Pith Number

pith:OVL6FRUP

pith:2025:OVL6FRUP7U4PSAGDECIDMPEFOR

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Monogenic functions over real alternative *-algebras: the several hypercomplex variables case

Chao Ding, Haiyan Wang, Zhenghua Xu

Monogenic functions in several hypercomplex variables over real alternative *-algebras satisfy the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.

arxiv:2506.08307 v3 · 2025-06-10 · math.CV

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\pithnumber{OVL6FRUP7U4PSAGDECIDMPEFOR}

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Record completeness

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Claims

C1strongest claim

We initiate the study of monogenic functions of several hypercomplex variables over real alternative *-algebras and develop fundamental properties such as the Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.

C2weakest assumption

That the single-variable monogenic theory over real alternative *-algebras extends directly to the several-variable case while preserving the listed integral and extension properties without additional structural restrictions on the algebra or the functions.

C3one line summary

Introduces monogenic functions of several hypercomplex variables over real alternative *-algebras and establishes Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:51.037427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2

Aliases

arxiv: 2506.08307 · arxiv_version: 2506.08307v3 · doi: 10.48550/arxiv.2506.08307 · pith_short_12: OVL6FRUP7U4P · pith_short_16: OVL6FRUP7U4PSAGD · pith_short_8: OVL6FRUP

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OVL6FRUP7U4PSAGDECIDMPEFOR \
  | 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: 7557e2c68ffd38f900c32090363c857454b6913d2af633e791aa9d57bbea53a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0f860f9d237ec421325610340ab1bf717dc5c438cbde5785428f4b723208c5d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2025-06-10T00:33:46Z",
    "title_canon_sha256": "a4d65e020a91a908c8084f44bea96284202eaf5409b3a1d069a12f7b8970988e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.08307",
    "kind": "arxiv",
    "version": 3
  }
}