Pith Number

pith:BLME25R2

pith:2026:BLME25R2ZFA3KJKTTK2TQK2ONS

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Noncommutative Geometry, Spectral Asymptotics, and Semiclassical Analysis

Raphael Ponge

Semiclassical Weyl laws and Connes integration formulas are obtained for a large class of spectral triples by removing dimension and regularity restrictions and replacing the prior Tauberian condition with a weaker Condition (W).

arxiv:2604.15008 v2 · 2026-04-16 · math.OA · math.DG · math.SP

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\pithnumber{BLME25R2ZFA3KJKTTK2TQK2ONS}

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Claims

C1strongest claim

We combine various techniques from functional analysis and spectral theory to obtain semiclassical Weyl laws and extensions of Connes' integration formula for a large class of noncommutative manifolds (i.e., spectral triples). These results generalize and simplify recent results of McDonald-Sukochev-Zanin. In particular, all the regularity assumptions and restrictions on dimension there are removed in our approach. Moreover, the Tauberian condition used by McDonald-Sukochev-Zanin is replaced by a weaker spectral theoretic condition, called Condition (W).

C2weakest assumption

Condition (W) holds for the spectral triples under consideration, and the Tauberian conditions that imply Condition (W) are satisfied in the listed examples (Dirichlet/Neumann problems, Riemannian manifolds, quantum tori, sub-Riemannian manifolds).

C3one line summary

Receipt and verification

First computed	2026-05-25T02:01:20.443021Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ad84d763ac941b525539ab5382b4e6cb7dbfc00670c5fad3f375aa38040b89d

Aliases

arxiv: 2604.15008 · arxiv_version: 2604.15008v2 · doi: 10.48550/arxiv.2604.15008 · pith_short_12: BLME25R2ZFA3 · pith_short_16: BLME25R2ZFA3KJKT · pith_short_8: BLME25R2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BLME25R2ZFA3KJKTTK2TQK2ONS \
  | 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: 0ad84d763ac941b525539ab5382b4e6cb7dbfc00670c5fad3f375aa38040b89d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ffe9843a504eaebb8d4ae4d70c4873126095c747f6e524d83944a82f59267b8",
    "cross_cats_sorted": [
      "math.DG",
      "math.SP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-04-16T13:36:00Z",
    "title_canon_sha256": "cee1ec962b2b1df0252657269bdf76ca3019ce0ce1aa8b2808099ac8f3b70a65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.15008",
    "kind": "arxiv",
    "version": 2
  }
}