Pith Number

pith:QR3XKLNU

pith:2026:QR3XKLNUXCFZKKZJN2ORGYKFBI

not attested not anchored not stored refs resolved

Coamenability and strong ergodicity

Ben Hayes

For coamenable inclusions of ergodic probability measure-preserving relations, strong ergodicity holds for one exactly when it holds for the other.

arxiv:2605.18433 v1 · 2026-05-18 · math.DS · math.GR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QR3XKLNUXCFZKKZJN2ORGYKFBI}

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

for coamenable inclusion S≤R of ergodic, probability measure-preserving relations, we have that R is strongly ergodic if and only if S is strongly ergodic.

C2weakest assumption

The inclusion S ≤ R is coamenable (following methods of Bannon-Marrakchi-Ozawa), with both relations ergodic and probability measure-preserving.

C3one line summary

For coamenable inclusions S ≤ R of ergodic pmp relations, R is strongly ergodic iff S is; extends to group actions with countably many strongly ergodic ergodic components.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] M. Abert, M. Fraczyk, and B. Hayes. Co-spectral radius for countable equivalence relations, 2023 2023

[2] J. Bannon, A. Marrakchi, and N. Ozawa. Full factors and co-amenable inclusions.Comm. Math. Phys., 378(2):1107–1121, 2020 2020

[3] B. Bekka. Operator-algebraic superridigity for SL n(Z),n≥3.Invent. Math., 169(2):401–425, 2007 2007

[4] B. Bekka, P. de la Harpe, and A. Valette.Kazhdan’s property (T), volume 11 ofNew Mathematical Monographs. Cambridge University Press, Cambridge, 2008 2008

[5] N. P. Brown and N. Ozawa.C ∗-algebras and finite-dimensional approximations, volume 88 ofGraduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2008 2008

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:06:00.700648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8477752db4b88b952b296e9d1361450a0085a5cc12e7b55b84fe5c80ad71585c

Aliases

arxiv: 2605.18433 · arxiv_version: 2605.18433v1 · doi: 10.48550/arxiv.2605.18433 · pith_short_12: QR3XKLNUXCFZ · pith_short_16: QR3XKLNUXCFZKKZJ · pith_short_8: QR3XKLNU

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/QR3XKLNUXCFZKKZJN2ORGYKFBI \
  | 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: 8477752db4b88b952b296e9d1361450a0085a5cc12e7b55b84fe5c80ad71585c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0625a1d2dadd320d1878c7c99fb2c2942ac4b35b06f3dc0efb6e8d16e13edbb",
    "cross_cats_sorted": [
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-18T14:05:54Z",
    "title_canon_sha256": "c0e0382f3f73c319fb1424539520760053ce6e0ef828fe92dea69f5b90148557"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18433",
    "kind": "arxiv",
    "version": 1
  }
}