{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IPIHAISDBHVYOKVGLZ42SXMDXY","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":"758a30643cfac1105900f0e0c9765fbcf47645a42e1611b24b196970903d6680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-29T00:53:18Z","title_canon_sha256":"a6b6966b3e3c8bfa25be99e950f4460d13f5d3f40b33aa3999086830342e8f24"},"schema_version":"1.0","source":{"id":"1201.6006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6006","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6006v1","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6006","created_at":"2026-05-18T03:21:31Z"},{"alias_kind":"pith_short_12","alias_value":"IPIHAISDBHVY","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IPIHAISDBHVYOKVG","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IPIHAISD","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:a24045bd2e7920639bde14bb8921dd466088bd1a0c9a582775d2d6c77d20c0ac","target":"graph","created_at":"2026-05-18T03:21:31Z","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 paper we define the closure under weak convergence of the class of p-tempered {\\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element in this class can be approximated by the distribution of a linear combination of elementary p-tempered {\\alpha}-stable random variables.","authors_text":"Michael Grabchak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-29T00:53:18Z","title":"Limit Theorems For Sequences of Tempered Stable and Related Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6006","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:ba784b7e41e750c55dfa37274703da569474322c9cdbd7c00bd5add16fb98641","target":"record","created_at":"2026-05-18T03:21:31Z","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":"758a30643cfac1105900f0e0c9765fbcf47645a42e1611b24b196970903d6680","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-29T00:53:18Z","title_canon_sha256":"a6b6966b3e3c8bfa25be99e950f4460d13f5d3f40b33aa3999086830342e8f24"},"schema_version":"1.0","source":{"id":"1201.6006","kind":"arxiv","version":1}},"canonical_sha256":"43d070224309eb872aa65e79a95d83be043a683af6d2b19278500ed28490b5b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43d070224309eb872aa65e79a95d83be043a683af6d2b19278500ed28490b5b5","first_computed_at":"2026-05-18T03:21:31.951765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:31.951765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WwJ6MDULWQEf6JSTo65pkjpB4/NDhE8OolGx6oILwqnzzEwRxhLq9Vxqvjm050oWQGSYtMF2U8Palf25SFnZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:31.952383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba784b7e41e750c55dfa37274703da569474322c9cdbd7c00bd5add16fb98641","sha256:a24045bd2e7920639bde14bb8921dd466088bd1a0c9a582775d2d6c77d20c0ac"],"state_sha256":"92d32b7a6792174113b540c75245f21e350d1b0f385d683057617dc4f5edb836"}