Pith Number

pith:LXP2S6ST

pith:2026:LXP2S6ST5DBCIR66IUQBVWUIRI

not attested not anchored not stored refs resolved

On quandle representations

Mohamad Maassarani

A finite-dimensional representation of a finite quandle over the complex numbers decomposes into irreducibles precisely when every matrix in its image is diagonalizable.

arxiv:2605.12692 v1 · 2026-05-12 · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LXP2S6ST5DBCIR66IUQBVWUIRI}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

A finite dimensional quandle representation ρ : Q → GL(V) of a finite quandle Q over ℂ is decomposable into a direct sum of irreducibles if and only if every element in the image of ρ is diagonalizable.

C2weakest assumption

The quandle Q is finite and the representation is finite-dimensional over ℂ; these hypotheses are used to invoke diagonalizability and determinant properties that may fail for infinite quandles or other fields.

C3one line summary

Finite-dimensional representations of finite quandles over ℂ decompose into irreducibles iff image elements are diagonalizable, and irreducibles are unitary for some inner product iff determinants have modulus 1.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] Eisermann, Michael, Quandle Coverings and Their Galois Correspondence. Fundamenta Mathematicae, vol. 225, no. 1, pp. 103–67, 2014 2014

[2] Elhamdadi, M. and Moutuou, E. kaïoum M.. Finitely stable racks and rack representations. Communications in Algebra, 46(11), 4787–4802, 2018 2018

[3] Journal of Pure and Applied Algebra, volume 225, 2021 2021

[4] Journal of Algebra and Its Applications, 2025 2025

[5] Maassarani Mohamad, Groups and quandles. arxiv, 2026 2026

Receipt and verification

First computed	2026-05-18T03:09:49.818761Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ddfa97a53e8c22447de45201ada888a1b333e7599b4da81c21a0c202399578a

Aliases

arxiv: 2605.12692 · arxiv_version: 2605.12692v1 · doi: 10.48550/arxiv.2605.12692 · pith_short_12: LXP2S6ST5DBC · pith_short_16: LXP2S6ST5DBCIR66 · pith_short_8: LXP2S6ST

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LXP2S6ST5DBCIR66IUQBVWUIRI \
  | 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: 5ddfa97a53e8c22447de45201ada888a1b333e7599b4da81c21a0c202399578a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66df5271a42959d3e4d6c4339b4f718cae85aa1dd4d6bdfa89ce49b6d05d4d7b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-12T19:40:50Z",
    "title_canon_sha256": "8497e795377eaf18248cdefdffdfef9f6543425d507ff73d1d839d07bce5fffb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12692",
    "kind": "arxiv",
    "version": 1
  }
}