{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CLX4CRIQ3FCDYLWARXCV76QZCN","short_pith_number":"pith:CLX4CRIQ","canonical_record":{"source":{"id":"2405.15128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-05-24T01:01:03Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b2e89e05c86eda49ae8816201a20309205fe002e13b2b7986c3cde8ddcd91524","abstract_canon_sha256":"56398c9b802bcb822ab052708e8975dd1e02eb89718be983486a2397d6256f92"},"schema_version":"1.0"},"canonical_sha256":"12efc14510d9443c2ec08dc55ffa191374ed0f62c4282e74f20ba8a5c41dec2c","source":{"kind":"arxiv","id":"2405.15128","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.15128","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"2405.15128v1","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15128","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"CLX4CRIQ3FCD","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"pith_short_16","alias_value":"CLX4CRIQ3FCDYLWA","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"pith_short_8","alias_value":"CLX4CRIQ","created_at":"2026-07-05T08:22:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CLX4CRIQ3FCDYLWARXCV76QZCN","target":"record","payload":{"canonical_record":{"source":{"id":"2405.15128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-05-24T01:01:03Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b2e89e05c86eda49ae8816201a20309205fe002e13b2b7986c3cde8ddcd91524","abstract_canon_sha256":"56398c9b802bcb822ab052708e8975dd1e02eb89718be983486a2397d6256f92"},"schema_version":"1.0"},"canonical_sha256":"12efc14510d9443c2ec08dc55ffa191374ed0f62c4282e74f20ba8a5c41dec2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:22:45.575072Z","signature_b64":"DdF4cnp8PaHbMLUd18BS4UwDep2rXfxOgaVuzosRN2r9nxE23Ul75KfmyTRk7C+crM3lJVHXl6aKL4fTefhdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12efc14510d9443c2ec08dc55ffa191374ed0f62c4282e74f20ba8a5c41dec2c","last_reissued_at":"2026-07-05T08:22:45.574545Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:22:45.574545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.15128","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":"2026-07-05T08:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXhu9KI82e1i3hwtlR1JTw43Dm+4q9GEZoLVpoBUrxrdxjaI/LnLKb+gqQhoGT3LLQeiUl8q54j5kkxrTCTpAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:08:23.916367Z"},"content_sha256":"06bec760f7ec065213d87c3eace4a599adc46491a88c51942600eef8a0efacbb","schema_version":"1.0","event_id":"sha256:06bec760f7ec065213d87c3eace4a599adc46491a88c51942600eef8a0efacbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CLX4CRIQ3FCDYLWARXCV76QZCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fluctuations around the mean-field limit for attractive Riesz potentials in the moderate regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Alexandra Holzinger, Ansgar J\\\"ungel, Li Chen","submitted_at":"2024-05-24T01:01:03Z","abstract_excerpt":"A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become asymptotically Gaussians in the limit of infinitely many particles. The methodology is inspired by the classical work of Oelschl\\\"ager on fluctuations for the porous-medium equation. The novelty in this work is that we can allow for attractive potentials in the moderate regime and still obtain asymptotic Gaussian fluctuations. The key element of the proof is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15128","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/2405.15128/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":"2026-07-05T08:22:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a25zoNtQeXiX6f5zwFYV8UIm3DNhG44NHzC1g7IOBrQEor9jsjSm6ZObLFnm0w8hlixuHIZB1t41Ru2x/NmkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:08:23.916878Z"},"content_sha256":"1c8fef72f52f5cf927c02a8542f82c4390a7369ffc925706bfca2c6024c9fa7c","schema_version":"1.0","event_id":"sha256:1c8fef72f52f5cf927c02a8542f82c4390a7369ffc925706bfca2c6024c9fa7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLX4CRIQ3FCDYLWARXCV76QZCN/bundle.json","state_url":"https://pith.science/pith/CLX4CRIQ3FCDYLWARXCV76QZCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLX4CRIQ3FCDYLWARXCV76QZCN/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":"2026-08-12T05:08:23Z","links":{"resolver":"https://pith.science/pith/CLX4CRIQ3FCDYLWARXCV76QZCN","bundle":"https://pith.science/pith/CLX4CRIQ3FCDYLWARXCV76QZCN/bundle.json","state":"https://pith.science/pith/CLX4CRIQ3FCDYLWARXCV76QZCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLX4CRIQ3FCDYLWARXCV76QZCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CLX4CRIQ3FCDYLWARXCV76QZCN","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":"56398c9b802bcb822ab052708e8975dd1e02eb89718be983486a2397d6256f92","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-05-24T01:01:03Z","title_canon_sha256":"b2e89e05c86eda49ae8816201a20309205fe002e13b2b7986c3cde8ddcd91524"},"schema_version":"1.0","source":{"id":"2405.15128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.15128","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"arxiv_version","alias_value":"2405.15128v1","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15128","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"pith_short_12","alias_value":"CLX4CRIQ3FCD","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"pith_short_16","alias_value":"CLX4CRIQ3FCDYLWA","created_at":"2026-07-05T08:22:45Z"},{"alias_kind":"pith_short_8","alias_value":"CLX4CRIQ","created_at":"2026-07-05T08:22:45Z"}],"graph_snapshots":[{"event_id":"sha256:1c8fef72f52f5cf927c02a8542f82c4390a7369ffc925706bfca2c6024c9fa7c","target":"graph","created_at":"2026-07-05T08:22:45Z","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/2405.15128/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become asymptotically Gaussians in the limit of infinitely many particles. The methodology is inspired by the classical work of Oelschl\\\"ager on fluctuations for the porous-medium equation. The novelty in this work is that we can allow for attractive potentials in the moderate regime and still obtain asymptotic Gaussian fluctuations. The key element of the proof is the","authors_text":"Alexandra Holzinger, Ansgar J\\\"ungel, Li Chen","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-05-24T01:01:03Z","title":"Fluctuations around the mean-field limit for attractive Riesz potentials in the moderate regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15128","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":"sha256:06bec760f7ec065213d87c3eace4a599adc46491a88c51942600eef8a0efacbb","target":"record","created_at":"2026-07-05T08:22:45Z","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":"56398c9b802bcb822ab052708e8975dd1e02eb89718be983486a2397d6256f92","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-05-24T01:01:03Z","title_canon_sha256":"b2e89e05c86eda49ae8816201a20309205fe002e13b2b7986c3cde8ddcd91524"},"schema_version":"1.0","source":{"id":"2405.15128","kind":"arxiv","version":1}},"canonical_sha256":"12efc14510d9443c2ec08dc55ffa191374ed0f62c4282e74f20ba8a5c41dec2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12efc14510d9443c2ec08dc55ffa191374ed0f62c4282e74f20ba8a5c41dec2c","first_computed_at":"2026-07-05T08:22:45.574545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:22:45.574545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DdF4cnp8PaHbMLUd18BS4UwDep2rXfxOgaVuzosRN2r9nxE23Ul75KfmyTRk7C+crM3lJVHXl6aKL4fTefhdAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:22:45.575072Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.15128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06bec760f7ec065213d87c3eace4a599adc46491a88c51942600eef8a0efacbb","sha256:1c8fef72f52f5cf927c02a8542f82c4390a7369ffc925706bfca2c6024c9fa7c"],"state_sha256":"6e8b8326918ea9b963990764b573770d278fcb66048a42e7af3ee894279d9537"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFYhyeIPOh6K/GlxehElvAJtZM4ZeowSGKJT1ZVRwZDZT9//ARiSqmYl2pgMckghxkeCXmzI07NKtQPWFvjkDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T05:08:23.920741Z","bundle_sha256":"2d48716ad7ac779aa6258585690890a6ba57a7f888fe5d5121ff70057370d413"}}