{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CUYOHCDH7YBTVRZJ4QSDWSJF2S","short_pith_number":"pith:CUYOHCDH","canonical_record":{"source":{"id":"1201.0590","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-03T08:43:31Z","cross_cats_sorted":["math.FA","math.PR","stat.TH"],"title_canon_sha256":"8184dfcc6932ad5659068ed203add5109875690532010673a69a33f639fc9523","abstract_canon_sha256":"1bdeab84f65e50a760940cfaadf4a4f89017772602ec78839907f5f920b607bd"},"schema_version":"1.0"},"canonical_sha256":"1530e38867fe033ac729e4243b4925d48f4ce2867384817138f4de1d30fa05f3","source":{"kind":"arxiv","id":"1201.0590","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0590","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0590v2","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0590","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"CUYOHCDH7YBT","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CUYOHCDH7YBTVRZJ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CUYOHCDH","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CUYOHCDH7YBTVRZJ4QSDWSJF2S","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0590","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-03T08:43:31Z","cross_cats_sorted":["math.FA","math.PR","stat.TH"],"title_canon_sha256":"8184dfcc6932ad5659068ed203add5109875690532010673a69a33f639fc9523","abstract_canon_sha256":"1bdeab84f65e50a760940cfaadf4a4f89017772602ec78839907f5f920b607bd"},"schema_version":"1.0"},"canonical_sha256":"1530e38867fe033ac729e4243b4925d48f4ce2867384817138f4de1d30fa05f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:47.994542Z","signature_b64":"dQg2CLrTYoiZ8HQkXGy4VBBb5m1oMSMJo38Ra9gNBSJ89sHOs1hyavXXT8jM4GDBNHt6yOS34e4DNcJxvwSACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1530e38867fe033ac729e4243b4925d48f4ce2867384817138f4de1d30fa05f3","last_reissued_at":"2026-05-18T03:48:47.993937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:47.993937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0590","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALpL71F3ss3hIGY9EnH2A6JHXXKfgit56yelyWwzECsIBV3vuSfM7ws7YmLUFRIYrdTj012OfdQM/iu9c4fgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:33:40.160188Z"},"content_sha256":"d05d3c5fea14b0d59cf0134b53dc486a1cb950bdcaa2f0f2fdf36dc8c693e0f4","schema_version":"1.0","event_id":"sha256:d05d3c5fea14b0d59cf0134b53dc486a1cb950bdcaa2f0f2fdf36dc8c693e0f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CUYOHCDH7YBTVRZJ4QSDWSJF2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Donsker Theorem for L\\'evy Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Markus Rei\\ss, Richard Nickl","submitted_at":"2012-01-03T08:43:31Z","abstract_excerpt":"Given $n$ equidistant realisations of a L\\'evy process $(L_t,\\,t\\ge 0)$, a natural estimator $\\hat N_n$ for the distribution function $N$ of the L\\'evy measure is constructed. Under a polynomial decay restriction on the characteristic function $\\phi$, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process $\\sqrt n (\\hat N_n -N)$ in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator ${\\cal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0590","kind":"arxiv","version":2},"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":"2026-05-18T03:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZlIn5+rJd9bRIuXTfWr8JZUkblJsjv9ZQnJvK8iANWfGFn/AKwhup9OGFhiymZJ08lXgV3RG9fJNkg+E32lmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:33:40.160679Z"},"content_sha256":"57234113f9ee708f6b588ce39698bcd89da3fe400be57b5f129acb45e8415281","schema_version":"1.0","event_id":"sha256:57234113f9ee708f6b588ce39698bcd89da3fe400be57b5f129acb45e8415281"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUYOHCDH7YBTVRZJ4QSDWSJF2S/bundle.json","state_url":"https://pith.science/pith/CUYOHCDH7YBTVRZJ4QSDWSJF2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUYOHCDH7YBTVRZJ4QSDWSJF2S/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":"2026-05-31T06:33:40Z","links":{"resolver":"https://pith.science/pith/CUYOHCDH7YBTVRZJ4QSDWSJF2S","bundle":"https://pith.science/pith/CUYOHCDH7YBTVRZJ4QSDWSJF2S/bundle.json","state":"https://pith.science/pith/CUYOHCDH7YBTVRZJ4QSDWSJF2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUYOHCDH7YBTVRZJ4QSDWSJF2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CUYOHCDH7YBTVRZJ4QSDWSJF2S","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":"1bdeab84f65e50a760940cfaadf4a4f89017772602ec78839907f5f920b607bd","cross_cats_sorted":["math.FA","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-03T08:43:31Z","title_canon_sha256":"8184dfcc6932ad5659068ed203add5109875690532010673a69a33f639fc9523"},"schema_version":"1.0","source":{"id":"1201.0590","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0590","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0590v2","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0590","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"CUYOHCDH7YBT","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CUYOHCDH7YBTVRZJ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CUYOHCDH","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:57234113f9ee708f6b588ce39698bcd89da3fe400be57b5f129acb45e8415281","target":"graph","created_at":"2026-05-18T03:48:47Z","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":"Given $n$ equidistant realisations of a L\\'evy process $(L_t,\\,t\\ge 0)$, a natural estimator $\\hat N_n$ for the distribution function $N$ of the L\\'evy measure is constructed. Under a polynomial decay restriction on the characteristic function $\\phi$, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process $\\sqrt n (\\hat N_n -N)$ in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator ${\\cal ","authors_text":"Markus Rei\\ss, Richard Nickl","cross_cats":["math.FA","math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-03T08:43:31Z","title":"A Donsker Theorem for L\\'evy Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0590","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:d05d3c5fea14b0d59cf0134b53dc486a1cb950bdcaa2f0f2fdf36dc8c693e0f4","target":"record","created_at":"2026-05-18T03:48:47Z","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":"1bdeab84f65e50a760940cfaadf4a4f89017772602ec78839907f5f920b607bd","cross_cats_sorted":["math.FA","math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-03T08:43:31Z","title_canon_sha256":"8184dfcc6932ad5659068ed203add5109875690532010673a69a33f639fc9523"},"schema_version":"1.0","source":{"id":"1201.0590","kind":"arxiv","version":2}},"canonical_sha256":"1530e38867fe033ac729e4243b4925d48f4ce2867384817138f4de1d30fa05f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1530e38867fe033ac729e4243b4925d48f4ce2867384817138f4de1d30fa05f3","first_computed_at":"2026-05-18T03:48:47.993937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:47.993937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dQg2CLrTYoiZ8HQkXGy4VBBb5m1oMSMJo38Ra9gNBSJ89sHOs1hyavXXT8jM4GDBNHt6yOS34e4DNcJxvwSACg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:47.994542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0590","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d05d3c5fea14b0d59cf0134b53dc486a1cb950bdcaa2f0f2fdf36dc8c693e0f4","sha256:57234113f9ee708f6b588ce39698bcd89da3fe400be57b5f129acb45e8415281"],"state_sha256":"f2c5011d99cdda91ce73c23c0a6fab73a93e0142d45f55b13bcd3f26d7dec0aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBkS0/hDHUPfqJ/ekx5+QR30Hjb4mauhFdRwMRdTVGz9cVjKYxX/f+4IbiLM3QllpoQmiaNU4tEmrOoPJcglAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:33:40.164134Z","bundle_sha256":"6d5cd0fbf9ba5161fa44b7da1154359e2d8f898bc4ea0a339249099751555be1"}}