{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VEKMFTLXGAQHHNGMFSNRUBLUWY","short_pith_number":"pith:VEKMFTLX","canonical_record":{"source":{"id":"1503.06623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-23T12:50:10Z","cross_cats_sorted":[],"title_canon_sha256":"3be8eb709adb2c94d262e9a409653c6bf3447beb68c9ff21e71570666f388d80","abstract_canon_sha256":"3e2ac192b09c3b56c3dbf69367742998581d75c1864d36162e86f86dc7bc3f6d"},"schema_version":"1.0"},"canonical_sha256":"a914c2cd77302073b4cc2c9b1a0574b60726302d0ce428efce52cd8ebddfeb6e","source":{"kind":"arxiv","id":"1503.06623","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06623","created_at":"2026-05-18T02:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06623v1","created_at":"2026-05-18T02:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06623","created_at":"2026-05-18T02:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"VEKMFTLXGAQH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VEKMFTLXGAQHHNGM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VEKMFTLX","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VEKMFTLXGAQHHNGMFSNRUBLUWY","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-23T12:50:10Z","cross_cats_sorted":[],"title_canon_sha256":"3be8eb709adb2c94d262e9a409653c6bf3447beb68c9ff21e71570666f388d80","abstract_canon_sha256":"3e2ac192b09c3b56c3dbf69367742998581d75c1864d36162e86f86dc7bc3f6d"},"schema_version":"1.0"},"canonical_sha256":"a914c2cd77302073b4cc2c9b1a0574b60726302d0ce428efce52cd8ebddfeb6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:37.793033Z","signature_b64":"1U0AM/RGC71OgkLcIhWeYOtm86AYnsD9IpfpFz/1KMm0rh5a+avtg+H0ChfkMetQuBBl22KQ29ylZXkABkgHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a914c2cd77302073b4cc2c9b1a0574b60726302d0ce428efce52cd8ebddfeb6e","last_reissued_at":"2026-05-18T02:20:37.792182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:37.792182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06623","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":"2026-05-18T02:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eB6F0NHeA1+lQ/wfYbpdajZVu0gh6Qy0XUETXXwEFadpUWEWujPSPTyUyE016mTRZEqYYelczlDELP6KdsXUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:32:15.760299Z"},"content_sha256":"ec1f8482bcf755303d0c752f91482c269bac343a6b9e4750b650f25cf5359741","schema_version":"1.0","event_id":"sha256:ec1f8482bcf755303d0c752f91482c269bac343a6b9e4750b650f25cf5359741"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VEKMFTLXGAQHHNGMFSNRUBLUWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multistable L\\'evy motions and their continuous approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jacques L\\'evy V\\'ehel, Xiequan Fan","submitted_at":"2015-03-23T12:50:10Z","abstract_excerpt":"Multistable L\\'evy motions are extensions of L\\'evy motions where the stability index is allowed to vary in time. Several constructions of these processes have been introduced recently, based on Poisson and Ferguson-Klass-LePage series representations and on multistable measures. In this work, we prove a functional central limit theorem for the independent-increments multistable L\\'evy motion, as well as of integrals with respect to these processes, using weighted sums of independent random variables. This allows us to construct continuous approximations of multistable L\\'evy motions. In parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06623","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":"2026-05-18T02:20:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DUQ+0bNImQYEGHAsWQxu5MuJQ51cArxrjpx0tzO89zZppq5K4wh97A8i2gehYMw/ics/cKLfbhPBL75QLNWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:32:15.760678Z"},"content_sha256":"ffb6e02fff49ab5f59ff368dc5ae6f33f5f66183e5cfb419b0e7eae7783e1e7a","schema_version":"1.0","event_id":"sha256:ffb6e02fff49ab5f59ff368dc5ae6f33f5f66183e5cfb419b0e7eae7783e1e7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VEKMFTLXGAQHHNGMFSNRUBLUWY/bundle.json","state_url":"https://pith.science/pith/VEKMFTLXGAQHHNGMFSNRUBLUWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VEKMFTLXGAQHHNGMFSNRUBLUWY/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":"2026-06-23T03:32:15Z","links":{"resolver":"https://pith.science/pith/VEKMFTLXGAQHHNGMFSNRUBLUWY","bundle":"https://pith.science/pith/VEKMFTLXGAQHHNGMFSNRUBLUWY/bundle.json","state":"https://pith.science/pith/VEKMFTLXGAQHHNGMFSNRUBLUWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VEKMFTLXGAQHHNGMFSNRUBLUWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VEKMFTLXGAQHHNGMFSNRUBLUWY","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":"3e2ac192b09c3b56c3dbf69367742998581d75c1864d36162e86f86dc7bc3f6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-23T12:50:10Z","title_canon_sha256":"3be8eb709adb2c94d262e9a409653c6bf3447beb68c9ff21e71570666f388d80"},"schema_version":"1.0","source":{"id":"1503.06623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06623","created_at":"2026-05-18T02:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06623v1","created_at":"2026-05-18T02:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06623","created_at":"2026-05-18T02:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"VEKMFTLXGAQH","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VEKMFTLXGAQHHNGM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VEKMFTLX","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:ffb6e02fff49ab5f59ff368dc5ae6f33f5f66183e5cfb419b0e7eae7783e1e7a","target":"graph","created_at":"2026-05-18T02:20:37Z","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":"Multistable L\\'evy motions are extensions of L\\'evy motions where the stability index is allowed to vary in time. Several constructions of these processes have been introduced recently, based on Poisson and Ferguson-Klass-LePage series representations and on multistable measures. In this work, we prove a functional central limit theorem for the independent-increments multistable L\\'evy motion, as well as of integrals with respect to these processes, using weighted sums of independent random variables. This allows us to construct continuous approximations of multistable L\\'evy motions. In parti","authors_text":"Jacques L\\'evy V\\'ehel, Xiequan Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-23T12:50:10Z","title":"Multistable L\\'evy motions and their continuous approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06623","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:ec1f8482bcf755303d0c752f91482c269bac343a6b9e4750b650f25cf5359741","target":"record","created_at":"2026-05-18T02:20:37Z","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":"3e2ac192b09c3b56c3dbf69367742998581d75c1864d36162e86f86dc7bc3f6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-23T12:50:10Z","title_canon_sha256":"3be8eb709adb2c94d262e9a409653c6bf3447beb68c9ff21e71570666f388d80"},"schema_version":"1.0","source":{"id":"1503.06623","kind":"arxiv","version":1}},"canonical_sha256":"a914c2cd77302073b4cc2c9b1a0574b60726302d0ce428efce52cd8ebddfeb6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a914c2cd77302073b4cc2c9b1a0574b60726302d0ce428efce52cd8ebddfeb6e","first_computed_at":"2026-05-18T02:20:37.792182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:37.792182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1U0AM/RGC71OgkLcIhWeYOtm86AYnsD9IpfpFz/1KMm0rh5a+avtg+H0ChfkMetQuBBl22KQ29ylZXkABkgHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:37.793033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec1f8482bcf755303d0c752f91482c269bac343a6b9e4750b650f25cf5359741","sha256:ffb6e02fff49ab5f59ff368dc5ae6f33f5f66183e5cfb419b0e7eae7783e1e7a"],"state_sha256":"eb49618fdeaad1d4496151bf5a5f2a4bf8aae003b0b7d0da72e9100f982ba6ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xq2Cl0RaKLGmf/uaJFWvzP76/gVFVMOYlAw9KMFmlJ1Qmb0W3jUOZWIGE3Q0VBwOjH2g++zK6IiP7OtU+eqsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:32:15.762613Z","bundle_sha256":"40e1234fc747d58f982d0726d3313c3df16f337540c7dc2f30e8b26176f1b844"}}