Pith Number

pith:FDCX3IT3

pith:2026:FDCX3IT3XPENTZV6UGL322DWLU

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Geometric construction of superintegrable Poisson projection chains via Poisson centralizers

Guorui Ma, Ian Marquette, Junze Zhang, Kai Jiang, Yao-Zhong Zhang

The inclusions of Poisson invariants under a maximal torus and the full group form a superintegrable projection chain on semisimple Lie algebras.

arxiv:2605.14490 v1 · 2026-05-14 · math-ph · math.MP

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Record completeness

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Claims

C1strongest claim

For a maximal torus T subset G, we prove that the inclusions S(g)^G subset S(g)^T subset S(g) determine a superintegrable chain and identify the associated quotient maps g to g//T to g//G.

C2weakest assumption

The construction begins from a chain of reductive subgroups of the semisimple Lie group G, with the invariant Poisson subalgebras and their centers behaving as expected under the Poisson structure.

C3one line summary

Inclusions of invariant subalgebras S(g)^G subset S(g)^T subset S(g) for a maximal torus T in a semisimple Lie group G form a superintegrable Poisson projection chain with matching dimension splits between Hamiltonians and integrals.

References

41 extracted · 41 resolved · 1 Pith anchors

[1] W. Miller Jr, S. Post, and P. Winternitz. Classical and quantum superintegrability with applications.J. Phys. A: Math. Theor., 46(42):423001, 97, 2013 2013

[2] N. Reshetikhin. Degenerately integrable systems.Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 433(Voprosy Kvantovo˘ ı Teorii Polya i Statistichesko˘ ı Fiziki. 23):224–245, 2015 2015

[3] J. Friˇ s, V. Mandrosov, Ya. A. Smorodinsky, M. Uhl´ ıˇ r, and P. Winternitz. On higher symmetries in quantum mechanics.Phys. Lett., 16:354–356, 1965 1965

[4] Action-angle variables and their generalizations.Trans 1968

[5] E. G. Kalnins, J. M. Kress, and W. Miller, Jr.Separation of variables and superintegrability. IOP Expanding Physics. IOP Publishing, Bristol, 2018. The symmetry of solvable systems 2018

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:06.440279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28c57da27bbbc8d9e6bea197bd68765d0e2ef70fb9ccdc860d1a5af9d72385ce

Aliases

arxiv: 2605.14490 · arxiv_version: 2605.14490v1 · doi: 10.48550/arxiv.2605.14490 · pith_short_12: FDCX3IT3XPEN · pith_short_16: FDCX3IT3XPENTZV6 · pith_short_8: FDCX3IT3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FDCX3IT3XPENTZV6UGL322DWLU \
  | 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: 28c57da27bbbc8d9e6bea197bd68765d0e2ef70fb9ccdc860d1a5af9d72385ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51d1870bdd9c0e93e3800f60aedc0ad009b4dc8aa3301c4f1cc9c31f4c951639",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-14T07:29:32Z",
    "title_canon_sha256": "ee8194bf1f8d015224f13d37181f178baae0bfb67f6e1fdb33080c7300f9df38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14490",
    "kind": "arxiv",
    "version": 1
  }
}