Pith Number

pith:WAROLJ4U

pith:2010:WAROLJ4UDTTQDOVSEW2GNORMET

not attested not anchored not stored refs pending

Nonfree Actions of Countable Groups and their Characters

A.Vershik

arxiv:1012.4604 v1 · 2010-12-21 · 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{WAROLJ4UDTTQDOVSEW2GNORMET}

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	2026-05-18T04:32:54.041263Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b022e5a7941ce701bab225b466ba2c24edaa8eabd6713b763a39004aba552680

Aliases

arxiv: 1012.4604 · arxiv_version: 1012.4604v1 · doi: 10.48550/arxiv.1012.4604 · pith_short_12: WAROLJ4UDTTQ · pith_short_16: WAROLJ4UDTTQDOVS · pith_short_8: WAROLJ4U

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/WAROLJ4UDTTQDOVSEW2GNORMET \
  | 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: b022e5a7941ce701bab225b466ba2c24edaa8eabd6713b763a39004aba552680

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2fe6bf4c485c9a812dd1b8282dfa6f4c4d78fd66119ef77f5450e9113b19f48",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-12-21T10:56:58Z",
    "title_canon_sha256": "25e1232c8ccba562bfc93e1f05b761c555ed04579fcecec1e5f21191290617fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4604",
    "kind": "arxiv",
    "version": 1
  }
}