Pith Number

pith:TWS5KN7L

pith:2026:TWS5KN7L4P3AW2PXWLLBAVFMOJ

not attested not anchored not stored refs pending

On quiver skew braces, their ideals and products

Davide Ferri

Quiver skew braces cannot be decomposed into a group of loops and vertices like connected groupoids can.

arxiv:2605.11903 v2 · 2026-05-12 · math.RT · math.GR · math.QA

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\usepackage{pith}
\pithnumber{TWS5KN7L4P3AW2PXWLLBAVFMOJ}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

It is known that connected groupoids can be expressed as the datum of a group of loops and a set of vertices. We demonstrate how no such decomposition holds for quiver skew braces, which makes their theory richer than the theory of groupoids.

C2weakest assumption

That the equivalence between quiver skew braces and braided groupoids is sufficiently strong to transfer the non-decomposition result and to support the new definitions of ideals and semidirect products without additional hidden conditions.

C3one line summary

Quiver skew braces lack the group-of-loops-plus-vertices decomposition that connected groupoids possess, and the paper equips them with ideals and two semidirect products.

Receipt and verification

First computed	2026-05-27T01:05:57.009525Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9da5d537ebe3f60b69f7b2d61054ac725e771d7c8b2575d78a275015c1873b6e

Aliases

arxiv: 2605.11903 · arxiv_version: 2605.11903v2 · doi: 10.48550/arxiv.2605.11903 · pith_short_12: TWS5KN7L4P3A · pith_short_16: TWS5KN7L4P3AW2PX · pith_short_8: TWS5KN7L

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TWS5KN7L4P3AW2PXWLLBAVFMOJ \
  | 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: 9da5d537ebe3f60b69f7b2d61054ac725e771d7c8b2575d78a275015c1873b6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1c2dbf83c7acff56ef620f4664be49a1cc33576c823f5d65c512fdb5cfc9956",
    "cross_cats_sorted": [
      "math.GR",
      "math.QA"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-12T10:16:51Z",
    "title_canon_sha256": "26285829679dedae124c87bca3d09655db6655a9ec6b3e0b87fe0dfa3898cee2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11903",
    "kind": "arxiv",
    "version": 2
  }
}