{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BADLEAPON6DY7ZDWZJXIDED2YJ","short_pith_number":"pith:BADLEAPO","canonical_record":{"source":{"id":"1011.0943","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-11-03T17:12:07Z","cross_cats_sorted":[],"title_canon_sha256":"5a6c8387394b5c6816a382ff6ae1d1f4f27cc06370691c4ddffae9fa98b1c27d","abstract_canon_sha256":"5643920c7c64e34fe8bd11ec039d4da6b3958096b3b3ba7b9252647f8226036b"},"schema_version":"1.0"},"canonical_sha256":"0806b201ee6f878fe476ca6e81907ac2634675884e595d4560061104e75b87df","source":{"kind":"arxiv","id":"1011.0943","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0943","created_at":"2026-05-18T04:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0943v3","created_at":"2026-05-18T04:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0943","created_at":"2026-05-18T04:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"BADLEAPON6DY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BADLEAPON6DY7ZDW","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BADLEAPO","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BADLEAPON6DY7ZDWZJXIDED2YJ","target":"record","payload":{"canonical_record":{"source":{"id":"1011.0943","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-11-03T17:12:07Z","cross_cats_sorted":[],"title_canon_sha256":"5a6c8387394b5c6816a382ff6ae1d1f4f27cc06370691c4ddffae9fa98b1c27d","abstract_canon_sha256":"5643920c7c64e34fe8bd11ec039d4da6b3958096b3b3ba7b9252647f8226036b"},"schema_version":"1.0"},"canonical_sha256":"0806b201ee6f878fe476ca6e81907ac2634675884e595d4560061104e75b87df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:51.095258Z","signature_b64":"xeJuF23RZXG3aEOsU+FMoJ1w4NvfoF02psSEyb3Ldqu01Ec67Q40gYACNuy2Tc6r+rCaoS0MshTD+hlEnKp0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0806b201ee6f878fe476ca6e81907ac2634675884e595d4560061104e75b87df","last_reissued_at":"2026-05-18T04:20:51.094711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:51.094711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.0943","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xXmA87gBshTjUmEVWDoh2BH0I2vQTjXYDLWM4o/NegM+OYi2LYg73Gm5o7XBeDXlOcLciM93OwpEDIjXA50nAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:56:18.109493Z"},"content_sha256":"1994bcf3ed8cdf25f9c6f23877109d0062e17b786f2143ba851559a63f172533","schema_version":"1.0","event_id":"sha256:1994bcf3ed8cdf25f9c6f23877109d0062e17b786f2143ba851559a63f172533"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BADLEAPON6DY7ZDWZJXIDED2YJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolating Thin-Shell and Sharp Large-Deviation Estimates For Isotropic Log-Concave Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Emanuel Milman, Olivier Gu\\'edon","submitted_at":"2010-11-03T17:12:07Z","abstract_excerpt":"Given an isotropic random vector $X$ with log-concave density in Euclidean space $\\Real^n$, we study the concentration properties of $|X|$ on all scales, both above and below its expectation. We show in particular that: \\[ \\P(\\abs{|X| -\\sqrt{n}} \\geq t \\sqrt{n}) \\leq C \\exp(-c n^{1/2} \\min(t^3,t)) \\;\\;\\; \\forall t \\geq 0 ~, \\] for some universal constants $c,C>0$. This improves the best known deviation results on the thin-shell and mesoscopic scales due to Fleury and Klartag, respectively, and recovers the sharp large-deviation estimate of Paouris. Another new feature of our estimate is that i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0943","kind":"arxiv","version":3},"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":"2026-05-18T04:20:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EIHRa2SAmCwIN2zoSgsPlXZNtIhPMXKiq1PGECt62wEnIPH0wt7jqvAi/59KafeYaaTxqYBc6neZdQ+Om6B9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:56:18.109900Z"},"content_sha256":"ac2992833c99bb4e1de547d87e25947771143c33cf4e75cc0036d79e0f6c15d6","schema_version":"1.0","event_id":"sha256:ac2992833c99bb4e1de547d87e25947771143c33cf4e75cc0036d79e0f6c15d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BADLEAPON6DY7ZDWZJXIDED2YJ/bundle.json","state_url":"https://pith.science/pith/BADLEAPON6DY7ZDWZJXIDED2YJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BADLEAPON6DY7ZDWZJXIDED2YJ/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":"2026-05-28T13:56:18Z","links":{"resolver":"https://pith.science/pith/BADLEAPON6DY7ZDWZJXIDED2YJ","bundle":"https://pith.science/pith/BADLEAPON6DY7ZDWZJXIDED2YJ/bundle.json","state":"https://pith.science/pith/BADLEAPON6DY7ZDWZJXIDED2YJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BADLEAPON6DY7ZDWZJXIDED2YJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BADLEAPON6DY7ZDWZJXIDED2YJ","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":"5643920c7c64e34fe8bd11ec039d4da6b3958096b3b3ba7b9252647f8226036b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-11-03T17:12:07Z","title_canon_sha256":"5a6c8387394b5c6816a382ff6ae1d1f4f27cc06370691c4ddffae9fa98b1c27d"},"schema_version":"1.0","source":{"id":"1011.0943","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0943","created_at":"2026-05-18T04:20:51Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0943v3","created_at":"2026-05-18T04:20:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0943","created_at":"2026-05-18T04:20:51Z"},{"alias_kind":"pith_short_12","alias_value":"BADLEAPON6DY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BADLEAPON6DY7ZDW","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BADLEAPO","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:ac2992833c99bb4e1de547d87e25947771143c33cf4e75cc0036d79e0f6c15d6","target":"graph","created_at":"2026-05-18T04:20:51Z","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 an isotropic random vector $X$ with log-concave density in Euclidean space $\\Real^n$, we study the concentration properties of $|X|$ on all scales, both above and below its expectation. We show in particular that: \\[ \\P(\\abs{|X| -\\sqrt{n}} \\geq t \\sqrt{n}) \\leq C \\exp(-c n^{1/2} \\min(t^3,t)) \\;\\;\\; \\forall t \\geq 0 ~, \\] for some universal constants $c,C>0$. This improves the best known deviation results on the thin-shell and mesoscopic scales due to Fleury and Klartag, respectively, and recovers the sharp large-deviation estimate of Paouris. Another new feature of our estimate is that i","authors_text":"Emanuel Milman, Olivier Gu\\'edon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-11-03T17:12:07Z","title":"Interpolating Thin-Shell and Sharp Large-Deviation Estimates For Isotropic Log-Concave Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0943","kind":"arxiv","version":3},"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":"sha256:1994bcf3ed8cdf25f9c6f23877109d0062e17b786f2143ba851559a63f172533","target":"record","created_at":"2026-05-18T04:20:51Z","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":"5643920c7c64e34fe8bd11ec039d4da6b3958096b3b3ba7b9252647f8226036b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-11-03T17:12:07Z","title_canon_sha256":"5a6c8387394b5c6816a382ff6ae1d1f4f27cc06370691c4ddffae9fa98b1c27d"},"schema_version":"1.0","source":{"id":"1011.0943","kind":"arxiv","version":3}},"canonical_sha256":"0806b201ee6f878fe476ca6e81907ac2634675884e595d4560061104e75b87df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0806b201ee6f878fe476ca6e81907ac2634675884e595d4560061104e75b87df","first_computed_at":"2026-05-18T04:20:51.094711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:51.094711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xeJuF23RZXG3aEOsU+FMoJ1w4NvfoF02psSEyb3Ldqu01Ec67Q40gYACNuy2Tc6r+rCaoS0MshTD+hlEnKp0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:51.095258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0943","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1994bcf3ed8cdf25f9c6f23877109d0062e17b786f2143ba851559a63f172533","sha256:ac2992833c99bb4e1de547d87e25947771143c33cf4e75cc0036d79e0f6c15d6"],"state_sha256":"b8b0efe3f1d2387d8f1abe9f10fa835039bb74407b447fbc03a1825eddd7e2bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gvn9JvJmKhdev7UtvWbkSpi4w/3jjXFV8lAjdnLcHDX0zqlPBF1Xyfq2364Y+OOyXaGv7cP0Uc01P6kguSpiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:56:18.112327Z","bundle_sha256":"21c37f018cce4fdbd12a2c81ba7bdcb327455fb11e563e01a826762f977f5748"}}