{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:W6XLMDYYXZRKPGE4KU4BXLU6H5","short_pith_number":"pith:W6XLMDYY","canonical_record":{"source":{"id":"2409.17901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-26T14:49:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d33fe0e01d03616e4627756d63ba53634519e03c627ddc8bead4be948c99a6be","abstract_canon_sha256":"c26acb4ca48449b8d38a5d58040f13a79203ad38346b9563d853ac0e99239345"},"schema_version":"1.0"},"canonical_sha256":"b7aeb60f18be62a7989c55381bae9e3f52ffc1dfe4941b8c3e76e5af00edfe71","source":{"kind":"arxiv","id":"2409.17901","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.17901","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"arxiv_version","alias_value":"2409.17901v1","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.17901","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"pith_short_12","alias_value":"W6XLMDYYXZRK","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"pith_short_16","alias_value":"W6XLMDYYXZRKPGE4","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"pith_short_8","alias_value":"W6XLMDYY","created_at":"2026-07-05T09:12:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:W6XLMDYYXZRKPGE4KU4BXLU6H5","target":"record","payload":{"canonical_record":{"source":{"id":"2409.17901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-26T14:49:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d33fe0e01d03616e4627756d63ba53634519e03c627ddc8bead4be948c99a6be","abstract_canon_sha256":"c26acb4ca48449b8d38a5d58040f13a79203ad38346b9563d853ac0e99239345"},"schema_version":"1.0"},"canonical_sha256":"b7aeb60f18be62a7989c55381bae9e3f52ffc1dfe4941b8c3e76e5af00edfe71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:12:17.295854Z","signature_b64":"6TDzPYgRY+0lvHNgFKkJYePB14LmDdmiKI6kkzSpSU6ItrCa7Fd9ihPsvbmYZHY8lNHAGLamCV+fZ3bC+9+PAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7aeb60f18be62a7989c55381bae9e3f52ffc1dfe4941b8c3e76e5af00edfe71","last_reissued_at":"2026-07-05T09:12:17.295368Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:12:17.295368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.17901","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":"2026-07-05T09:12:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rnjjv8UnqkCjukuDa6RBv5aBvYAx+jDdSJ4MTywY7779rRhbacUe1oAZs3KGyc5NZWswk8akoetZTxLF8a+dAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T08:23:11.407213Z"},"content_sha256":"108904bf453ae45d4bbc866c8b20e232788f2a468776525657a452c74b62359b","schema_version":"1.0","event_id":"sha256:108904bf453ae45d4bbc866c8b20e232788f2a468776525657a452c74b62359b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:W6XLMDYYXZRKPGE4KU4BXLU6H5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform log-Sobolev inequalities for mean field particles beyond flat-convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Pierre Monmarch\\'e","submitted_at":"2024-09-26T14:49:56Z","abstract_excerpt":"In the nice recent work [48], S. Wang established uniform log-Sobolev inequalities for mean field particles when the energy is flat convex. In this note we comment how to extend his proof to some semi-convex energies provided the curvature lower-bound is not too negative. It is not clear that this could be obtained simply by applying a posteriori a perturbation argument to Wang's result. Rather, we follow his proof and, at steps where the convexity is used, we notice that the uniform conditional or local functional inequalities assumed give some room to allow for a bit of concavity. In particu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17901","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/2409.17901/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":"2026-07-05T09:12:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XB1Ovkzd6kf82WfB0LJiBJEfh6PK80q8tRe16Rm23plGwf4GUQBxbrmIC5/9VF645vGBv57ncEqkVKa+ca+XDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T08:23:11.407719Z"},"content_sha256":"ef2761708873b7f2a96de654af0d7a2d94fdbfdba0a86ca7e3488554c512f88d","schema_version":"1.0","event_id":"sha256:ef2761708873b7f2a96de654af0d7a2d94fdbfdba0a86ca7e3488554c512f88d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6XLMDYYXZRKPGE4KU4BXLU6H5/bundle.json","state_url":"https://pith.science/pith/W6XLMDYYXZRKPGE4KU4BXLU6H5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6XLMDYYXZRKPGE4KU4BXLU6H5/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":"2026-08-21T08:23:11Z","links":{"resolver":"https://pith.science/pith/W6XLMDYYXZRKPGE4KU4BXLU6H5","bundle":"https://pith.science/pith/W6XLMDYYXZRKPGE4KU4BXLU6H5/bundle.json","state":"https://pith.science/pith/W6XLMDYYXZRKPGE4KU4BXLU6H5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6XLMDYYXZRKPGE4KU4BXLU6H5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:W6XLMDYYXZRKPGE4KU4BXLU6H5","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":"c26acb4ca48449b8d38a5d58040f13a79203ad38346b9563d853ac0e99239345","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-26T14:49:56Z","title_canon_sha256":"d33fe0e01d03616e4627756d63ba53634519e03c627ddc8bead4be948c99a6be"},"schema_version":"1.0","source":{"id":"2409.17901","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.17901","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"arxiv_version","alias_value":"2409.17901v1","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.17901","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"pith_short_12","alias_value":"W6XLMDYYXZRK","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"pith_short_16","alias_value":"W6XLMDYYXZRKPGE4","created_at":"2026-07-05T09:12:17Z"},{"alias_kind":"pith_short_8","alias_value":"W6XLMDYY","created_at":"2026-07-05T09:12:17Z"}],"graph_snapshots":[{"event_id":"sha256:ef2761708873b7f2a96de654af0d7a2d94fdbfdba0a86ca7e3488554c512f88d","target":"graph","created_at":"2026-07-05T09:12:17Z","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/2409.17901/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the nice recent work [48], S. Wang established uniform log-Sobolev inequalities for mean field particles when the energy is flat convex. In this note we comment how to extend his proof to some semi-convex energies provided the curvature lower-bound is not too negative. It is not clear that this could be obtained simply by applying a posteriori a perturbation argument to Wang's result. Rather, we follow his proof and, at steps where the convexity is used, we notice that the uniform conditional or local functional inequalities assumed give some room to allow for a bit of concavity. In particu","authors_text":"Pierre Monmarch\\'e","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-26T14:49:56Z","title":"Uniform log-Sobolev inequalities for mean field particles beyond flat-convexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17901","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":"sha256:108904bf453ae45d4bbc866c8b20e232788f2a468776525657a452c74b62359b","target":"record","created_at":"2026-07-05T09:12:17Z","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":"c26acb4ca48449b8d38a5d58040f13a79203ad38346b9563d853ac0e99239345","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-09-26T14:49:56Z","title_canon_sha256":"d33fe0e01d03616e4627756d63ba53634519e03c627ddc8bead4be948c99a6be"},"schema_version":"1.0","source":{"id":"2409.17901","kind":"arxiv","version":1}},"canonical_sha256":"b7aeb60f18be62a7989c55381bae9e3f52ffc1dfe4941b8c3e76e5af00edfe71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7aeb60f18be62a7989c55381bae9e3f52ffc1dfe4941b8c3e76e5af00edfe71","first_computed_at":"2026-07-05T09:12:17.295368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:12:17.295368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6TDzPYgRY+0lvHNgFKkJYePB14LmDdmiKI6kkzSpSU6ItrCa7Fd9ihPsvbmYZHY8lNHAGLamCV+fZ3bC+9+PAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:12:17.295854Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.17901","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:108904bf453ae45d4bbc866c8b20e232788f2a468776525657a452c74b62359b","sha256:ef2761708873b7f2a96de654af0d7a2d94fdbfdba0a86ca7e3488554c512f88d"],"state_sha256":"aa9d0546784e830503fd8d0dcdf8905b75bd398110aa5ae0cedfbf8e2f4c106c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kVd+MFuuffYmeIQiLZqEV/6NDepkH6AfvL9i10O4I81Y/RHTZXT4+5oM6UBunscJOIGEIPdFW/AMzZ6wpQ9QDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T08:23:11.413509Z","bundle_sha256":"48409a979ecf2355c5f953628454acd8c3bd3582b657ff58fb83dea826f62d82"}}