{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VVHLVLG4AVJFTWQF2MOYJN6F7B","short_pith_number":"pith:VVHLVLG4","canonical_record":{"source":{"id":"1405.5577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-05-22T00:04:40Z","cross_cats_sorted":[],"title_canon_sha256":"3cc50cc39fa7ae96e935c5ec7914316a8003f87e2a1eaa0057a0aef1fe893e51","abstract_canon_sha256":"fd005b1d2ac34677414eefb9449545002ac595e666f35091ffbbea44766c8134"},"schema_version":"1.0"},"canonical_sha256":"ad4ebaacdc055259da05d31d84b7c5f848d5d9c540d5d026be209f354f3ff445","source":{"kind":"arxiv","id":"1405.5577","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5577","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5577v1","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5577","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"pith_short_12","alias_value":"VVHLVLG4AVJF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VVHLVLG4AVJFTWQF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VVHLVLG4","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VVHLVLG4AVJFTWQF2MOYJN6F7B","target":"record","payload":{"canonical_record":{"source":{"id":"1405.5577","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-05-22T00:04:40Z","cross_cats_sorted":[],"title_canon_sha256":"3cc50cc39fa7ae96e935c5ec7914316a8003f87e2a1eaa0057a0aef1fe893e51","abstract_canon_sha256":"fd005b1d2ac34677414eefb9449545002ac595e666f35091ffbbea44766c8134"},"schema_version":"1.0"},"canonical_sha256":"ad4ebaacdc055259da05d31d84b7c5f848d5d9c540d5d026be209f354f3ff445","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:16.370931Z","signature_b64":"VsdLiAmzmdlsZJVkrjXZSg/h3TDd39TuQYkYJjXdbMHnesx+KbThaMQok7/FwXKXujSthmIrn2+HiJ43KrZ3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad4ebaacdc055259da05d31d84b7c5f848d5d9c540d5d026be209f354f3ff445","last_reissued_at":"2026-05-18T02:51:16.370328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:16.370328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.5577","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":"2026-05-18T02:51:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gfEjJXKF7Uw5fbq1ar4IirNLLCNq+7Vm0+AdhpRAV5OeZKP8VB5XI2b5d8aO4vOu/lzxmgproThKYFRhKjHLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:55:30.130713Z"},"content_sha256":"f407be58599b513eb53b63f306a0f0f634167d913e68338a5b70b08089e20396","schema_version":"1.0","event_id":"sha256:f407be58599b513eb53b63f306a0f0f634167d913e68338a5b70b08089e20396"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VVHLVLG4AVJFTWQF2MOYJN6F7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple note on some empirical stochastic process as a tool in uniform L-statistics weak laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Gane Samb Lo","submitted_at":"2014-05-22T00:04:40Z","abstract_excerpt":"In this paper, we are concerned with the stochastic process \\begin{equation} \\beta_{n}(q_{t},t)=\\beta_{n}(t)=\\frac{1}{\\sqrt{n}}\\sum_{j=1}^{n}\\left\\{G_{t,n}(Y(t))-G_{t}(Y_{j}(t))\\right\\} q_{t}(Y_{j}(t)), \\tag{A} \\end{equation} where for $n\\geq1$ and $T>0$, the sequences $\\{Y_{1}(t),Y_{2}(t),...,Y_{n}(t),t\\in [0,T]\\}$ are independant observations of some real stochastic process ${Y(t),t\\in [0,T]}$, for each $t \\in [0,T]$, $G_{t}$ is the distribution function of $% Y(t)$ and $G_{t,n}$ is the empirical distribution function based on $% Y_{1}(t),Y_{2}(t),...,Y_{n}(t)$, and finally $q_{t}$ is a boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5577","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":"2026-05-18T02:51:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rSLE7e+dXSKPhLXCHlyXu8AQ1o0sdAm1VG6ZRDKME13nYUCRal5xbm1PO1FP/f0yEETHSLniQShU8rTe/6kYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T11:55:30.131229Z"},"content_sha256":"7ccab38e9be55d696fed976f8327a0f4fd0c6dec611c3188fcb3aba9c2b98812","schema_version":"1.0","event_id":"sha256:7ccab38e9be55d696fed976f8327a0f4fd0c6dec611c3188fcb3aba9c2b98812"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVHLVLG4AVJFTWQF2MOYJN6F7B/bundle.json","state_url":"https://pith.science/pith/VVHLVLG4AVJFTWQF2MOYJN6F7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVHLVLG4AVJFTWQF2MOYJN6F7B/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":"2026-06-25T11:55:30Z","links":{"resolver":"https://pith.science/pith/VVHLVLG4AVJFTWQF2MOYJN6F7B","bundle":"https://pith.science/pith/VVHLVLG4AVJFTWQF2MOYJN6F7B/bundle.json","state":"https://pith.science/pith/VVHLVLG4AVJFTWQF2MOYJN6F7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVHLVLG4AVJFTWQF2MOYJN6F7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VVHLVLG4AVJFTWQF2MOYJN6F7B","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":"fd005b1d2ac34677414eefb9449545002ac595e666f35091ffbbea44766c8134","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-05-22T00:04:40Z","title_canon_sha256":"3cc50cc39fa7ae96e935c5ec7914316a8003f87e2a1eaa0057a0aef1fe893e51"},"schema_version":"1.0","source":{"id":"1405.5577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.5577","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"arxiv_version","alias_value":"1405.5577v1","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.5577","created_at":"2026-05-18T02:51:16Z"},{"alias_kind":"pith_short_12","alias_value":"VVHLVLG4AVJF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VVHLVLG4AVJFTWQF","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VVHLVLG4","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:7ccab38e9be55d696fed976f8327a0f4fd0c6dec611c3188fcb3aba9c2b98812","target":"graph","created_at":"2026-05-18T02:51:16Z","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 are concerned with the stochastic process \\begin{equation} \\beta_{n}(q_{t},t)=\\beta_{n}(t)=\\frac{1}{\\sqrt{n}}\\sum_{j=1}^{n}\\left\\{G_{t,n}(Y(t))-G_{t}(Y_{j}(t))\\right\\} q_{t}(Y_{j}(t)), \\tag{A} \\end{equation} where for $n\\geq1$ and $T>0$, the sequences $\\{Y_{1}(t),Y_{2}(t),...,Y_{n}(t),t\\in [0,T]\\}$ are independant observations of some real stochastic process ${Y(t),t\\in [0,T]}$, for each $t \\in [0,T]$, $G_{t}$ is the distribution function of $% Y(t)$ and $G_{t,n}$ is the empirical distribution function based on $% Y_{1}(t),Y_{2}(t),...,Y_{n}(t)$, and finally $q_{t}$ is a boun","authors_text":"Gane Samb Lo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-05-22T00:04:40Z","title":"A simple note on some empirical stochastic process as a tool in uniform L-statistics weak laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5577","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:f407be58599b513eb53b63f306a0f0f634167d913e68338a5b70b08089e20396","target":"record","created_at":"2026-05-18T02:51:16Z","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":"fd005b1d2ac34677414eefb9449545002ac595e666f35091ffbbea44766c8134","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-05-22T00:04:40Z","title_canon_sha256":"3cc50cc39fa7ae96e935c5ec7914316a8003f87e2a1eaa0057a0aef1fe893e51"},"schema_version":"1.0","source":{"id":"1405.5577","kind":"arxiv","version":1}},"canonical_sha256":"ad4ebaacdc055259da05d31d84b7c5f848d5d9c540d5d026be209f354f3ff445","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad4ebaacdc055259da05d31d84b7c5f848d5d9c540d5d026be209f354f3ff445","first_computed_at":"2026-05-18T02:51:16.370328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:16.370328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VsdLiAmzmdlsZJVkrjXZSg/h3TDd39TuQYkYJjXdbMHnesx+KbThaMQok7/FwXKXujSthmIrn2+HiJ43KrZ3AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:16.370931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.5577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f407be58599b513eb53b63f306a0f0f634167d913e68338a5b70b08089e20396","sha256:7ccab38e9be55d696fed976f8327a0f4fd0c6dec611c3188fcb3aba9c2b98812"],"state_sha256":"a4d92b9eff53de1bc53dec221fca411218d3ded2d7264f772813e68a4880b8ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MeZTeC+4YF/P6o7UbMwU8chixI7ADz6a3hPaZK9ISnmaVJJBwYJc2AUGQol4vSSNnI+H5Jo2Ps9W2Qm0U6DdBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T11:55:30.133416Z","bundle_sha256":"ab3c4b63d25b7b7e49d9d1177831a28e9eb04448888984ad99f05e132e68e9d0"}}