{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6WBKTSTDYTVJEL5W74YRYCHKG7","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":"dff7b7d519ce3de35db6fee1738125e9e1abce35a23b3afbaade047a376d090c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-06T17:25:34Z","title_canon_sha256":"0e3deb889d24b686393126834f1317c7c4d1708d92bf12dac0e893642467808f"},"schema_version":"1.0","source":{"id":"1809.02103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02103","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02103v1","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02103","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"6WBKTSTDYTVJ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6WBKTSTDYTVJEL5W","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6WBKTSTD","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:4708ae5bb71dfb29d51a422ad6edcb1d0de5056ca9dfc5bdbf79f32538917ece","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":"In this article, we introduce an infinite-dimensional analogue of the $\\alpha$-stable L\\'evy motion, defined as a L\\'evy process $Z=\\{Z(t)\\}_{t \\geq 0}$ with values in the space $\\mathbb{D}$ of c\\`adl\\`ag functions on $[0,1]$, equipped with Skorokhod's $J_1$ topology. For each $t \\geq 0$, $Z(t)$ is an $\\alpha$-stable process with sample paths in $\\mathbb{D}$, denoted by $\\{Z(t,s)\\}_{s\\in [0,1]}$. Intuitively, $Z(t,s)$ gives the value of the process $Z$ at time $t$ and location $s$ in space. This process is closely related to the concept of regular variation for random elements in $\\mathbb{D}$ ","authors_text":"Becem Saidani, Raluca M. Balan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-06T17:25:34Z","title":"Stable L\\'evy motion with values in the Skorokhod space: construction and approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02103","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:ecc386a5769ac9ada6053302dbfd7203fda8fe87531050579e9533dd93321844","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":"dff7b7d519ce3de35db6fee1738125e9e1abce35a23b3afbaade047a376d090c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-06T17:25:34Z","title_canon_sha256":"0e3deb889d24b686393126834f1317c7c4d1708d92bf12dac0e893642467808f"},"schema_version":"1.0","source":{"id":"1809.02103","kind":"arxiv","version":1}},"canonical_sha256":"f582a9ca63c4ea922fb6ff311c08ea37e2b117b94eb47849c7c4ac4a6e8ee5aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f582a9ca63c4ea922fb6ff311c08ea37e2b117b94eb47849c7c4ac4a6e8ee5aa","first_computed_at":"2026-05-18T00:06:21.371470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:21.371470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BbrQrA61fcf22YwmUuFl6Y4x8S7UXfgbygkvudjXBBkVRZdohbxmzFVMX/JCGNYQTgGBrDGNRBBgZlYPIEC2DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:21.371811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecc386a5769ac9ada6053302dbfd7203fda8fe87531050579e9533dd93321844","sha256:4708ae5bb71dfb29d51a422ad6edcb1d0de5056ca9dfc5bdbf79f32538917ece"],"state_sha256":"38696940bed2799fc7349bf5d35260946ef8bee3298c58fab048a656a792f0f0"}