Pith Number

pith:U7EWNGLH

pith:2018:U7EWNGLH4Y2XO3ZMRTBT6WMP3V

not attested not anchored not stored refs pending

On the rigidity of rank gradient in a group of intermediate growth

Rostislav Grigorchuk, Rostyslav Kravchenko

arxiv:1802.08387 v1 · 2018-02-23 · math.DS · 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{U7EWNGLH4Y2XO3ZMRTBT6WMP3V}

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	2026-05-18T00:22:43.848227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7c9669967e635776f2c8cc33f598fdd61488c57df8415f5a4d0a959cdd20210

Aliases

arxiv: 1802.08387 · arxiv_version: 1802.08387v1 · doi: 10.48550/arxiv.1802.08387 · pith_short_12: U7EWNGLH4Y2X · pith_short_16: U7EWNGLH4Y2XO3ZM · pith_short_8: U7EWNGLH

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/U7EWNGLH4Y2XO3ZMRTBT6WMP3V \
  | 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: a7c9669967e635776f2c8cc33f598fdd61488c57df8415f5a4d0a959cdd20210

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36aa9fcaa6e40d2da0af690464e87fc0ff402470d79467dc27af04c12593412e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-02-23T04:56:55Z",
    "title_canon_sha256": "aeaad8c9355cf5bab21c5852b75768965a94b65f6ef1b68892b36996fbe93307"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.08387",
    "kind": "arxiv",
    "version": 1
  }
}