{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SMKB3MKKAY4Z6I35P3QOWBTDNR","short_pith_number":"pith:SMKB3MKK","canonical_record":{"source":{"id":"1306.5431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-23T16:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"dd3caf433c7e6e1a4f1c9166a88adf8311f29e4c84cae71d44ae577cc4a323e7","abstract_canon_sha256":"6c83b6d15b61830bb594c341c3d3603201bbc864c92b5b62527b28e8427cf86c"},"schema_version":"1.0"},"canonical_sha256":"93141db14a06399f237d7ee0eb06636c5a4bea93cc5c6b5f78f932fbe05d381b","source":{"kind":"arxiv","id":"1306.5431","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5431","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5431v2","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5431","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"SMKB3MKKAY4Z","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SMKB3MKKAY4Z6I35","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SMKB3MKK","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SMKB3MKKAY4Z6I35P3QOWBTDNR","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5431","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-23T16:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"dd3caf433c7e6e1a4f1c9166a88adf8311f29e4c84cae71d44ae577cc4a323e7","abstract_canon_sha256":"6c83b6d15b61830bb594c341c3d3603201bbc864c92b5b62527b28e8427cf86c"},"schema_version":"1.0"},"canonical_sha256":"93141db14a06399f237d7ee0eb06636c5a4bea93cc5c6b5f78f932fbe05d381b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:23.347797Z","signature_b64":"h/qy/x2vQ2LGzRUmKrDYpK9YzNaRBPfuYBKiyBpiPeSgw0LZWkqez3LGbbndBIwNQ4AKU+1t0+yrwWm+dUcQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93141db14a06399f237d7ee0eb06636c5a4bea93cc5c6b5f78f932fbe05d381b","last_reissued_at":"2026-05-18T02:51:23.347175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:23.347175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5431","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":"2026-05-18T02:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8eUI83YRmoLA9XQO2sT6VVYuxEvAenJUmM3qufQOMy82c7SwG6V40IHzHJqZrj4GI0SGbrREOqwcoudz4u2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:37:17.557886Z"},"content_sha256":"cf21305089d29739b71a467c644b78aa34a235f30dd468b0ab60be147d1e0623","schema_version":"1.0","event_id":"sha256:cf21305089d29739b71a467c644b78aa34a235f30dd468b0ab60be147d1e0623"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SMKB3MKKAY4Z6I35P3QOWBTDNR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional weak laws for the weighted mean losses or gains and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Gane Samb Lo, Pape Djiby Mergane, Serigne Touba Sall","submitted_at":"2013-06-23T16:13:39Z","abstract_excerpt":"We show in this paper that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are garthered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions $w$ and $d$. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison between statistics in terms of dependence and mutu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5431","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":"2026-05-18T02:51:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJs2JAiS2AS2yweDSwRrNqcA76xSRzo9gez28T1aFjoOr4RHNyHwT5mBi/g+2hL7L/LMIX8s1TjaavH7TYw3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:37:17.558233Z"},"content_sha256":"974991293fade69f742f62e36c95e22f0d942f79e0c5f54f9bfa95c7d5473ce0","schema_version":"1.0","event_id":"sha256:974991293fade69f742f62e36c95e22f0d942f79e0c5f54f9bfa95c7d5473ce0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMKB3MKKAY4Z6I35P3QOWBTDNR/bundle.json","state_url":"https://pith.science/pith/SMKB3MKKAY4Z6I35P3QOWBTDNR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMKB3MKKAY4Z6I35P3QOWBTDNR/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":"2026-06-25T09:37:17Z","links":{"resolver":"https://pith.science/pith/SMKB3MKKAY4Z6I35P3QOWBTDNR","bundle":"https://pith.science/pith/SMKB3MKKAY4Z6I35P3QOWBTDNR/bundle.json","state":"https://pith.science/pith/SMKB3MKKAY4Z6I35P3QOWBTDNR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMKB3MKKAY4Z6I35P3QOWBTDNR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SMKB3MKKAY4Z6I35P3QOWBTDNR","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":"6c83b6d15b61830bb594c341c3d3603201bbc864c92b5b62527b28e8427cf86c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-23T16:13:39Z","title_canon_sha256":"dd3caf433c7e6e1a4f1c9166a88adf8311f29e4c84cae71d44ae577cc4a323e7"},"schema_version":"1.0","source":{"id":"1306.5431","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5431","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5431v2","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5431","created_at":"2026-05-18T02:51:23Z"},{"alias_kind":"pith_short_12","alias_value":"SMKB3MKKAY4Z","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SMKB3MKKAY4Z6I35","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SMKB3MKK","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:974991293fade69f742f62e36c95e22f0d942f79e0c5f54f9bfa95c7d5473ce0","target":"graph","created_at":"2026-05-18T02:51:23Z","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":"We show in this paper that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are garthered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions $w$ and $d$. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison between statistics in terms of dependence and mutu","authors_text":"Gane Samb Lo, Pape Djiby Mergane, Serigne Touba Sall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-23T16:13:39Z","title":"Functional weak laws for the weighted mean losses or gains and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5431","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:cf21305089d29739b71a467c644b78aa34a235f30dd468b0ab60be147d1e0623","target":"record","created_at":"2026-05-18T02:51:23Z","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":"6c83b6d15b61830bb594c341c3d3603201bbc864c92b5b62527b28e8427cf86c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-23T16:13:39Z","title_canon_sha256":"dd3caf433c7e6e1a4f1c9166a88adf8311f29e4c84cae71d44ae577cc4a323e7"},"schema_version":"1.0","source":{"id":"1306.5431","kind":"arxiv","version":2}},"canonical_sha256":"93141db14a06399f237d7ee0eb06636c5a4bea93cc5c6b5f78f932fbe05d381b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93141db14a06399f237d7ee0eb06636c5a4bea93cc5c6b5f78f932fbe05d381b","first_computed_at":"2026-05-18T02:51:23.347175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:23.347175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h/qy/x2vQ2LGzRUmKrDYpK9YzNaRBPfuYBKiyBpiPeSgw0LZWkqez3LGbbndBIwNQ4AKU+1t0+yrwWm+dUcQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:23.347797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5431","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf21305089d29739b71a467c644b78aa34a235f30dd468b0ab60be147d1e0623","sha256:974991293fade69f742f62e36c95e22f0d942f79e0c5f54f9bfa95c7d5473ce0"],"state_sha256":"054751fab4555be3e2bc49d71fb00a26457f172c772dae0a85b397722a3eed5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJkWRtwxLGFoAT1fgZgFZaCO72UwmgVLqGi6tHb9uew54DuF4PCBE1l+2b7fjNvJ7QT7Cy4PR+1r4rNGVUeHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:37:17.560197Z","bundle_sha256":"816f640aacefea857e907029d17bdea3a7aeb5b660409f7c4d16ac859cfe5672"}}