Pith Number

pith:WDM3YCSK

pith:2026:WDM3YCSKUZCSJRGZ7RT5Z3PNAU

not attested not anchored not stored refs resolved

Groups with classifiable actions on the line

Joaqu\'in Brum, Mart\'in Gilabert Vio, Nicol\'as Matte Bon

A finitely generated group G lies outside class C but is amenable precisely when Thompson's group F is amenable.

arxiv:2605.13406 v1 · 2026-05-13 · math.GR · math.DS · math.LO

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Record completeness

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4 Citations open

5 Replications open

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Claims

C1strongest claim

We exhibit a finitely generated group G that is not in C, such that G is amenable if and only if Thompson's group F is amenable.

C2weakest assumption

That the smoothness of the conjugacy relation (existence of a Borel transversal) is the right notion for 'classifiable' actions and that the explicit construction of G satisfies all the claimed dynamical and group-theoretic properties without hidden assumptions on the actions.

C3one line summary

Introduces class C of groups with smooth conjugacy for minimal line actions, proves stability and inclusion of piecewise affine groups, and exhibits a finitely generated G not in C with amenability equivalent to Thompson's F.

References

49 extracted · 49 resolved · 0 Pith anchors

[1] V. A. Antonov, Modeling of processes of cyclic evolution type. S ynchronization by a random signal , Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya (1984), no. vyp. 2, pp. 67- 1984

[2] Richard Arens, Topologies for homeomorphism groups https://doi.org/10.2307/2371787, American Journal of Mathematics 68 (1946), pp. 593--610 1946 · doi:10.2307/2371787

[3] Arsenin, Sur les projections de certains ensembles mesurables B , Doklady Akademii Nauk SSSR 27 (1940), pp 1940

[4] Brin, and Justin Tatch Moore, https://doi.org/10.4171/jca/49 Complexity among the finitely generated subgroups of T hompson's group , Journal of Combinatorial Algebra 5 (2021), no 2021 · doi:10.4171/jca/49

[5] Kechris, https://doi.org/10.1017/CBO9780511735264 The descriptive set theory of P olish group actions , London Mathematical Society Lecture Note Series, vol 1996 · doi:10.1017/cbo9780511735264

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:47.511825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0d9bc0a4aa64524c4d9fc67dceded0519412f4a97e4f646514ece9aa9c85350

Aliases

arxiv: 2605.13406 · arxiv_version: 2605.13406v1 · doi: 10.48550/arxiv.2605.13406 · pith_short_12: WDM3YCSKUZCS · pith_short_16: WDM3YCSKUZCSJRGZ · pith_short_8: WDM3YCSK

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WDM3YCSKUZCSJRGZ7RT5Z3PNAU \
  | 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: b0d9bc0a4aa64524c4d9fc67dceded0519412f4a97e4f646514ece9aa9c85350

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f13462e345735ba9e708b837f953f02eb1ef22e16ebc3c11335d83799904dd51",
    "cross_cats_sorted": [
      "math.DS",
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-13T12:00:43Z",
    "title_canon_sha256": "a735d9c9f4d71f6eebe8f94c217581602b002ec34c69ffb98ee5387f489de4f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13406",
    "kind": "arxiv",
    "version": 1
  }
}