Pith Number

pith:GEKRZTHQ

pith:2012:GEKRZTHQXWHU4OZADNEJ4PLEZU

not attested not anchored not stored refs pending

Counting spanning trees in a small-world Farey graph

Bin Wu, Yuan Lin, Zhongzhi Zhang

arxiv:1201.4228 v1 · 2012-01-20 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GEKRZTHQXWHU4OZADNEJ4PLEZU}

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	2026-05-18T03:57:26.599853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31151cccf0bd8f4e3b201b489e3d64cd04f9ae901ec0900f3083421089643d82

Aliases

arxiv: 1201.4228 · arxiv_version: 1201.4228v1 · doi: 10.48550/arxiv.1201.4228 · pith_short_12: GEKRZTHQXWHU · pith_short_16: GEKRZTHQXWHU4OZA · pith_short_8: GEKRZTHQ

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/GEKRZTHQXWHU4OZADNEJ4PLEZU \
  | 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: 31151cccf0bd8f4e3b201b489e3d64cd04f9ae901ec0900f3083421089643d82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eaa0dc3d982914226032a942174380aeff7c2d7ae90249c272194af9be8db652",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2012-01-20T08:27:44Z",
    "title_canon_sha256": "e40bdf938ac3f50b452c769faf10008119317aae95e02e603078b0a7ffda96c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4228",
    "kind": "arxiv",
    "version": 1
  }
}