Pith Number

pith:4GR6DMXB

pith:2026:4GR6DMXBRRJOUZE327WP4JBBMJ

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Associative half-densities on symplectic groupoids and quantization

Alejandro Cabrera, Gabriel Gonzalo Ledesma Valenotti

Symplectic groupoids admit associative half-densities that classify the semiclassical corrections needed to quantize the underlying Poisson manifold.

arxiv:2604.08201 v2 · 2026-04-09 · math.SG · math-ph · math.MP

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Claims

C1strongest claim

We show the existence and classification of such associative half-densities, and further apply this theory to the understanding of semiclassical factors in Kontsevich's quantization formula. In the particular case of a linear Poisson structure, we recover the factors appearing in the Duflo isomorphism and its Kashiwara-Vergne extensions as a canonical associative enhancement.

C2weakest assumption

The structural motivation that an associativity condition on half-densities supplies the complete semiclassical-analytic approximation to a star product for the underlying Poisson manifold; this premise is invoked to justify the entire construction but is not independently verified in the abstract.

C3one line summary

Associative half-densities on symplectic groupoids exist, admit classification, and canonically recover semiclassical factors from Kontsevich quantization and the Duflo isomorphism in linear cases.

Receipt and verification

First computed	2026-05-21T01:05:18.715787Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1a3e1b2e18c52ea649bd7ecfe24216241a98ba76c599143698c485db9971c46

Aliases

arxiv: 2604.08201 · arxiv_version: 2604.08201v2 · doi: 10.48550/arxiv.2604.08201 · pith_short_12: 4GR6DMXBRRJO · pith_short_16: 4GR6DMXBRRJOUZE3 · pith_short_8: 4GR6DMXB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4GR6DMXBRRJOUZE327WP4JBBMJ \
  | 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: e1a3e1b2e18c52ea649bd7ecfe24216241a98ba76c599143698c485db9971c46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "252634c0ff7d43be3bd60ba93a8cf8ee2fda5b62157ad52a7776a6a15390f3f7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2026-04-09T13:03:01Z",
    "title_canon_sha256": "9e9eb9979b3b88116c267e9291e45afbb6033ab3ac2e498ff37098075fb39e88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08201",
    "kind": "arxiv",
    "version": 2
  }
}