Pith Number

pith:GHS7C7LQ

pith:2026:GHS7C7LQRHPEWSPDKLTWQNNYD2

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Derived Symplectic Reduction in Differential Geometry

Nikolay Sheshko

The symplectic quotient is modeled as a dg-groupoid to prove a derived version of the Marsden-Weinstein-Meyer reduction theorem.

arxiv:2605.16226 v1 · 2026-05-15 · math.SG

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Claims

C1strongest claim

We prove a derived version of the Marsden-Weinstein-Meyer symplectic reduction theorem. We model the symplectic quotient as a dg-groupoid. We then construct the reduced symplectic form inside the Bott-Shulman complex of the groupoid. Finally, we show that the reduced form satisfies a derived analogue of the non-degeneracy condition.

C2weakest assumption

The modeling of the symplectic quotient as a dg-groupoid is an appropriate and sufficient representation that captures the derived structure needed for the reduction to hold.

C3one line summary

Proves a derived symplectic reduction theorem by modeling the quotient as a dg-groupoid and constructing a non-degenerate reduced form in the Bott-Shulman complex.

References

34 extracted · 34 resolved · 3 Pith anchors

[1] The Geometry of the Master Equation and Topological Quan- tum Field Theory 1997

[2] Towards Non-Perturbative BV-theory via Derived Differential Geometry 2023

[3] Toward Differentiation and Integration between Hopf Algebroids and Lie Algebroids 2023 · doi:10.5565/publmat6712301

[4] Geometric and Algebraic Re- duction for Singular Momentum Maps 1990 · doi:10.1016/0001-8708(90)90058-u

[5] Topology- Agnostic Detection of Temporal Money Laundering Flows in Billion-Scale Transactions 2017 · doi:10.1007/978-

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:58.974970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31e5f17d7089de4b49e352e76835b81ebb8a0e9019d11e18bdf7b9be557ae45f

Aliases

arxiv: 2605.16226 · arxiv_version: 2605.16226v1 · doi: 10.48550/arxiv.2605.16226 · pith_short_12: GHS7C7LQRHPE · pith_short_16: GHS7C7LQRHPEWSPD · pith_short_8: GHS7C7LQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GHS7C7LQRHPEWSPDKLTWQNNYD2 \
  | 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: 31e5f17d7089de4b49e352e76835b81ebb8a0e9019d11e18bdf7b9be557ae45f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8de60f018fc5102ca7723ee383c534215246b9dcc77c99854e5d13c53954ac4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2026-05-15T17:37:59Z",
    "title_canon_sha256": "2e2d922d91058aa4e2f74d57b3eb3b9ff3dbadf23c3ecc41385adba7a7830317"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16226",
    "kind": "arxiv",
    "version": 1
  }
}