Pith Number

pith:FODZEOKM

pith:2026:FODZEOKMT773JDJDOIIDJPRZWH

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Gibbons-Tsarev type systems and Eventual identities

Alessandro Arsie, Karoline van Gemst, Paolo Lorenzoni, Sara Perletti

Non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist, proven via a generalized Gibbons-Tsarev system defined by eventual identities.

arxiv:2605.13505 v1 · 2026-05-13 · math-ph · math.MP

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\pithnumber{FODZEOKMT773JDJDOIIDJPRZWH}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations 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 non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist.

C2weakest assumption

The underlying F-manifold is regular and non-semisimple, with the reductions defined via the standard association to the multiplication operator and eventual identities.

C3one line summary

Non-diagonalisable reductions of the dKP equation associated with regular non-semisimple F-manifolds cannot exist, proven via a generalized Gibbons-Tsarev system defined by eventual identities.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] A. Arsie and P. Lorenzoni,F-manifolds with eventual identities, bidifferential calculus and twisted Lenard-Magri chains, International Mathematics Research Notices, Vol. 2013, No. 17, 3931–3976 2013

[2] A. Bolsinov, A.Y. Konyaev and V.S. Matveev,Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures, Nonlinearity 2024

[3] L. David and C. Hertling,Regular F-manifolds: initial conditions and Frobenius metrics, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XVII (2017), 1121–1152 2017

[4] L. David and I. A. B. Strachan,Dubrovin’s duality forF-manifolds with eventual identities, Adv. Math. Volume 226, Issue 5, 20 March 2011, Pages 4031–4060 2011

[5] C. Hertling and Yu. I. Manin,Weak Frobenius manifolds, International Mathematics Research Notices, Vol. 1999, No. 6, 277–286 (1999) 1999

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T02:44:24.654765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b8792394c9fffb48d23721034be39b1e352ab337d9a4bcac350537b93aef4bb

Aliases

arxiv: 2605.13505 · arxiv_version: 2605.13505v1 · doi: 10.48550/arxiv.2605.13505 · pith_short_12: FODZEOKMT773 · pith_short_16: FODZEOKMT773JDJD · pith_short_8: FODZEOKM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FODZEOKMT773JDJDOIIDJPRZWH \
  | 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: 2b8792394c9fffb48d23721034be39b1e352ab337d9a4bcac350537b93aef4bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17fc987eb19845421e4b8aa3ea52f3b90a552bdf3f515282b9bade3fcf6c953c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-13T13:26:36Z",
    "title_canon_sha256": "e1c325c8b1c26b64818afb0de36bd136ad5246b13d2f3196c90690cbeeaf82be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13505",
    "kind": "arxiv",
    "version": 1
  }
}