Pith Number

pith:4GT4Y6MB

pith:2011:4GT4Y6MB57VOXBZ4NY5YK32BD7

not attested not anchored not stored refs pending

Distinguishability of infinite groups and graphs

Mark E. Watkins, Simon M. Smith, Thomas W. Tucker

arxiv:1106.4778 v1 · 2011-06-23 · math.CO · 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{4GT4Y6MB57VOXBZ4NY5YK32BD7}

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	2026-05-18T03:33:26.630751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1a7cc7981efeaeb873c6e3b856f411fc031e68464b1aaa4cf1f01f1f442e0d1

Aliases

arxiv: 1106.4778 · arxiv_version: 1106.4778v1 · doi: 10.48550/arxiv.1106.4778 · pith_short_12: 4GT4Y6MB57VO · pith_short_16: 4GT4Y6MB57VOXBZ4 · pith_short_8: 4GT4Y6MB

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/4GT4Y6MB57VOXBZ4NY5YK32BD7 \
  | 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: e1a7cc7981efeaeb873c6e3b856f411fc031e68464b1aaa4cf1f01f1f442e0d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e0f1e4853b543cb6f4275dab0ec063bf1c10c187b74ccd82b437c5d831bea54",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-23T17:26:11Z",
    "title_canon_sha256": "ec0dc8e5cd4bb12448202d3e3e20bc2df866fdc1292243909c11148ba0aa22d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4778",
    "kind": "arxiv",
    "version": 1
  }
}