Pith Number

pith:TXDGQP3I

pith:2026:TXDGQP3I75HB7F5E2V7F2GTYTH

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A Unified Framework for Structured Flow Modeling: From Continuous Fields to Data-Driven Representations

Diego Casadei

Structured flows in dynamical systems can be modeled uniformly by connecting continuous Helmholtz-Hodge decompositions to discrete graph representations.

arxiv:2605.18250 v1 · 2026-05-18 · physics.data-an · cs.LG

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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

This work provides a unified perspective on such systems by connecting continuous formulations based on the Helmholtz-Hodge decomposition with discrete and data-driven representations, supported by a cross-domain validation strategy that leverages datasets from well-understood physical systems.

C2weakest assumption

That the recently proposed Graph Vector Field framework and the introduced hierarchy of models (parametric conditional, linear graph dynamical systems, reduced Hodge representations) can be systematically evaluated for trade-offs in complexity, interpretability, and performance using cross-domain physical datasets to verify correctness independently of the target application.

C3one line summary

Proposes a unified framework linking Helmholtz-Hodge decompositions to Graph Vector Field models and reduced variants, with cross-domain validation on physical datasets to balance expressivity and tractability.

References

14 extracted · 14 resolved · 0 Pith anchors

[1] Graph vector field: A unified framework for multimodal health risk assessment from heterogeneous wearable and environ- mental data streams, 2026 2026

[2] Cambridge University Press, 2002 2002

[3] Thomas J. R. Hughes.The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice Hall, 1987 1987

[4] Klaus-Jürgen Bathe.Finite Element Procedures, 2nd Ed.Pearson Education, 2014 2014

[5] Hodge laplacians on graphs.SIAM Review, 62(3):685–715, 2020 2020 · doi:10.1137/18m1223101

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:52.148420Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9dc6683f68ff4e1f97a4d57e5d1a7899d20a203f65be31fe8f66d55e65dad00c

Aliases

arxiv: 2605.18250 · arxiv_version: 2605.18250v1 · doi: 10.48550/arxiv.2605.18250 · pith_short_12: TXDGQP3I75HB · pith_short_16: TXDGQP3I75HB7F5E · pith_short_8: TXDGQP3I

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TXDGQP3I75HB7F5E2V7F2GTYTH \
  | 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: 9dc6683f68ff4e1f97a4d57e5d1a7899d20a203f65be31fe8f66d55e65dad00c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bbb9d20c32a51b5204a1209cd3e017c1d604719c6fe85906c0ef7f1f44874c4",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.data-an",
    "submitted_at": "2026-05-18T11:52:09Z",
    "title_canon_sha256": "7fc325787fc3871e9556877448b200c8d38a5e63063c650345e5aa548a0d5bd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18250",
    "kind": "arxiv",
    "version": 1
  }
}