Pith Number

pith:MAOLMWN2

pith:2026:MAOLMWN2KAJSEQDQHYYDWUAZRP

not attested not anchored not stored refs pending

Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics

Satoshi Noguchi, Yoshinobu Kawahara

Mesh-based physics admits a local factorization into port-Hamiltonian form where mesh topology alone fixes the conservative interconnection.

arxiv:2605.00394 v2 · 2026-05-01 · cs.LG

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Claims

C1strongest claim

We prove a reduction theorem for mesh-based physics. Under these conditions, the physical dynamics admit a local factorization into a port-Hamiltonian form: the conservative interconnection is fixed uniquely by mesh topology, whereas metric effects enter only through constitutive relations and dissipation.

C2weakest assumption

The minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality) are sufficient to guarantee that the conservative interconnection is fixed uniquely by mesh topology alone.

C3one line summary

Mesh Field Theory reduces mesh-based physics to port-Hamiltonian form with topology fixing interconnections and metrics entering only via constitutive relations, enabling MeshFT-Net to achieve near-zero energy drift, correct dispersion, momentum conservation, and strong out-of-distribution fidelity.

Receipt and verification

First computed	2026-05-28T01:04:41.220543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

601cb659ba50132240703e303b50198bc4faff499de787b904a410149385e293

Aliases

arxiv: 2605.00394 · arxiv_version: 2605.00394v2 · doi: 10.48550/arxiv.2605.00394 · pith_short_12: MAOLMWN2KAJS · pith_short_16: MAOLMWN2KAJSEQDQ · pith_short_8: MAOLMWN2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MAOLMWN2KAJSEQDQHYYDWUAZRP \
  | 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: 601cb659ba50132240703e303b50198bc4faff499de787b904a410149385e293

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8108f2924fb1497ebe61fdc5904548e4796374f8d72bf290a371f686995ccc33",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-01T04:35:21Z",
    "title_canon_sha256": "939519751febf7bc8c84095b8d73760e3213639a58b7a03b87ca123977401bd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00394",
    "kind": "arxiv",
    "version": 2
  }
}