Pith Number

pith:QRKLIXN7

pith:2026:QRKLIXN7OPMCLY2JWHWQWKVQ7W

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Matrix-noise Jacobians in stochastic-calculus inference and optimal paths

Surachate Limkumnerd

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.

arxiv:2605.12972 v1 · 2026-05-13 · cond-mat.stat-mech

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

21 extracted · 21 resolved · 3 Pith anchors

[1] J. M. Sancho, M. San Miguel, and D. D¨ urr, Journal of Statistical Physics28, 291 (1982) 1982

[2] R. Kupferman, G. A. Pavliotis, and A. M. Stuart, Phys- ical Review E70, 036120 (2004) 2004

[3] State-dependent diffusion: thermodynamic consistency and its path integral formulation 2007 · arXiv:0707.2234

[4] G. Volpe and J. Wehr, Reports on Progress in Physics 79, 053901 (2016) 2016

[5] G. Pesce, A. McDaniel, S. Hottovy, J. Wehr, and G. Volpe, Nature Communications4, 2733 (2013) 2013

Receipt and verification

First computed	2026-05-18T03:09:08.903244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8454b45dbf73d825e349b1ed0b2ab0fdbcf79efdfbd26928c2a0deb8a9b615a1

Aliases

arxiv: 2605.12972 · arxiv_version: 2605.12972v1 · doi: 10.48550/arxiv.2605.12972 · pith_short_12: QRKLIXN7OPMC · pith_short_16: QRKLIXN7OPMCLY2J · pith_short_8: QRKLIXN7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QRKLIXN7OPMCLY2JWHWQWKVQ7W \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 8454b45dbf73d825e349b1ed0b2ab0fdbcf79efdfbd26928c2a0deb8a9b615a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d199b3abb74c3a9814c2bdae5d8bdbf1ac9e2dc23cbe6672836c7c38d71c523",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-13T04:07:31Z",
    "title_canon_sha256": "e42f1f39baaae5c65dfc1f3e4013a0667a69f75692691ed5ee94afc10fb3f4e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12972",
    "kind": "arxiv",
    "version": 1
  }
}