Pith Number

pith:2PW23DLT

pith:2011:2PW23DLT43S7VOLVZCRFCIMWLU

not attested not anchored not stored refs pending

Notes on the Schreier graphs of the Grigorchuk group

Yaroslav Vorobets

arxiv:1112.4574 v1 · 2011-12-20 · 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{2PW23DLT43S7VOLVZCRFCIMWLU}

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	2026-05-18T04:05:58.507830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3edad8d73e6e5fab975c8a25121965d23f6acac6c1f1abdca009c3b5420f5ad

Aliases

arxiv: 1112.4574 · arxiv_version: 1112.4574v1 · doi: 10.48550/arxiv.1112.4574 · pith_short_12: 2PW23DLT43S7 · pith_short_16: 2PW23DLT43S7VOLV · pith_short_8: 2PW23DLT

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/2PW23DLT43S7VOLVZCRFCIMWLU \
  | 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: d3edad8d73e6e5fab975c8a25121965d23f6acac6c1f1abdca009c3b5420f5ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08bde35406c91563df24dbfa3d620be8c533249209b1fa48e35940c9889ce485",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-20T05:21:05Z",
    "title_canon_sha256": "3c048a5a27e6130673e68cff5eb8d663286dca4b988f98d9df165e7ef9e35b50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4574",
    "kind": "arxiv",
    "version": 1
  }
}