{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7NQWHRZTTXFWKH2D3ASWZKZJAG","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":"8bdbdfcf26956c68f63e3fd192ce4b4c3d7c6511359e4c2b4a21b7c002f0a65d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-18T14:24:10Z","title_canon_sha256":"8c5d20f7b76df8dd4a9d8d0e992719896afd2e594f727615d525d18de0f3e0d4"},"schema_version":"1.0","source":{"id":"1207.4381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4381","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4381v2","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4381","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"7NQWHRZTTXFW","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7NQWHRZTTXFWKH2D","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7NQWHRZT","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:f392e26b670cb88ae9687d11ccc72aab302ceff28d18f2d39effbd83ad3df99d","target":"graph","created_at":"2026-05-18T01:22:03Z","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 inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive a relationship between weak convergence of a Levy process to an infinite variance stable distribution when time approaches zero and weak convergence of a different Levy process as time approaches infinity. This allows us to get self contained conditions for a Levy process to converge to an infinite variance stable distribution as time approaches zero. We formulate our results both for general Levy processes and for t","authors_text":"Michael Grabchak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-18T14:24:10Z","title":"Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4381","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":"sha256:56ae4feab212b00c8aeb078901f8527d96c00fbed2510113f137419dcbcf9522","target":"record","created_at":"2026-05-18T01:22:03Z","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":"8bdbdfcf26956c68f63e3fd192ce4b4c3d7c6511359e4c2b4a21b7c002f0a65d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-18T14:24:10Z","title_canon_sha256":"8c5d20f7b76df8dd4a9d8d0e992719896afd2e594f727615d525d18de0f3e0d4"},"schema_version":"1.0","source":{"id":"1207.4381","kind":"arxiv","version":2}},"canonical_sha256":"fb6163c7339dcb651f43d8256cab29018bc80f56376e6aa30e121fd013099de7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb6163c7339dcb651f43d8256cab29018bc80f56376e6aa30e121fd013099de7","first_computed_at":"2026-05-18T01:22:03.602355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:03.602355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+jdIyIqzdwCc2BxQ69+YhvjxFkGkM4IuBZjbCdHz2gH40tSusiFH8KnGVfoy0VbYOFli/UxWvXHtJskClgotAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:03.602897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56ae4feab212b00c8aeb078901f8527d96c00fbed2510113f137419dcbcf9522","sha256:f392e26b670cb88ae9687d11ccc72aab302ceff28d18f2d39effbd83ad3df99d"],"state_sha256":"035fb946688ede934b18b7e2805679df758dd537fe69daf8e002404d4d8423e6"}