{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:NJT5MNO7DKZL5XLFIHHSA7WQ45","short_pith_number":"pith:NJT5MNO7","canonical_record":{"source":{"id":"2306.07811","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-13T14:39:09Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"da230e8f8ad731c27356fbc9768097cf35570a8a4a64e68d2b6be613f720c0e7","abstract_canon_sha256":"b7c0eadd262f5e7b3ce27d57e07a2d78fb7f3843810f47f40ece8a9cca1bcfe8"},"schema_version":"1.0"},"canonical_sha256":"6a67d635df1ab2bedd6541cf207ed0e766e145246f65290785a56be32bb3746b","source":{"kind":"arxiv","id":"2306.07811","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.07811","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"2306.07811v1","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.07811","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"NJT5MNO7DKZL","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"pith_short_16","alias_value":"NJT5MNO7DKZL5XLF","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"pith_short_8","alias_value":"NJT5MNO7","created_at":"2026-07-05T06:20:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:NJT5MNO7DKZL5XLFIHHSA7WQ45","target":"record","payload":{"canonical_record":{"source":{"id":"2306.07811","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-13T14:39:09Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"da230e8f8ad731c27356fbc9768097cf35570a8a4a64e68d2b6be613f720c0e7","abstract_canon_sha256":"b7c0eadd262f5e7b3ce27d57e07a2d78fb7f3843810f47f40ece8a9cca1bcfe8"},"schema_version":"1.0"},"canonical_sha256":"6a67d635df1ab2bedd6541cf207ed0e766e145246f65290785a56be32bb3746b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:20:09.229791Z","signature_b64":"9c9QPG0GhIzgTlUc4kFoM+hykaIl8EMKZR/nkMIdEQc/+OgyA+NA0vNl++/sKHgrQRt3T8MYvFo1qQMOHiyZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a67d635df1ab2bedd6541cf207ed0e766e145246f65290785a56be32bb3746b","last_reissued_at":"2026-07-05T06:20:09.229436Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:20:09.229436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.07811","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":"2026-07-05T06:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ja+7u94khrbRWs9r5XI1mFhudWp9I5TujyYyiST+YgUGF4mt4lE9jOaA/fELlRNZOrAYEutSM4Zl63w05VPzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:30:27.977253Z"},"content_sha256":"ec6e417735352c1ce92ca4e291ceedde7693f3e45cd486930cf8fb0e0142c2df","schema_version":"1.0","event_id":"sha256:ec6e417735352c1ce92ca4e291ceedde7693f3e45cd486930cf8fb0e0142c2df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:NJT5MNO7DKZL5XLFIHHSA7WQ45","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight lower bounds for anti-concentration of Rademacher sums and Tomaszewski's counterpart problem","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Julien Portier, Lawrence Hollom","submitted_at":"2023-06-13T14:39:09Z","abstract_excerpt":"In this paper we prove that $\\mathbb{P}(|X| \\geq \\sqrt{\\text{Var}(X)}) \\geq 7/32$ for every finite Rademacher sum $X$, confirming a conjecture by Hitczenko and Kwapie{\\'n} from 1994, and improving upon results from Burkholder, Oleszkiewicz, and Dvo\\v{r}\\'ak and Klein. Moreover we fully determine the function $f(y)= \\inf_X \\mathbb{P}(|X| \\geq y\\sqrt{\\text{Var}(X)})$ where the $\\inf$ is taken over all finite Rademacher sums $X$, confirming a conjecture by Lowther and giving a partial answer to a question by Keller and Klein."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07811","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.07811/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":"2026-07-05T06:20:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F55x9T0/Pol6aswd8f+wQC5BSk0dHj6zOegmrB1JcRU6cly/fVdRhLm7Vzr2Hnb1ijpHg39p+Tyn/IDxGXAeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T01:30:27.977634Z"},"content_sha256":"fabd068939e7aeeedfb13d74205f1330ad4c6ee1910cf692b7ae481f8bbcb388","schema_version":"1.0","event_id":"sha256:fabd068939e7aeeedfb13d74205f1330ad4c6ee1910cf692b7ae481f8bbcb388"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJT5MNO7DKZL5XLFIHHSA7WQ45/bundle.json","state_url":"https://pith.science/pith/NJT5MNO7DKZL5XLFIHHSA7WQ45/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJT5MNO7DKZL5XLFIHHSA7WQ45/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":"2026-08-05T01:30:28Z","links":{"resolver":"https://pith.science/pith/NJT5MNO7DKZL5XLFIHHSA7WQ45","bundle":"https://pith.science/pith/NJT5MNO7DKZL5XLFIHHSA7WQ45/bundle.json","state":"https://pith.science/pith/NJT5MNO7DKZL5XLFIHHSA7WQ45/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJT5MNO7DKZL5XLFIHHSA7WQ45/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NJT5MNO7DKZL5XLFIHHSA7WQ45","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":"b7c0eadd262f5e7b3ce27d57e07a2d78fb7f3843810f47f40ece8a9cca1bcfe8","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-13T14:39:09Z","title_canon_sha256":"da230e8f8ad731c27356fbc9768097cf35570a8a4a64e68d2b6be613f720c0e7"},"schema_version":"1.0","source":{"id":"2306.07811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.07811","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"arxiv_version","alias_value":"2306.07811v1","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.07811","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"pith_short_12","alias_value":"NJT5MNO7DKZL","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"pith_short_16","alias_value":"NJT5MNO7DKZL5XLF","created_at":"2026-07-05T06:20:09Z"},{"alias_kind":"pith_short_8","alias_value":"NJT5MNO7","created_at":"2026-07-05T06:20:09Z"}],"graph_snapshots":[{"event_id":"sha256:fabd068939e7aeeedfb13d74205f1330ad4c6ee1910cf692b7ae481f8bbcb388","target":"graph","created_at":"2026-07-05T06:20:09Z","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/2306.07811/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we prove that $\\mathbb{P}(|X| \\geq \\sqrt{\\text{Var}(X)}) \\geq 7/32$ for every finite Rademacher sum $X$, confirming a conjecture by Hitczenko and Kwapie{\\'n} from 1994, and improving upon results from Burkholder, Oleszkiewicz, and Dvo\\v{r}\\'ak and Klein. Moreover we fully determine the function $f(y)= \\inf_X \\mathbb{P}(|X| \\geq y\\sqrt{\\text{Var}(X)})$ where the $\\inf$ is taken over all finite Rademacher sums $X$, confirming a conjecture by Lowther and giving a partial answer to a question by Keller and Klein.","authors_text":"Julien Portier, Lawrence Hollom","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-13T14:39:09Z","title":"Tight lower bounds for anti-concentration of Rademacher sums and Tomaszewski's counterpart problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07811","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:ec6e417735352c1ce92ca4e291ceedde7693f3e45cd486930cf8fb0e0142c2df","target":"record","created_at":"2026-07-05T06:20:09Z","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":"b7c0eadd262f5e7b3ce27d57e07a2d78fb7f3843810f47f40ece8a9cca1bcfe8","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2023-06-13T14:39:09Z","title_canon_sha256":"da230e8f8ad731c27356fbc9768097cf35570a8a4a64e68d2b6be613f720c0e7"},"schema_version":"1.0","source":{"id":"2306.07811","kind":"arxiv","version":1}},"canonical_sha256":"6a67d635df1ab2bedd6541cf207ed0e766e145246f65290785a56be32bb3746b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a67d635df1ab2bedd6541cf207ed0e766e145246f65290785a56be32bb3746b","first_computed_at":"2026-07-05T06:20:09.229436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:20:09.229436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9c9QPG0GhIzgTlUc4kFoM+hykaIl8EMKZR/nkMIdEQc/+OgyA+NA0vNl++/sKHgrQRt3T8MYvFo1qQMOHiyZAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:20:09.229791Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.07811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec6e417735352c1ce92ca4e291ceedde7693f3e45cd486930cf8fb0e0142c2df","sha256:fabd068939e7aeeedfb13d74205f1330ad4c6ee1910cf692b7ae481f8bbcb388"],"state_sha256":"ab0e94a85cc2d2dcc9fd93b76d7349329a87cc175f62978c0d01269d618c3fd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IN0DycrHZ6N4zk+JkYddgT4a1L0ymLgZTbO+CjnynWTvid1IWU8VTHNBftYq+Z75TkASOnWBW503le+o47LjAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T01:30:28.017264Z","bundle_sha256":"30dea8f1b52a637021a9da68b527f518b39e495e878d6abc896f106acb894d14"}}