Pith Number

pith:VARIBMTL

pith:2011:VARIBMTLIAWD7MDZUVK5ST7EUZ

not attested not anchored not stored refs pending

Quasi-invariant means and Zimmer amenability

Adam Timar, Gabor Elek

arxiv:1109.5863 v2 · 2011-09-27 · math.FA · 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{VARIBMTLIAWD7MDZUVK5ST7EUZ}

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	2026-05-18T04:11:20.039162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a82280b26b402c3fb079a555d94fe4a6544ae4e27739f0f212a054a83b444904

Aliases

arxiv: 1109.5863 · arxiv_version: 1109.5863v2 · doi: 10.48550/arxiv.1109.5863 · pith_short_12: VARIBMTLIAWD · pith_short_16: VARIBMTLIAWD7MDZ · pith_short_8: VARIBMTL

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/VARIBMTLIAWD7MDZUVK5ST7EUZ \
  | 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: a82280b26b402c3fb079a555d94fe4a6544ae4e27739f0f212a054a83b444904

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec6bd1c589c0c5263ff52f70a628e1a58c6033dc3fe43b39e462c341042de48f",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-09-27T12:47:09Z",
    "title_canon_sha256": "ace2974bca97c7255364b89c96b7caa7e9936e283f3910bf382f6bd676d84999"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5863",
    "kind": "arxiv",
    "version": 2
  }
}