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Although the empirical measure of this system converges to the same McKean--Vlasov limit as in the corresponding exchangeable mean-field system, the sequential structure remains visible at the $N^{-1/2}$ fluctuation scale. We introduce the logarithmically weighted fluctuation fields \\[ Y_t^{N,n} =\n\\frac{1}{\\sqrt{N}} \\sum_{i=1}^N \\frac{\\bigl(\\log(N/i)\\bigr)^n}{n!} (\\delta_{X_t^i}-\\bar\\rho_t), \\qquad n\\ge 0, \\] and prove joint convergence of the entir"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.22470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-07-24T16:37:32Z","cross_cats_sorted":[],"title_canon_sha256":"26839eb24788e6420955f8ca16e968d1e6a3897136e74d8593e65b74cfd9f492","abstract_canon_sha256":"62d186a1f259f161139fa38d0d176e4c5bda5ea99b215c383b31eecd0d0f3d99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-27T01:21:22.722451Z","signature_b64":"DoodMCagAHyTV7f3cIQaT9sB+10jydsvKpCIHX/Z3LICKz/uEj7aaXYjMktssvHih+EWILRk5twverYoqv5sDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"475fcc071548fb094053ec391ff3acc7af7b6f2e514472b211c95c1de0a58d1e","last_reissued_at":"2026-07-27T01:21:22.721550Z","signature_status":"signed_v1","first_computed_at":"2026-07-27T01:21:22.721550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Logarithmic Fluctuation Hierarchy for Sequential Interacting Diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xianliang Zhao, Zhenfu Wang","submitted_at":"2026-07-24T16:37:32Z","abstract_excerpt":"We study Gaussian fluctuations for a lower-triangular system of interacting diffusions in which particle $i$ interacts only with its predecessors. Although the empirical measure of this system converges to the same McKean--Vlasov limit as in the corresponding exchangeable mean-field system, the sequential structure remains visible at the $N^{-1/2}$ fluctuation scale. We introduce the logarithmically weighted fluctuation fields \\[ Y_t^{N,n} =\n\\frac{1}{\\sqrt{N}} \\sum_{i=1}^N \\frac{\\bigl(\\log(N/i)\\bigr)^n}{n!} (\\delta_{X_t^i}-\\bar\\rho_t), \\qquad n\\ge 0, \\] and prove joint convergence of the entir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22470","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/2607.22470/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.22470","created_at":"2026-07-27T01:21:22.722012+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.22470v1","created_at":"2026-07-27T01:21:22.722012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22470","created_at":"2026-07-27T01:21:22.722012+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5P4YBYVJD5Q","created_at":"2026-07-27T01:21:22.722012+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5P4YBYVJD5QSQCT","created_at":"2026-07-27T01:21:22.722012+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5P4YBYV","created_at":"2026-07-27T01:21:22.722012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6","json":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6.json","graph_json":"https://pith.science/api/pith-number/I5P4YBYVJD5QSQCT5Q4R745MY6/graph.json","events_json":"https://pith.science/api/pith-number/I5P4YBYVJD5QSQCT5Q4R745MY6/events.json","paper":"https://pith.science/paper/I5P4YBYV"},"agent_actions":{"view_html":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6","download_json":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6.json","view_paper":"https://pith.science/paper/I5P4YBYV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.22470&json=true","fetch_graph":"https://pith.science/api/pith-number/I5P4YBYVJD5QSQCT5Q4R745MY6/graph.json","fetch_events":"https://pith.science/api/pith-number/I5P4YBYVJD5QSQCT5Q4R745MY6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6/action/storage_attestation","attest_author":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6/action/author_attestation","sign_citation":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6/action/citation_signature","submit_replication":"https://pith.science/pith/I5P4YBYVJD5QSQCT5Q4R745MY6/action/replication_record"}},"created_at":"2026-07-27T01:21:22.722012+00:00","updated_at":"2026-07-27T01:21:22.722012+00:00"}