{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:VX6GTYRQMFMYW6LF6SAOVJOYQ7","short_pith_number":"pith:VX6GTYRQ","canonical_record":{"source":{"id":"2011.13661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-27T10:55:51Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"d4615edac33ddd5a97d45127724e5373eb7d25627eb1b81a2c2aa21cd23c7b94","abstract_canon_sha256":"b1625c695087da12ba8b92d1ff0b47c46fdb05aa9ab574716118f0cfea1e1805"},"schema_version":"1.0"},"canonical_sha256":"adfc69e23061598b7965f480eaa5d887d06a33337f85e693611e7bad3502b1d7","source":{"kind":"arxiv","id":"2011.13661","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.13661","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"2011.13661v2","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.13661","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"VX6GTYRQMFMY","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"pith_short_16","alias_value":"VX6GTYRQMFMYW6LF","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"pith_short_8","alias_value":"VX6GTYRQ","created_at":"2026-07-05T02:06:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:VX6GTYRQMFMYW6LF6SAOVJOYQ7","target":"record","payload":{"canonical_record":{"source":{"id":"2011.13661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-27T10:55:51Z","cross_cats_sorted":["math.FA","math.MG"],"title_canon_sha256":"d4615edac33ddd5a97d45127724e5373eb7d25627eb1b81a2c2aa21cd23c7b94","abstract_canon_sha256":"b1625c695087da12ba8b92d1ff0b47c46fdb05aa9ab574716118f0cfea1e1805"},"schema_version":"1.0"},"canonical_sha256":"adfc69e23061598b7965f480eaa5d887d06a33337f85e693611e7bad3502b1d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:06:33.301126Z","signature_b64":"Ui+TwVtGLQaJr4EeaOD9YoJVobMJJL4asuBMs2jUGlzZ8Nobyu/CgtjEmhA9dB2un7ryfz1TqGG+2LBDaEkqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adfc69e23061598b7965f480eaa5d887d06a33337f85e693611e7bad3502b1d7","last_reissued_at":"2026-07-05T02:06:33.300763Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:06:33.300763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.13661","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":"2026-07-05T02:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dSpfZtnVs8CFkKmk3Dz8UI10sm9/oIBMSaT6LlnnI+aJCFksF+R2LF9wRmxPd26KjAnyk0zm1yVVoUBBC4sZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T10:34:45.068882Z"},"content_sha256":"d39a12fbc340eb0729f834ffedd8be223be939dd63c6ca8ac21bb1450ac1c280","schema_version":"1.0","event_id":"sha256:d39a12fbc340eb0729f834ffedd8be223be939dd63c6ca8ac21bb1450ac1c280"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:VX6GTYRQMFMYW6LF6SAOVJOYQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MG"],"primary_cat":"math.PR","authors_text":"Yuansi Chen","submitted_at":"2020-11-27T10:55:51Z","abstract_excerpt":"We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency $d^{-o_d(1)}$. When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency $d^{-1/4}$. Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many implications, including improvements of the current best bounds in Bourgain's slicing conjecture and in the thin-shell conjecture, better concentration inequalities for Lipschitz functions of log-concav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.13661","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/2011.13661/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":"2026-07-05T02:06:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUlfoe88RFORxspKMsbkaqcVleLiCY855nMsyhKcSAa1pTNTjwSykDGFsXW+54h4EqjOJvyQvZEtRxevZn8UBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T10:34:45.069263Z"},"content_sha256":"d78c00268a1340d8ffef576c3894c63b7fd4d48d3605dc3f38e697e3552b78f1","schema_version":"1.0","event_id":"sha256:d78c00268a1340d8ffef576c3894c63b7fd4d48d3605dc3f38e697e3552b78f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VX6GTYRQMFMYW6LF6SAOVJOYQ7/bundle.json","state_url":"https://pith.science/pith/VX6GTYRQMFMYW6LF6SAOVJOYQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VX6GTYRQMFMYW6LF6SAOVJOYQ7/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":"2026-07-05T10:34:45Z","links":{"resolver":"https://pith.science/pith/VX6GTYRQMFMYW6LF6SAOVJOYQ7","bundle":"https://pith.science/pith/VX6GTYRQMFMYW6LF6SAOVJOYQ7/bundle.json","state":"https://pith.science/pith/VX6GTYRQMFMYW6LF6SAOVJOYQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VX6GTYRQMFMYW6LF6SAOVJOYQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:VX6GTYRQMFMYW6LF6SAOVJOYQ7","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":"b1625c695087da12ba8b92d1ff0b47c46fdb05aa9ab574716118f0cfea1e1805","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-27T10:55:51Z","title_canon_sha256":"d4615edac33ddd5a97d45127724e5373eb7d25627eb1b81a2c2aa21cd23c7b94"},"schema_version":"1.0","source":{"id":"2011.13661","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.13661","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"2011.13661v2","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.13661","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"VX6GTYRQMFMY","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"pith_short_16","alias_value":"VX6GTYRQMFMYW6LF","created_at":"2026-07-05T02:06:33Z"},{"alias_kind":"pith_short_8","alias_value":"VX6GTYRQ","created_at":"2026-07-05T02:06:33Z"}],"graph_snapshots":[{"event_id":"sha256:d78c00268a1340d8ffef576c3894c63b7fd4d48d3605dc3f38e697e3552b78f1","target":"graph","created_at":"2026-07-05T02:06:33Z","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/2011.13661/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency $d^{-o_d(1)}$. When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency $d^{-1/4}$. Improving the current best lower bound of the isoperimetric coefficient in the KLS conjecture has many implications, including improvements of the current best bounds in Bourgain's slicing conjecture and in the thin-shell conjecture, better concentration inequalities for Lipschitz functions of log-concav","authors_text":"Yuansi Chen","cross_cats":["math.FA","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-27T10:55:51Z","title":"An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.13661","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:d39a12fbc340eb0729f834ffedd8be223be939dd63c6ca8ac21bb1450ac1c280","target":"record","created_at":"2026-07-05T02:06:33Z","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":"b1625c695087da12ba8b92d1ff0b47c46fdb05aa9ab574716118f0cfea1e1805","cross_cats_sorted":["math.FA","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-27T10:55:51Z","title_canon_sha256":"d4615edac33ddd5a97d45127724e5373eb7d25627eb1b81a2c2aa21cd23c7b94"},"schema_version":"1.0","source":{"id":"2011.13661","kind":"arxiv","version":2}},"canonical_sha256":"adfc69e23061598b7965f480eaa5d887d06a33337f85e693611e7bad3502b1d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adfc69e23061598b7965f480eaa5d887d06a33337f85e693611e7bad3502b1d7","first_computed_at":"2026-07-05T02:06:33.300763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:06:33.300763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ui+TwVtGLQaJr4EeaOD9YoJVobMJJL4asuBMs2jUGlzZ8Nobyu/CgtjEmhA9dB2un7ryfz1TqGG+2LBDaEkqAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:06:33.301126Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.13661","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d39a12fbc340eb0729f834ffedd8be223be939dd63c6ca8ac21bb1450ac1c280","sha256:d78c00268a1340d8ffef576c3894c63b7fd4d48d3605dc3f38e697e3552b78f1"],"state_sha256":"e4d55b92827d4fe9adc3a39846be038d03764d840cd1ddf8c377081d4d9d0e11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2Nx7s7iFMOVsMK+TAeXxF6EwCeLbAi/Vv5x7hpIVIhkCpC7wsUYhBCA0dt9tBYv9ZeuTVKhkhLR5S4HoNI8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T10:34:45.071487Z","bundle_sha256":"a12d4e25dc1ed0791aced40b4f4f61ad26bb9a4d0235cdeacdf2ca646d41f014"}}