Pith Number

pith:VXWTQE3Z

pith:2026:VXWTQE3ZPQF4GMSEFDXL6X7TU2

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Co-rotating Vortices on Surfaces of Variable Negative Curvature: Hamiltonian Structure and Curvature-Induced Drift

Gaurang Mangesh Joshi, Rickmoy Samanta

Two identical vortices on a catenoid rotate rigidly at fixed latitude with speed set by the curvature gradient

arxiv:2604.25682 v2 · 2026-04-28 · math-ph · cond-mat.quant-gas · math.MP · nlin.SI · physics.flu-dyn

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\usepackage{pith}
\pithnumber{VXWTQE3ZPQF4GMSEFDXL6X7TU2}

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Record completeness

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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 two identical vortices we find an exact antipodal solution in which the pair rotates rigidly at fixed latitude, with angular velocity Ω=(Γ/16π) K'(V)/√(-K(V)), where K(V) is the Gaussian curvature. Thus the motion is governed by the curvature gradient rather than the curvature itself. The symmetric state is linearly unstable, with growth rate λ=√3|Ω|.

C2weakest assumption

The point-vortex idealization and the specific Hamiltonian structure derived from the Biot-Savart law or Green's function on the catenoid metric remain valid for the co-rotating pairs; the derivation assumes the surface is minimal and the vortices are identical in strength and sign.

C3one line summary

Co-rotating vortex pairs on a catenoid rotate rigidly at fixed latitude driven by curvature gradient rather than curvature value, with the symmetric state linearly unstable at growth rate √3|Ω| and generic pairs reducing to bounded oscillations plus secular drift.

Receipt and verification

First computed	2026-05-21T01:04:26.321883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aded3813797c0bc3324428eebf5ff3a699e998e85d54ce56b8dac28b782db268

Aliases

arxiv: 2604.25682 · arxiv_version: 2604.25682v2 · doi: 10.48550/arxiv.2604.25682 · pith_short_12: VXWTQE3ZPQF4 · pith_short_16: VXWTQE3ZPQF4GMSE · pith_short_8: VXWTQE3Z

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VXWTQE3ZPQF4GMSEFDXL6X7TU2 \
  | 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: aded3813797c0bc3324428eebf5ff3a699e998e85d54ce56b8dac28b782db268

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5122ac5fdfd65c6c4335ddf2c0b882fb312d8a43710bc845e4cac02003501d5f",
    "cross_cats_sorted": [
      "cond-mat.quant-gas",
      "math.MP",
      "nlin.SI",
      "physics.flu-dyn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-04-28T14:12:29Z",
    "title_canon_sha256": "b1ca4cf9382c98093ff446adc5e7a69dd2642bbe10e86186229aa399aa6e6d6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25682",
    "kind": "arxiv",
    "version": 2
  }
}