{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XA52PFDCNTWFHAF5LJT4O4K2ZL","short_pith_number":"pith:XA52PFDC","canonical_record":{"source":{"id":"2502.07699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-02-11T16:51:25Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"5a88cd956117c9974b13eebfde88a37c454e32985a19a33197d24386cbf7b744","abstract_canon_sha256":"5302fea6a1b64e1782643b4320a3fb61fc2faec0f913dbe8dc5fc3a974c9f207"},"schema_version":"1.0"},"canonical_sha256":"b83ba794626cec5380bd5a67c7715acadaf7424caf729c167e9411f333650193","source":{"kind":"arxiv","id":"2502.07699","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07699","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07699v2","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07699","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"XA52PFDCNTWF","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"pith_short_16","alias_value":"XA52PFDCNTWFHAF5","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"pith_short_8","alias_value":"XA52PFDC","created_at":"2026-07-05T11:46:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XA52PFDCNTWFHAF5LJT4O4K2ZL","target":"record","payload":{"canonical_record":{"source":{"id":"2502.07699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-02-11T16:51:25Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"5a88cd956117c9974b13eebfde88a37c454e32985a19a33197d24386cbf7b744","abstract_canon_sha256":"5302fea6a1b64e1782643b4320a3fb61fc2faec0f913dbe8dc5fc3a974c9f207"},"schema_version":"1.0"},"canonical_sha256":"b83ba794626cec5380bd5a67c7715acadaf7424caf729c167e9411f333650193","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:39.112781Z","signature_b64":"Q9l7SvrMNZ2cnIMyQeviTloGHQXb496wb6Ep0oVM7WaJUV60/CaBP4EMcTz/koP1C43HbU6aOgaiJfsI7cNZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b83ba794626cec5380bd5a67c7715acadaf7424caf729c167e9411f333650193","last_reissued_at":"2026-07-05T11:46:39.112209Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:39.112209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.07699","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":"2026-07-05T11:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"InYyXcGdQQoiVxSZvGs3cPPGeNXOrJnoW8waQHjjvvOHFHYYEs5P4mc61yVz3PBtB+4v+PLOo1XuNg/NiolbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:11:39.071963Z"},"content_sha256":"f63d3c2f641521ea301d055bdce30858968cceb4434f291cf4141b42041b5bf5","schema_version":"1.0","event_id":"sha256:f63d3c2f641521ea301d055bdce30858968cceb4434f291cf4141b42041b5bf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XA52PFDCNTWFHAF5LJT4O4K2ZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp Anti-Concentration Inequalities for Extremum Statistics via Copulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Matias D. Cattaneo, Ricardo P. Masini, William G. Underwood","submitted_at":"2025-02-11T16:51:25Z","abstract_excerpt":"We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal law of the samples or on the copula describing their joint distribution. We show that, in general, strictly sublinear dependence of the concentration function on the dimension $d$ is not possible. We then introduce a new class of copulas, namely those with a convex diagonal section, and demonstrate that restricting to this class yields a sharper upper bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07699","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.07699/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dEOXTtoq+3CtAS6NPvjqvJ4P+j+dEob8W+oCsS0YVVajfUIoRlDiHfXJLyBlnuR5xodVZwsceZNwQrWqt2o2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:11:39.072460Z"},"content_sha256":"bf18fdcd5602b89835db0dfd206ac87a7794aaf509ec77648271dcd9f8d0fdfa","schema_version":"1.0","event_id":"sha256:bf18fdcd5602b89835db0dfd206ac87a7794aaf509ec77648271dcd9f8d0fdfa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XA52PFDCNTWFHAF5LJT4O4K2ZL/bundle.json","state_url":"https://pith.science/pith/XA52PFDCNTWFHAF5LJT4O4K2ZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XA52PFDCNTWFHAF5LJT4O4K2ZL/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":"2026-08-16T12:11:39Z","links":{"resolver":"https://pith.science/pith/XA52PFDCNTWFHAF5LJT4O4K2ZL","bundle":"https://pith.science/pith/XA52PFDCNTWFHAF5LJT4O4K2ZL/bundle.json","state":"https://pith.science/pith/XA52PFDCNTWFHAF5LJT4O4K2ZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XA52PFDCNTWFHAF5LJT4O4K2ZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XA52PFDCNTWFHAF5LJT4O4K2ZL","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":"5302fea6a1b64e1782643b4320a3fb61fc2faec0f913dbe8dc5fc3a974c9f207","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-02-11T16:51:25Z","title_canon_sha256":"5a88cd956117c9974b13eebfde88a37c454e32985a19a33197d24386cbf7b744"},"schema_version":"1.0","source":{"id":"2502.07699","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07699","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07699v2","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07699","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"XA52PFDCNTWF","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"pith_short_16","alias_value":"XA52PFDCNTWFHAF5","created_at":"2026-07-05T11:46:39Z"},{"alias_kind":"pith_short_8","alias_value":"XA52PFDC","created_at":"2026-07-05T11:46:39Z"}],"graph_snapshots":[{"event_id":"sha256:bf18fdcd5602b89835db0dfd206ac87a7794aaf509ec77648271dcd9f8d0fdfa","target":"graph","created_at":"2026-07-05T11:46:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.07699/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal law of the samples or on the copula describing their joint distribution. We show that, in general, strictly sublinear dependence of the concentration function on the dimension $d$ is not possible. We then introduce a new class of copulas, namely those with a convex diagonal section, and demonstrate that restricting to this class yields a sharper upper bound","authors_text":"Matias D. Cattaneo, Ricardo P. Masini, William G. Underwood","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-02-11T16:51:25Z","title":"Sharp Anti-Concentration Inequalities for Extremum Statistics via Copulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07699","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:f63d3c2f641521ea301d055bdce30858968cceb4434f291cf4141b42041b5bf5","target":"record","created_at":"2026-07-05T11:46:39Z","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":"5302fea6a1b64e1782643b4320a3fb61fc2faec0f913dbe8dc5fc3a974c9f207","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-02-11T16:51:25Z","title_canon_sha256":"5a88cd956117c9974b13eebfde88a37c454e32985a19a33197d24386cbf7b744"},"schema_version":"1.0","source":{"id":"2502.07699","kind":"arxiv","version":2}},"canonical_sha256":"b83ba794626cec5380bd5a67c7715acadaf7424caf729c167e9411f333650193","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b83ba794626cec5380bd5a67c7715acadaf7424caf729c167e9411f333650193","first_computed_at":"2026-07-05T11:46:39.112209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:39.112209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q9l7SvrMNZ2cnIMyQeviTloGHQXb496wb6Ep0oVM7WaJUV60/CaBP4EMcTz/koP1C43HbU6aOgaiJfsI7cNZDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:39.112781Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.07699","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f63d3c2f641521ea301d055bdce30858968cceb4434f291cf4141b42041b5bf5","sha256:bf18fdcd5602b89835db0dfd206ac87a7794aaf509ec77648271dcd9f8d0fdfa"],"state_sha256":"7f5bfa4d261f977c821161f2e36c5caf4893ad8d757e6348921caa1db18b2ad7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tLfCrlJhBZtyDGwLYd9sDdzg0GAE5Da4RII1yAzEMmkngklYJDSMfkWyHK710W6tYdxQH3A7VpjDclmmzdhbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:11:39.075798Z","bundle_sha256":"790da787d9d5d0b1f86d65921f4c47e23a3b039109bc54fe072271483c7c9757"}}