Pith Number

pith:4B7MHPJS

pith:2026:4B7MHPJS626YZTNK42EE2IM7EI

not attested not anchored not stored refs resolved

Boundary dynamics, triple transitivity, and mixed identities in weakly hyperbolic groups

Ekaterina Rybak

A dynamical lim-free criterion for hyperbolic group actions is equivalent to being mixed identity free.

arxiv:2605.14159 v1 · 2026-05-13 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4B7MHPJS626YZTNK42EE2IM7EI}

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

satisfying the criterion is equivalent to a purely algebraic property of being mixed identity free, generalizing results from FMMS and BM. For the subclass of not lim-free groups, we give the rigidity result for all 3-transitive faithful actions and bound the transitivity degree by 3.

C2weakest assumption

The groups admit a general type action on a δ-hyperbolic space such that the induced action on the limit set of the Gromov boundary is faithful.

C3one line summary

Lim-free dynamical criterion for faithful boundary actions on hyperbolic spaces is equivalent to the algebraic property of being mixed identity free, with transitivity degree bounded by 3 for non-lim-free groups.

References

27 extracted · 27 resolved · 1 Pith anchors

[1] [AMS] R. Aoun, P. Mathieu and C ¸ . Sert, Random walks on hyperbolic spaces: second order expansion of the rate function at the drift, J. ´Ec. polytech. Math.10(2023), 549–573. [AS] R. Aoun and C ¸ . 2023

[2] Bass, Covering theory for graphs of groups,J 1993

[3] [BEH] C. Bleak, L. Elliott, J. T. Hyde, Sufficient conditions for a group of homeomorphisms of the Cantor set to be two-generated,J. Inst. Math. Jussieu23(2024), no. 6, 2825 – 2024

[4] [BFFHZ] J. Belk, F. Fournier-Facio, J. Hyde, M. C. B. Zaremsky, Boone-Higman embed- dings ofAut(F n) and mapping class groups of punctured surfaces, arXiv:2503.21882v2. [BFGS] S.Balasubramanya, F. Fou 2025

[5] [BM] A. Le Boudec, N. Matte Bon, Triple transitivity and non-free actions in dimension one,J. Lond. Math. Soc.105(2022), 2, 884 – 2022

Receipt and verification

First computed	2026-05-17T23:39:11.503475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e07ec3bd32f6bd8ccdaae6884d219f223c373bf047cd6de131a99273611ecc4a

Aliases

arxiv: 2605.14159 · arxiv_version: 2605.14159v1 · doi: 10.48550/arxiv.2605.14159 · pith_short_12: 4B7MHPJS626Y · pith_short_16: 4B7MHPJS626YZTNK · pith_short_8: 4B7MHPJS

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/4B7MHPJS626YZTNK42EE2IM7EI \
  | 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: e07ec3bd32f6bd8ccdaae6884d219f223c373bf047cd6de131a99273611ecc4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b9fab2128cb992dc4f6a53ec262eb8a70f94fa7741586c2a183396e9ff15121",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-13T22:24:20Z",
    "title_canon_sha256": "c0b667674541d24b55b158e87ae93638b688644883b9da8af122243f4fca65ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14159",
    "kind": "arxiv",
    "version": 1
  }
}