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pith:AQTTOD37

pith:2026:AQTTOD37VFBKNSKOKOQYZBMEKP

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A Variational Lagrangian Framework for Log-Homotopy Particle Flow Filters

Domonkos Csuzdi, Oliv\'er T\"or\H{o}, Tam\'as B\'ecsi

Treating particle flow as pressureless fluid motion and minimizing a kinetic energy action under continuity and log-homotopy constraints produces an irrotational potential flow governed by a Hamilton-Jacobi equation isomorphic to Madelung's

arxiv:2605.15379 v1 · 2026-05-14 · eess.SY · cs.SY · physics.flu-dyn

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Claims

C1strongest claim

Applying the principle of least action to a Lagrangian defined by kinetic energy subject to the continuity equation and log-homotopy evolution yields Euler-Lagrange equations that produce an irrotational potential flow, resulting in a coupled Hamilton-Jacobi equation structurally isomorphic to Madelung's hydrodynamic formulation of quantum mechanics.

C2weakest assumption

The particle flow can be modeled as the motion of a pressureless inviscid fluid, allowing a well-defined Lagrangian action based solely on kinetic energy that is minimized under the continuity and log-homotopy constraints to produce the claimed optimal flow structure.

C3one line summary

A variational Lagrangian based on kinetic energy under continuity and log-homotopy constraints produces an irrotational flow for particle filters that is structurally isomorphic to Madelung's quantum fluid equations.

References

29 extracted · 29 resolved · 1 Pith anchors

[1] M.-H. Chen, Q.-M. Shao, and J. G. Ibrahim,Monte Carlo methods in Bayesian computation. Springer Science & Business Media, 2012 2012

[2] C. P. Robert and G. Casella,Monte Carlo Statistical Methods. Springer, 2nd ed., 2004 2004

[3] Novel approach to nonlinear/non-Gaussian Bayesian state estimation, 1993

[4] Curse of dimensionality and particle filters, 2003

[5] Curse-of-dimensionality revisited: Collapse of the particle filter in very large scale systems, 2008

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:55.379933Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0427370f7fa942a6c94e53a18c858453e6a07a6794fdd6daed14e03caa93c31e

Aliases

arxiv: 2605.15379 · arxiv_version: 2605.15379v1 · doi: 10.48550/arxiv.2605.15379 · pith_short_12: AQTTOD37VFBK · pith_short_16: AQTTOD37VFBKNSKO · pith_short_8: AQTTOD37

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AQTTOD37VFBKNSKOKOQYZBMEKP \
  | 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: 0427370f7fa942a6c94e53a18c858453e6a07a6794fdd6daed14e03caa93c31e

Canonical record JSON

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    "abstract_canon_sha256": "d3cb9ab6465cd48205037a7928ef2aa852a4fec7795416c0c3d3fc475c3bdff2",
    "cross_cats_sorted": [
      "cs.SY",
      "physics.flu-dyn"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-05-14T20:09:33Z",
    "title_canon_sha256": "ac3472087915b514e0dbd835b1be140fffa98b9ebf48a8d2f0fcf1af145eea5d"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}