Pith Number

pith:NCCK2JBE

pith:2026:NCCK2JBEVE6WZAWAVGWQ2HEM3U

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Solvability and Rigidity for Topological Skew Braces

Andrea Loi, Marco Damele

If a connected locally compact Hausdorff topological skew brace has a solvable additive group, then its multiplicative group is also solvable.

arxiv:2605.07609 v2 · 2026-05-08 · math.GR · math.GN

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\pithnumber{NCCK2JBEVE6WZAWAVGWQ2HEM3U}

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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

Our main theorem proves an affirmative result in the connected locally compact Hausdorff setting: if B=(B,·,∘) is a connected locally compact Hausdorff topological skew brace and the additive group (B,·) is solvable, then the multiplicative group (B,∘) is solvable.

C2weakest assumption

The reduction of the additive group to a solvable Lie quotient together with the applicability of the cited affine-action theorem for connected Lie groups acting affinely with solvable stabilizer identity component.

C3one line summary

In connected locally compact Hausdorff topological skew braces, solvability of the additive group forces solvability of the multiplicative group, with the two operations coinciding when the additive group is abelian and the brace is compact.

Receipt and verification

First computed	2026-05-20T00:05:46.521423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6884ad2424a93d6c82c0a9ad0d1c8cdd026cbd0fc6c477a2a0060e028502aa8f

Aliases

arxiv: 2605.07609 · arxiv_version: 2605.07609v2 · doi: 10.48550/arxiv.2605.07609 · pith_short_12: NCCK2JBEVE6W · pith_short_16: NCCK2JBEVE6WZAWA · pith_short_8: NCCK2JBE

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/NCCK2JBEVE6WZAWAVGWQ2HEM3U \
  | 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: 6884ad2424a93d6c82c0a9ad0d1c8cdd026cbd0fc6c477a2a0060e028502aa8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03d2d1432b8cbd216d684179e2714a429100e8121f9b77b35cea985c95437560",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-08T11:35:51Z",
    "title_canon_sha256": "4a9ed33f28189e83b867ffedde2a6425341168d3e48c3e1280440d23254ad017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.07609",
    "kind": "arxiv",
    "version": 2
  }
}