Pith Number

pith:4X6GG7LQ

pith:2026:4X6GG7LQV6LHZBGC4XBVQFGSDW

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Weighted $\alpha$-subharmonic measure

Dilnur Salaeva, Kobiljon Kuldoshev

The weighted α-subharmonic measure of a compact set K is Hölder continuous everywhere if it is Hölder continuous relative to K.

arxiv:2605.16851 v1 · 2026-05-16 · math.CV

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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

If the weighted α-subharmonic measure of the compact set K is Hölder continuous with respect to K, then it is Hölder continuous everywhere.

C2weakest assumption

The weight function ψ is chosen so that the weighted α-subharmonic measure is well-defined and inherits the basic comparison and monotonicity properties of the unweighted α-subharmonic measure (implicit in the reduction statement when ψ ≡ -1).

C3one line summary

Defines the weighted α-subharmonic measure and proves its continuity properties plus a characterization of (α,ψ)-regularity for compact sets.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] Fundamental directions 2021

[2] Abdullaev B., Sadullaev A.,Potential theory in the class ofm-shfunctions.Proceedings of the Steklov Institute of Mathematics. 279 (2012), no. 1, p. 155–180 2012

[3] Abdullaev B., Sharipov R.,Local and globalα−polar sets.Bulletin of the Institute of Mathematics. 5 (2019), p. 4–8 2019

[4] Blocki Z.,Weak solutions to the complex Hessian equation.Ann. Ins. Fourier, Grenoble. 55 (2005), no.5, p. 1735–1756 2005

[5] and Kolodziej S.,A priori estimates for the complex Hessian equation.Analysis and PDE 2014

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:26.180233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5fc637d70af967c84c2e5c35814d21d8dd808a3a1a15d474f2b4142bf5561d4

Aliases

arxiv: 2605.16851 · arxiv_version: 2605.16851v1 · doi: 10.48550/arxiv.2605.16851 · pith_short_12: 4X6GG7LQV6LH · pith_short_16: 4X6GG7LQV6LHZBGC · pith_short_8: 4X6GG7LQ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4X6GG7LQV6LHZBGC4XBVQFGSDW \
  | 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: e5fc637d70af967c84c2e5c35814d21d8dd808a3a1a15d474f2b4142bf5561d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "914aa74fb44b182545014b55145e3ea1b03a43fc3f5d7884478e08537935d770",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-05-16T07:31:28Z",
    "title_canon_sha256": "19a421856d6a4ecc1a02843a449881eec548d2adb150f2f35bb29ec3d23150b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16851",
    "kind": "arxiv",
    "version": 1
  }
}