Pith Number

pith:SNLCTE63

pith:2026:SNLCTE63OHRWNIBMZLAMVEDP75

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2-dimensional finite-gap Schr\"{o}dinger operator whose spectrum admits two involutions

O.K.Sheinman

New potentiality conditions let 2D finite-gap Schrödinger operators have spectra with two involutions.

arxiv:2605.18388 v1 · 2026-05-18 · math.AG · math-ph · math.MP

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Record completeness

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Claims

C1strongest claim

In the present work we propose the new potentiality conditions for the Schrödinger operators in question, and a related approach to identification of isoPrymians of smooth double coverings of curves of a certain class, with more than two branch points.

C2weakest assumption

That the new potentiality conditions can be stated so the spectrum admits two involutions while preserving the finite-gap property at one energy level, allowing the link to isoPrymians of coverings with more than two branch points to hold.

C3one line summary

Proposes new potentiality conditions for 2D finite-gap Schrödinger operators and an approach to identify isoPrymians of smooth double coverings with multiple branch points.

References

12 extracted · 12 resolved · 1 Pith anchors

[1] B. A. Dubrovin, I. M. Krichever, S. P. Novikov.The Schr¨ odinger equation in a periodic field and Riemann surfaces. Dokl. Akad. Nauk SSSR, 1976, Vol. 229, issue 1, p. 15–18 1976

[2] A. P. Veselov, S. P. Novikov.Finite-gap two-dimensional potential Schrodinger operators. Explicit formulas and evolution equations. Dokl. Akad. Nauk SSSR, 1984, Vol. 279, issue 1, p. 20–24 1984

[3] Potential operators 1984

[4] I. A. Taimanov.Prym varieties of branched coverings and nonlinear equations. Math. USSR-Sb., 1991, Vol. 70, issue 2, p. 367–384 1991

[5] I. A. Taimanov.Secants of Abelian varieties, theta functions, and soliton equations. Russian Math. Surveys, 1997, Vol. 52, issue 1, p. 147–218 1997

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:05:58.350913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93562993db71e366a02ccac0ca906fff4faf4db0cbc4d7424b915a7850c5b912

Aliases

arxiv: 2605.18388 · arxiv_version: 2605.18388v1 · doi: 10.48550/arxiv.2605.18388 · pith_short_12: SNLCTE63OHRW · pith_short_16: SNLCTE63OHRWNIBM · pith_short_8: SNLCTE63

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SNLCTE63OHRWNIBMZLAMVEDP75 \
  | 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: 93562993db71e366a02ccac0ca906fff4faf4db0cbc4d7424b915a7850c5b912

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8a659c193046c869f458e1a849122ac1a16683822194bf7ff56cb86f87e10ae",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-18T13:33:54Z",
    "title_canon_sha256": "2f8b0038605918863f787d86d98df4215f4a174b069da27c2414be10ca3bfe6e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18388",
    "kind": "arxiv",
    "version": 1
  }
}