Pith Number

pith:YTNPZPA3

pith:2012:YTNPZPA3XUY7AM3GCO54TYG2EG

not attested not anchored not stored refs pending

Amenability and Uniqueness

A. Ciuperca, P. W. Ng, T. Giordano, Z. Niu

arxiv:1207.6741 v1 · 2012-07-29 · 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{YTNPZPA3XUY7AM3GCO54TYG2EG}

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	2026-05-18T03:49:48.884974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4dafcbc1bbd31f0336613bbc9e0da2187107b4db69d25a36e52a06263ab2892

Aliases

arxiv: 1207.6741 · arxiv_version: 1207.6741v1 · doi: 10.48550/arxiv.1207.6741 · pith_short_12: YTNPZPA3XUY7 · pith_short_16: YTNPZPA3XUY7AM3G · pith_short_8: YTNPZPA3

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/YTNPZPA3XUY7AM3GCO54TYG2EG \
  | 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: c4dafcbc1bbd31f0336613bbc9e0da2187107b4db69d25a36e52a06263ab2892

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1e12f57a78e5dcfd1158e94b839e489e9f357764fc0176bf2b84aa726154e65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-07-29T03:07:55Z",
    "title_canon_sha256": "ea11027ec2befa2f4ca727ee1fe873fe6c52185ec7205922bae5dfaf72162c08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6741",
    "kind": "arxiv",
    "version": 1
  }
}