Pith Number

pith:ZGCZXOVY

pith:2018:ZGCZXOVY4FBJJXQGO6SQNDMFDY

not attested not anchored not stored refs pending

What Is... A Thin Group?

Alan W. Reid, Alexander Lubotzky, Alex Kontorovich, D. Darren Long

arxiv:1812.02330 v1 · 2018-12-06 · math.NT · 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{ZGCZXOVY4FBJJXQGO6SQNDMFDY}

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	2026-05-17T23:58:56.556185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9859bbab8e14294de0677a5068d851e132e701e000bb49bbb399565e7f6070e

Aliases

arxiv: 1812.02330 · arxiv_version: 1812.02330v1 · doi: 10.48550/arxiv.1812.02330 · pith_short_12: ZGCZXOVY4FBJ · pith_short_16: ZGCZXOVY4FBJJXQG · pith_short_8: ZGCZXOVY

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/ZGCZXOVY4FBJJXQGO6SQNDMFDY \
  | 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: c9859bbab8e14294de0677a5068d851e132e701e000bb49bbb399565e7f6070e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c346af02bdedfdb95d4d722a08d1689b58883cb3db29c431a64448bd4c95f7fe",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-12-06T03:06:21Z",
    "title_canon_sha256": "373a56359b5b6c406dc4a68f6bcd19473d4fb48a5faa34ecc674b72b35ac843b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.02330",
    "kind": "arxiv",
    "version": 1
  }
}