Pith Number

pith:ANQ2NC27

pith:2026:ANQ2NC273PLJGEPCSKIOEGMK3S

not attested not anchored not stored refs resolved

Non-arithmeticity of length spectra of subgroups of mapping class groups

Dongryul M. Kim, Inhyeok Choi

Every non-elementary subgroup of the mapping class group has a non-arithmetic Teichmüller length spectrum.

arxiv:2605.13064 v1 · 2026-05-13 · math.GT · math.DS · math.GR

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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

every non-elementary subgroup of the mapping class group of a surface has non-arithmetic Teichmüller length spectrum. Namely, Teichmüller translation lengths of its pseudo-Anosov elements generate a dense additive subgroup of R.

C2weakest assumption

The cross-ratios on MF and PMF satisfy the geometric and dynamical properties needed to force density of the length spectrum, despite the absence of negative curvature or conformal structure.

C3one line summary

Non-elementary subgroups of mapping class groups have non-arithmetic Teichmüller length spectra, shown via new cross-ratios on measured foliations and projective measured foliations.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] Effective mapping class group dynamics III : counting filling closed curves on surfaces 2024

[2] Propri\'et\'es asymptotiques des groupes lin\'eaires 1997

[3] An extremal problem for quasiconformal mappings and a theorem by T hurston 1978

[4] M. Bourdon. Structure conforme au bord et flot g\' e od\' e sique d'un CAT (-1) -espace. Enseign. Math. (2) , 41(1-2):63--102, 1995 1995

[5] Inhyeok Choi and Dongryul M. Kim. Invariant measures on the space of measured laminations for subgroups of mapping class group. arXiv preprint arXiv:2510.23256 , 2025 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:08:59.017349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0361a68b5fdbd69311e29290e2198adc83aff26d5ff915cd3969a674b688e71c

Aliases

arxiv: 2605.13064 · arxiv_version: 2605.13064v1 · doi: 10.48550/arxiv.2605.13064 · pith_short_12: ANQ2NC273PLJ · pith_short_16: ANQ2NC273PLJGEPC · pith_short_8: ANQ2NC27

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ANQ2NC273PLJGEPCSKIOEGMK3S \
  | 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: 0361a68b5fdbd69311e29290e2198adc83aff26d5ff915cd3969a674b688e71c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43df843e1e79ce78916b14b7e2710d936144508c1d1e1e977a6e437375084ec8",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-05-13T06:39:25Z",
    "title_canon_sha256": "210085fb17522b6e8d045f899684d9719b74a7d0182c534263cf7a18dc906d56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13064",
    "kind": "arxiv",
    "version": 1
  }
}