Pith Number

pith:Q5NH2EKQ

pith:2011:Q5NH2EKQK5XRW63ZRLQ7LHPQ4Y

not attested not anchored not stored refs pending

On a family of Schreier graphs of intermediate growth associated with a self-similar group

Alfredo Donno, Ievgen Bondarenko, Tullio Ceccherini-Silberstein, Volodymyr Nekrashevych

arxiv:1106.3979 v1 · 2011-06-20 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q5NH2EKQK5XRW63ZRLQ7LHPQ4Y}

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	2026-05-18T01:20:54.194145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

875a7d1150576f1b7b798ae1f59df0e62e9e14418c6e01cfdca311599b65739b

Aliases

arxiv: 1106.3979 · arxiv_version: 1106.3979v1 · doi: 10.48550/arxiv.1106.3979 · pith_short_12: Q5NH2EKQK5XR · pith_short_16: Q5NH2EKQK5XRW63Z · pith_short_8: Q5NH2EKQ

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/Q5NH2EKQK5XRW63ZRLQ7LHPQ4Y \
  | 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: 875a7d1150576f1b7b798ae1f59df0e62e9e14418c6e01cfdca311599b65739b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e708dea00497884e782d5696ac31196b5d6c362efb058ae6cf672ad577042090",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-20T18:16:12Z",
    "title_canon_sha256": "e7bf68c80b20034e0d7318b62f84884949405578fe08d4fc8cb802f54891c644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3979",
    "kind": "arxiv",
    "version": 1
  }
}