Pith Number

pith:IIKRGJRO

pith:2026:IIKRGJRORWIBC4MPB2VVYWHCMM

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Emergence of Complex Web Structures

Francisco-Shu Kitaura

A Lagrangian-Eulerian transport map governs density amplification through its Jacobian while anisotropic collapse follows from the eigenvalues of successive deformation tensors.

arxiv:2604.11481 v2 · 2026-04-13 · astro-ph.CO · math-ph · math.MP · nlin.PS · physics.data-an · stat.AP

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Claims

C1strongest claim

Using a Lagrangian--Eulerian transport map, we show how density amplification is governed by the Jacobian of the deformation and how anisotropic collapse arises from the eigenvalues of a hierarchy of deformation tensors... the nonlocal tidal level becomes relevant already at moderate overdensity.

C2weakest assumption

That the proposed Lagrangian-Eulerian transport geometry and its connection to a maximum-entropy Gaussian baseline plus Landau-Ginzburg effective description accurately capture the dynamics and entropy behavior across the relevant scales without additional unstated assumptions about the underlying microscopic interactions.

C3one line summary

Coarse-grained spatial ordering can increase during structure formation even as full phase-space entropy grows through nonlocal transport, Jacobian-governed density amplification, and activation of lower free-energy branches in a Landau-Ginzburg description.

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1 paper in Pith

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Receipt and verification

First computed	2026-05-27T01:05:54.393507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

421513262e8d9011718f0eab5c58e26308f26499a17377895da93b3ae04f8bfc

Aliases

arxiv: 2604.11481 · arxiv_version: 2604.11481v2 · doi: 10.48550/arxiv.2604.11481 · pith_short_12: IIKRGJRORWIB · pith_short_16: IIKRGJRORWIBC4MP · pith_short_8: IIKRGJRO

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IIKRGJRORWIBC4MPB2VVYWHCMM \
  | 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: 421513262e8d9011718f0eab5c58e26308f26499a17377895da93b3ae04f8bfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83bcc42c653344a90c45bb78a0c85879bd05f85ebf9c88cc07fdebfb4faa6659",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "nlin.PS",
      "physics.data-an",
      "stat.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2026-04-13T13:47:35Z",
    "title_canon_sha256": "96ed80d205fac666dad17f338a12a351ebd2157df52d6d4715ab22a4130e4e27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11481",
    "kind": "arxiv",
    "version": 2
  }
}