Pith Number

pith:FGDJJGCA

pith:2010:FGDJJGCAOSIFGID4GKSDHALUXG

not attested not anchored not stored refs pending

Nonamenable Liouville Graphs

Gady Kozma, Itai Benjamini

arxiv:1010.3365 v1 · 2010-10-16 · math.MG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FGDJJGCAOSIFGID4GKSDHALUXG}

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	2026-05-18T04:39:09.323338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2986949840749053207c32a4338174b9be08de239676cf1da14a72a34dbf8431

Aliases

arxiv: 1010.3365 · arxiv_version: 1010.3365v1 · doi: 10.48550/arxiv.1010.3365 · pith_short_12: FGDJJGCAOSIF · pith_short_16: FGDJJGCAOSIFGID4 · pith_short_8: FGDJJGCA

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/FGDJJGCAOSIFGID4GKSDHALUXG \
  | 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: 2986949840749053207c32a4338174b9be08de239676cf1da14a72a34dbf8431

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba5132bae0cdf59bbb87dd02ff6176be10b3d71b2a90cbf51bb60ad335a3bf6e",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-10-16T18:35:45Z",
    "title_canon_sha256": "7a40a7058c7b0b2dbda50f5ad1a86f058a5cd36206922b9261fab4cf20f44faa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3365",
    "kind": "arxiv",
    "version": 1
  }
}