Pith Number

pith:QQZNFGUT

pith:2019:QQZNFGUTT2DZ2JOIROKWSXRX3M

not attested not anchored not stored refs pending

A finitary structure theorem for vertex-transitive graphs of polynomial growth

Matthew Tointon, Romain Tessera

arxiv:1908.06044 v3 · 2019-08-16 · math.CO · math.GN · math.GR · 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{QQZNFGUTT2DZ2JOIROKWSXRX3M}

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	2026-07-05T02:11:19.710783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8432d29a939e879d25c88b95695e37db287a739c763585c5284c1be4e6de325f

Aliases

arxiv: 1908.06044 · arxiv_version: 1908.06044v3 · doi: 10.48550/arxiv.1908.06044 · pith_short_12: QQZNFGUTT2DZ · pith_short_16: QQZNFGUTT2DZ2JOI · pith_short_8: QQZNFGUT

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/QQZNFGUTT2DZ2JOIROKWSXRX3M \
  | 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: 8432d29a939e879d25c88b95695e37db287a739c763585c5284c1be4e6de325f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b01e01d26d4151fb97599ed78d59475597e96845b091942fbb76663e386034c",
    "cross_cats_sorted": [
      "math.GN",
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-16T16:09:19Z",
    "title_canon_sha256": "8af6645f74271a13fccd17332cd281a3b875c8ce8b62f82d1b37e55a64004292"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06044",
    "kind": "arxiv",
    "version": 3
  }
}