Pith Number

pith:YUGEE6Q2

pith:2026:YUGEE6Q24VP625KJ4FGUYDUXOW

not attested not anchored not stored refs resolved

Coupled double Poisson brackets

Nikita Safonkin

Pairs of coupled double Poisson brackets stand in bijection with wheeled Poisson brackets.

arxiv:2605.17696 v1 · 2026-05-17 · math.QA · math.RA · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YUGEE6Q24VP625KJ4FGUYDUXOW}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 establish a bijection between pairs of coupled double Poisson brackets and wheeled Poisson brackets of Ginzburg and Schedler. On free polynomial algebras, we establish a one-to-one correspondence between linear coupled double Poisson brackets and Poisson-left-pre-Lie algebras, and describe quadratic ones via solutions of the associative and classical Yang-Baxter equations satisfying a compatibility condition.

C2weakest assumption

The cross-Jacobi identity is imposed as part of the definition of a coupled pair; if this identity fails to hold for natural choices of the two component brackets, the bijection with wheeled Poisson brackets would not apply to those choices.

C3one line summary

Introduces coupled double Poisson brackets, proves bijection to wheeled Poisson brackets, and gives correspondences to Poisson-left-pre-Lie algebras and Yang-Baxter solutions on free polynomial algebras.

References

115 extracted · 115 resolved · 25 Pith anchors

[1] Classification of constant solutions for associative Yang-Baxter equation on $gl(3)$ 2013 · arXiv:1212.6421

[2] Letters in Mathematical Physics , volume= 2003

[3] Transactions of the American Mathematical Society , volume= 2008

[4] Noncommutative geometry and Cayley-smooth orders , author=. 2007 , publisher= 2007

[5] Universal localizations, Atiyah conjectures and graphs of groups , author=. 2024 , eprint= 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:53.296861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c50c427a1ae55fed7549e14d4c0e97759126d64f9c7d43a9e9cc5c91ef42c056

Aliases

arxiv: 2605.17696 · arxiv_version: 2605.17696v1 · doi: 10.48550/arxiv.2605.17696 · pith_short_12: YUGEE6Q24VP6 · pith_short_16: YUGEE6Q24VP625KJ · pith_short_8: YUGEE6Q2

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/YUGEE6Q24VP625KJ4FGUYDUXOW \
  | 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: c50c427a1ae55fed7549e14d4c0e97759126d64f9c7d43a9e9cc5c91ef42c056

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fb7dd87a55015b8f17d589721ad29264569f1f9d1cb98581667bcefe3d602b4",
    "cross_cats_sorted": [
      "math.RA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2026-05-17T23:34:03Z",
    "title_canon_sha256": "60d8516d73a28100c8c127caa96846cbe585c930324edc775749146d8534630b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17696",
    "kind": "arxiv",
    "version": 1
  }
}