Pith Number

pith:PEUUP5P7

pith:2020:PEUUP5P7CDCWP47QUPZM6ZUBSG

not attested not anchored not stored refs pending

Sharp relations between volume growth, isoperimetry and escape probability in vertex-transitive graphs

Matthew Tointon, Romain Tessera

arxiv:2001.01467 v2 · 2020-01-06 · math.PR · 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{PEUUP5P7CDCWP47QUPZM6ZUBSG}

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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T08:38:31.284326Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

792947f5ff10c567f3f0a3f2cf6681918c7171a8b6d927cec4a00d2cd5460f93

Aliases

arxiv: 2001.01467 · arxiv_version: 2001.01467v2 · doi: 10.48550/arxiv.2001.01467 · pith_short_12: PEUUP5P7CDCW · pith_short_16: PEUUP5P7CDCWP47Q · pith_short_8: PEUUP5P7

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/PEUUP5P7CDCWP47QUPZM6ZUBSG \
  | 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: 792947f5ff10c567f3f0a3f2cf6681918c7171a8b6d927cec4a00d2cd5460f93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8334025ffc0b133f79605a88b11accf80486ecc432ef83b33522b59926b6ba46",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-01-06T10:23:44Z",
    "title_canon_sha256": "8c647ddf1fd8051cbe9c757c2d6fcdc3aeafd3c04fdee6bd72ec052673f29f74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.01467",
    "kind": "arxiv",
    "version": 2
  }
}