Pith Number

pith:ZAHH7ESR

pith:2026:ZAHH7ESR3MIJU6W3O2ZSG2NTQE

not attested not anchored not stored refs pending

Metric mean dimension of amenable group actions: localization and non-uniformity

Guohua Zhang, Ruifeng Zhang, Xinyao He

arxiv:2606.13270 v1 · 2026-06-11 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZAHH7ESR3MIJU6W3O2ZSG2NTQE}

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.

Receipt and verification

First computed	2026-06-12T01:09:49.750561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c80e7f9251db109a7adb76b32369b3813be214b24e56faa28d7ef704964f3609

Aliases

arxiv: 2606.13270 · arxiv_version: 2606.13270v1 · doi: 10.48550/arxiv.2606.13270 · pith_short_12: ZAHH7ESR3MIJ · pith_short_16: ZAHH7ESR3MIJU6W3 · pith_short_8: ZAHH7ESR

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/ZAHH7ESR3MIJU6W3O2ZSG2NTQE \
  | 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: c80e7f9251db109a7adb76b32369b3813be214b24e56faa28d7ef704964f3609

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53e882b95e403c134bad0b8e0c24c8ce7f8d668ceffaca732f3b583f09648ff7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-06-11T12:24:54Z",
    "title_canon_sha256": "e7f1841da8a44ff50573698104d3718bcffb60c7e74647d2772099887c74722b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.13270",
    "kind": "arxiv",
    "version": 1
  }
}