Pith Number

pith:NR24VK6X

pith:2026:NR24VK6XHVS3P23IVR4WMUAOL2

not attested not anchored not stored refs resolved

Presentations and Representations of the Multi-Virtual Twin Group and Associated Subgroups

Madeti Prabhakar, Mohamad N. Nasser, Taher I. Mayassi, Vaibhav Keshari

The multi-virtual twin group M_kVT_n has exactly eight types of homogeneous 2-local representations into GL_n(C) for n at least 3.

arxiv:2605.13090 v1 · 2026-05-13 · math.GT · math.GR · 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{NR24VK6XHVS3P23IVR4WMUAOL2}

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

We classify all homogeneous 2-local representations of M_kVT_n into GL_n(C) for all k >= 1 and n >= 3, and show that they fall into exactly eight distinct types.

C2weakest assumption

The multi-virtual twin group is presented by a specific set of generators and relations that correctly capture the intended multi-virtual and twin structure; the notion of homogeneous 2-local representation is the right restriction for obtaining a complete finite classification.

C3one line summary

The multi-virtual twin group M_kVT_n admits exactly eight distinct homogeneous 2-local representations into GL_n(C) for n >= 3; these are generally unfaithful but irreducible under explicit conditions, with induced non-local representations constructed for the pure subgroup.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] V. Bardakov, M. Singh, and A. Vesnin,Structural aspects of twin and pure twin groups, Geometriae Dedicata, 203, 135–154, (2019) 2019

[2] C. Caprau and M. Nasser,The virtual singular twin monoid and group: presentations and representations, arXiv:2601.01707, (2026) 2026

[3] M. Chreif, M. Dally,On the irreducibility of local representations of the Braid groupB n, Arab. J. Math., (2024) 2024

[4] Kauffman,Multi-virtual knot theory, Journal of Knot Theory and Its Ramifications, 34, 2540002, (2025) 2025

[5] V.Keshari, M.Nasser, andM.Prabhakar,On representations of the multi- virtual braid groupM kV Bn and the multi-welded braid groupMkW Bn, arXiv:2508.04168, (2025). 26 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:08:58.462056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c75caabd73d65b7eb68ac7966500e5eb811134c20067ccd7bd8c94b25e8dcaa

Aliases

arxiv: 2605.13090 · arxiv_version: 2605.13090v1 · doi: 10.48550/arxiv.2605.13090 · pith_short_12: NR24VK6XHVS3 · pith_short_16: NR24VK6XHVS3P23I · pith_short_8: NR24VK6X

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/NR24VK6XHVS3P23IVR4WMUAOL2 \
  | 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: 6c75caabd73d65b7eb68ac7966500e5eb811134c20067ccd7bd8c94b25e8dcaa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d22e5fccb331d0c34acad16b9b6093bf6a7c0d2bb98fb8ab623b14ccd328e9e1",
    "cross_cats_sorted": [
      "math.GR",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T07:01:00Z",
    "title_canon_sha256": "86be66f5b6d7c5349715f11448322d163e816f224539081d31d0ef70fe43a55f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13090",
    "kind": "arxiv",
    "version": 1
  }
}