{"paper":{"title":"Matrix-noise Jacobians in stochastic-calculus inference and optimal paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"In multidimensional systems with matrix-valued multiplicative noise, a Jacobian term from the noise amplitude survives scalar cancellations and alters fitted stochastic prescriptions and optimal paths.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Surachate Limkumnerd","submitted_at":"2026-05-13T04:07:31Z","abstract_excerpt":"Multiplicative noise makes stochastic dynamics depend on how the white-noise limit is interpreted. In multidimensional systems with matrix-valued noise amplitudes $\\sigma(x)$, this dependence includes a local Jacobian contribution that is absent from the scalar examples most often used to build intuition. We formulate a finite-step path-likelihood framework for $\\theta$-discretized diffusions and show that its short-time expansion isolates the scalar $J_\\sigma=\\partial_j\\sigma_{ik}\\partial_i\\sigma_{jk}-(\\partial_i\\sigma_{ik})(\\partial_l\\sigma_{lk})$. For a specified noise-amplitude representat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For a specified noise-amplitude representation σ, the quantity J_σ vanishes in one-dimensional, scalar-isotropic, and strictly diagonal cases, but can survive when state-dependent noise directions mix different components and produce measurable changes in fitted stochastic prescriptions and Onsager-Machlup paths.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The finite-step path-likelihood framework for θ-discretized diffusions accurately isolates the continuous-limit Jacobian contribution without additional discretization artifacts that would cancel J_σ.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A matrix-noise Jacobian J_σ = ∂_j σ_ik ∂_i σ_jk − (∂_i σ_ik)(∂_l σ_lk) survives scalar cancellations and measurably affects path likelihoods and Onsager-Machlup paths in multidimensional systems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In multidimensional systems with matrix-valued multiplicative noise, a Jacobian term from the noise amplitude survives scalar cancellations and alters fitted stochastic prescriptions and optimal paths.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"208e90b2db586d4ebdc1a08b44993092508cb0d5fc95c1478a945b65b1743047"},"source":{"id":"2605.12972","kind":"arxiv","version":1},"verdict":{"id":"8655b720-7c49-4c7e-84b8-b5c124f2912d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:40:16.713159Z","strongest_claim":"For a specified noise-amplitude representation σ, the quantity J_σ vanishes in one-dimensional, scalar-isotropic, and strictly diagonal cases, but can survive when state-dependent noise directions mix different components and produce measurable changes in fitted stochastic prescriptions and Onsager-Machlup paths.","one_line_summary":"A matrix-noise Jacobian J_σ = ∂_j σ_ik ∂_i σ_jk − (∂_i σ_ik)(∂_l σ_lk) survives scalar cancellations and measurably affects path likelihoods and Onsager-Machlup paths in multidimensional systems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The finite-step path-likelihood framework for θ-discretized diffusions accurately isolates the continuous-limit Jacobian contribution without additional discretization artifacts that would cancel J_σ.","pith_extraction_headline":"In multidimensional systems with matrix-valued multiplicative noise, a Jacobian term from the noise amplitude survives scalar cancellations and alters fitted stochastic prescriptions and optimal paths."},"references":{"count":21,"sample":[{"doi":"","year":1982,"title":"J. 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Volpe, Nature Communications4, 2733 (2013)","work_id":"ebc8a42b-6ae8-4f31-ae5e-7b80d5b241b0","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":21,"snapshot_sha256":"f8cace8c5891905b06edc179c4d44445c4e37160d73fd61b7db2398422deece5","internal_anchors":3},"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"}