Pith Number

pith:2ZL4JJXY

pith:2026:2ZL4JJXYJUSMABPGCZYEC52WT2

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Equivariant nonlinear partial differential operators on constant curvature spaces

Erlend Grong, Francesco Ballerin

Nonlinear equivariant differential operators on constant-curvature spaces are classified by a vector space of multigraph equivalence classes.

arxiv:2605.16847 v1 · 2026-05-16 · math.AP

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Record completeness

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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

We show that the classifying space for such operators can be realized as the vector space spanned by equivalence-classes of multigraphs.

C2weakest assumption

The nonlinear operators under consideration are precisely those that can be written as a polynomial in linear operators, as stated in the abstract; if this polynomial restriction does not capture the intended class of operators, the classifying space construction would not apply to the broader set of nonlinear equivariant operators.

C3one line summary

The classifying space for polynomial nonlinear isometry-equivariant operators on simply connected constant curvature spaces is realized as the vector space spanned by equivalence classes of multigraphs.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] E. Andersdotter, D. Persson, and F. Ohlsson. Equivariant manifold neural odes and differential invariants. arXiv preprint arXiv:2401.14131, 2024 2024

[2] A. Bella¨ ıche. The tangent space in sub-riemannian geometry. InSub-Riemannian geometry, pages 1–78. Springer, 1996 1996

[3] E. Berge and E. Grong. OnG2 and sub-riemannian model spaces of step and rank three.Mathematische Zeitschrift, 298(3):1853–1885, 2021 2021

[4] Bollob´ as.Modern Graph Theory, volume 184 ofGraduate Texts in Mathematics 1998

[5] L. Gao, Y. Du, H. Li, and G. Lin. Roteqnet: Rotation-equivariant network for fluid systems with symmetric high-order tensors.Journal of Computational Physics, 461:111205, 2022 2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:25.944747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d657c4a6f84d24c005e616704177569e9c720ef21d80ce0ce117e71556a34f1a

Aliases

arxiv: 2605.16847 · arxiv_version: 2605.16847v1 · doi: 10.48550/arxiv.2605.16847 · pith_short_12: 2ZL4JJXYJUSM · pith_short_16: 2ZL4JJXYJUSMABPG · pith_short_8: 2ZL4JJXY

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2ZL4JJXYJUSMABPGCZYEC52WT2 \
  | 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: d657c4a6f84d24c005e616704177569e9c720ef21d80ce0ce117e71556a34f1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0653923e668c338973175464048163bbe774ad1bf4a05d06f93be43f0b2152d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-16T07:09:45Z",
    "title_canon_sha256": "42034da99796507a037537766a7a2ada952d073bb7969ce55eb00b12c2a9cba3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16847",
    "kind": "arxiv",
    "version": 1
  }
}