,\\infty)^d$ if the identity in law \\[(c_iX_t^{i,x_i/c_i};i=1,\\dots,d)_{t\\ge0}\\ed(X_{ct}^{(x)})_{t\\ge0}\\,,\\] where $c=\\prod_{i=1}^dc_i^{\\alpha_i}$, is satisfied for all $c_1,\\dots,c_d>0$ and all starting point $x$. Multi-self-similar Markov processes were introduced by Jacobsen and Yor \\cite{jy} in the aim of extending the Lamperti transformation of positive self-similar Markov processes to $\\mathbb{R}^d_+$-value","authors_text":"Lo\\\"ic Chaumont, Salem Lamine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-06T16:43:13Z","title":"On $\\mathbb{R}^d$-valued multi-self-similar Markov processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02085","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:df62cdd497507ed82436fde2a7de1e26e79d5c32ba988dcd9093b4a7f4344564","target":"record","created_at":"2026-05-18T00:06:21Z","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":"8e096473d8fb85beac10c2e221fbd59e8a0ee3a1a7eb118751516bb1c96ee644","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-06T16:43:13Z","title_canon_sha256":"1b09074b2dd7b479af0c154b383a28b80ba472130d79fb22e1f338f61abae32a"},"schema_version":"1.0","source":{"id":"1809.02085","kind":"arxiv","version":1}},"canonical_sha256":"819880a4f293fb85387334149888c0b69176e1758728540f71d36846257e95ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"819880a4f293fb85387334149888c0b69176e1758728540f71d36846257e95ee","first_computed_at":"2026-05-18T00:06:21.401101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:21.401101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ofBTi5c8ch935R31qVAkaNujVcBL90ZXJNws0em2TvZsP4UbTGb/jbpzLyJ1x1NO8n0h9V23cuXFyRFFaZjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:21.401566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df62cdd497507ed82436fde2a7de1e26e79d5c32ba988dcd9093b4a7f4344564","sha256:2bc713199d80484f6242714edc466f16fa14a38c9dcd3ec81cc8e05d946a1572"],"state_sha256":"f9a25ec8992a2a0ac9396b2aba2d9907fd6808043ac147d379d957d16abc2f80"}