{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OOOMWGSFPJX7VRNDJNIO2P6KXC","short_pith_number":"pith:OOOMWGSF","canonical_record":{"source":{"id":"1406.4621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T07:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"9e13f60d5bae99117ec07a45b958d0d3287078e3167d134a1d6ab842cf262829","abstract_canon_sha256":"db22c07ec080bfc635176608a263f173b13208ebb02b979fc033015a5597f4d8"},"schema_version":"1.0"},"canonical_sha256":"739ccb1a457a6ffac5a34b50ed3fcab8be983bfe5ba98b78244054a727bfb7bc","source":{"kind":"arxiv","id":"1406.4621","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4621","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4621v1","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4621","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"OOOMWGSFPJX7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OOOMWGSFPJX7VRND","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OOOMWGSF","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OOOMWGSFPJX7VRNDJNIO2P6KXC","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T07:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"9e13f60d5bae99117ec07a45b958d0d3287078e3167d134a1d6ab842cf262829","abstract_canon_sha256":"db22c07ec080bfc635176608a263f173b13208ebb02b979fc033015a5597f4d8"},"schema_version":"1.0"},"canonical_sha256":"739ccb1a457a6ffac5a34b50ed3fcab8be983bfe5ba98b78244054a727bfb7bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:31.131733Z","signature_b64":"NeeehgJzfC9Cf5R85PzE36xHKamiCx4Ce1pkRWDS+/RUNaDy5dmRUl+dj5dCojmTbM7Ws50LhW5jegP6/Xj5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"739ccb1a457a6ffac5a34b50ed3fcab8be983bfe5ba98b78244054a727bfb7bc","last_reissued_at":"2026-05-18T02:49:31.131305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:31.131305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4621","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":"2026-05-18T02:49:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63OrI0sTFZzo6HA3imoSK+C/9pr05hZuZq3AO4fTAXTqudVr204Nes6w1Z41PGTbBQyy35v4ZtCEXD75/qxjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:51:17.527718Z"},"content_sha256":"211e08d331410952a084ae1e4d2ffb5109cfb5f86909c113b726bb46226e1ee5","schema_version":"1.0","event_id":"sha256:211e08d331410952a084ae1e4d2ffb5109cfb5f86909c113b726bb46226e1ee5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OOOMWGSFPJX7VRNDJNIO2P6KXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral gap for spherically symmetric log-concave probability measures, and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ald\\'eric Joulin (IMT), Michel Bonnefont (IMB), Yutao ma","submitted_at":"2014-06-18T07:07:12Z","abstract_excerpt":"Let $\\mu$ be a probability measure on $\\rr^n$ ($n \\geq 2$) with Lebesgue density proportional to $e^{-V (\\Vert x\\Vert )}$, where $V : \\rr_+ \\to \\rr$ is a smooth convex potential. We show that the associated spectral gap in $L^2 (\\mu)$ lies between $(n-1) / \\int_{\\rr^n} \\Vert x\\Vert ^2 \\mu(dx)$ and $n / \\int_{\\rr^n} \\Vert x\\Vert ^2 \\mu(dx)$, improving a well-known two-sided estimate due to Bobkov. Our Markovian approach is remarkably simple and is sufficiently robust to be extended beyond the log-concave case, at the price of potentially modifying the underlying dynamics in the energy, leading "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4621","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":"2026-05-18T02:49:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uiT1tGjojsYVYLmzJ2yPabMMenj20t4bBv6ER9WKGI4egWzm7QlfYZnP4o5+2S7LY87/psRIoRTaqC826bpEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T22:51:17.528076Z"},"content_sha256":"5b2fbc8587aa630f8b529ee89fcba77a6adf028cfa8fa9bb199b6e3ecfe7dabb","schema_version":"1.0","event_id":"sha256:5b2fbc8587aa630f8b529ee89fcba77a6adf028cfa8fa9bb199b6e3ecfe7dabb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOOMWGSFPJX7VRNDJNIO2P6KXC/bundle.json","state_url":"https://pith.science/pith/OOOMWGSFPJX7VRNDJNIO2P6KXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOOMWGSFPJX7VRNDJNIO2P6KXC/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":"2026-06-03T22:51:17Z","links":{"resolver":"https://pith.science/pith/OOOMWGSFPJX7VRNDJNIO2P6KXC","bundle":"https://pith.science/pith/OOOMWGSFPJX7VRNDJNIO2P6KXC/bundle.json","state":"https://pith.science/pith/OOOMWGSFPJX7VRNDJNIO2P6KXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOOMWGSFPJX7VRNDJNIO2P6KXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OOOMWGSFPJX7VRNDJNIO2P6KXC","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":"db22c07ec080bfc635176608a263f173b13208ebb02b979fc033015a5597f4d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T07:07:12Z","title_canon_sha256":"9e13f60d5bae99117ec07a45b958d0d3287078e3167d134a1d6ab842cf262829"},"schema_version":"1.0","source":{"id":"1406.4621","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4621","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4621v1","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4621","created_at":"2026-05-18T02:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"OOOMWGSFPJX7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OOOMWGSFPJX7VRND","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OOOMWGSF","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:5b2fbc8587aa630f8b529ee89fcba77a6adf028cfa8fa9bb199b6e3ecfe7dabb","target":"graph","created_at":"2026-05-18T02:49:31Z","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":"Let $\\mu$ be a probability measure on $\\rr^n$ ($n \\geq 2$) with Lebesgue density proportional to $e^{-V (\\Vert x\\Vert )}$, where $V : \\rr_+ \\to \\rr$ is a smooth convex potential. We show that the associated spectral gap in $L^2 (\\mu)$ lies between $(n-1) / \\int_{\\rr^n} \\Vert x\\Vert ^2 \\mu(dx)$ and $n / \\int_{\\rr^n} \\Vert x\\Vert ^2 \\mu(dx)$, improving a well-known two-sided estimate due to Bobkov. Our Markovian approach is remarkably simple and is sufficiently robust to be extended beyond the log-concave case, at the price of potentially modifying the underlying dynamics in the energy, leading ","authors_text":"Ald\\'eric Joulin (IMT), Michel Bonnefont (IMB), Yutao ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T07:07:12Z","title":"Spectral gap for spherically symmetric log-concave probability measures, and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4621","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":"sha256:211e08d331410952a084ae1e4d2ffb5109cfb5f86909c113b726bb46226e1ee5","target":"record","created_at":"2026-05-18T02:49:31Z","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":"db22c07ec080bfc635176608a263f173b13208ebb02b979fc033015a5597f4d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-18T07:07:12Z","title_canon_sha256":"9e13f60d5bae99117ec07a45b958d0d3287078e3167d134a1d6ab842cf262829"},"schema_version":"1.0","source":{"id":"1406.4621","kind":"arxiv","version":1}},"canonical_sha256":"739ccb1a457a6ffac5a34b50ed3fcab8be983bfe5ba98b78244054a727bfb7bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"739ccb1a457a6ffac5a34b50ed3fcab8be983bfe5ba98b78244054a727bfb7bc","first_computed_at":"2026-05-18T02:49:31.131305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:31.131305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NeeehgJzfC9Cf5R85PzE36xHKamiCx4Ce1pkRWDS+/RUNaDy5dmRUl+dj5dCojmTbM7Ws50LhW5jegP6/Xj5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:31.131733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4621","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:211e08d331410952a084ae1e4d2ffb5109cfb5f86909c113b726bb46226e1ee5","sha256:5b2fbc8587aa630f8b529ee89fcba77a6adf028cfa8fa9bb199b6e3ecfe7dabb"],"state_sha256":"3def6efa67d856e0cd565557493598d2074dde645a16b9bdc2616a1716b91758"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZZbJCM5bZthL6j31N85evzhST0AM6N4zaBbVBbbuJq6xUzOuduvNC3VAbh5HMQ8sqwd4FOtzRpTu1i/XZWdAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T22:51:17.530127Z","bundle_sha256":"9a0900e9e8b2589e0df6fd8b490e4632278ad5e0fb8a28fc456377eb12873199"}}