Pith Number

pith:LKVCEYCV

pith:2026:LKVCEYCV6C2EBHAD24UXC554XB

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Resolving the viscosity operator ambiguity on Riemannian manifolds via a kinematic selection principle

Samuel L. Braunstein, Zhi-Wei Wang

A Lagrangian kinematic construction uniquely selects the deformation Laplacian as the viscous operator for fluids on Riemannian manifolds.

arxiv:2605.17502 v1 · 2026-05-17 · math-ph · math.AP · math.DG · math.MP · physics.flu-dyn

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Claims

C1strongest claim

A Lagrangian kinematic construction, in which the strain rate is built from the rate of change of inner products of Lie-dragged connecting vectors, uniquely selects the deformation Laplacian for fluids whose configuration space is intrinsically the manifold.

C2weakest assumption

The strain rate constructed from inner-product geometry of Lie-dragged vectors is symmetric and possesses no antisymmetric part, which is invoked to exclude the Hodge Laplacian at the kinematic step before constitutive assumptions.

C3one line summary

A Lagrangian kinematic construction from inner-product changes of Lie-dragged vectors uniquely selects the deformation Laplacian for intrinsic fluid configuration spaces on Riemannian manifolds.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] Czubak, In search of the viscosity operator on Riemannian manifolds,Notices Amer 2024

[2] D.G. Ebin and J. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid,Ann. Math.92(1970) 102–163 1970

[3] Arnold, Sur la g´ eom´ etrie diff´ erentielle des groupes de Lie de dimension infinie et ses applications ` a l’hydrodynamique des fluides parfaits,Ann 1966

[4] Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evo- lution equations,Comm 1992

[5] Taylor,Partial Differential Equations III: Nonlinear Equations, 2nd ed., Springer, 2011 2011

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:42.509931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5aaa226055f0b4409c03d7297177bcb8496ec6cc015e99757b3203c241880d2a

Aliases

arxiv: 2605.17502 · arxiv_version: 2605.17502v1 · doi: 10.48550/arxiv.2605.17502 · pith_short_12: LKVCEYCV6C2E · pith_short_16: LKVCEYCV6C2EBHAD · pith_short_8: LKVCEYCV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LKVCEYCV6C2EBHAD24UXC554XB \
  | 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: 5aaa226055f0b4409c03d7297177bcb8496ec6cc015e99757b3203c241880d2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10e377c8d495fe64e7b0568f201c7627cfa974af5a5a680b900004878fa75c00",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG",
      "math.MP",
      "physics.flu-dyn"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-17T15:22:49Z",
    "title_canon_sha256": "f5ec37fdaa817b8ffb6064663ece4dc546700d8e63485a5c195f2944919c1cb9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17502",
    "kind": "arxiv",
    "version": 1
  }
}