Pith Number

pith:AW2IHHJB

pith:2011:AW2IHHJBP2FR2ZCLBLDOYO7NGC

not attested not anchored not stored refs pending

Milnor's Problem on the Growth of Groups and its Consequences

Rostislav Grigorchuk

arxiv:1111.0512 v4 · 2011-11-02 · 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{AW2IHHJBP2FR2ZCLBLDOYO7NGC}

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	2026-05-18T03:25:46.681147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05b4839d217e8b1d644b0ac6ec3bed308e78122bc7ca0520d8c05e0be213f5ab

Aliases

arxiv: 1111.0512 · arxiv_version: 1111.0512v4 · doi: 10.48550/arxiv.1111.0512 · pith_short_12: AW2IHHJBP2FR · pith_short_16: AW2IHHJBP2FR2ZCL · pith_short_8: AW2IHHJB

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/AW2IHHJBP2FR2ZCLBLDOYO7NGC \
  | 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: 05b4839d217e8b1d644b0ac6ec3bed308e78122bc7ca0520d8c05e0be213f5ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f68c0c354560f0b0970020ea9818db57c5ddefd7930447b12be22547530c55f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-11-02T14:24:59Z",
    "title_canon_sha256": "70b765ac422df0faed1c2fb1ce303b3a1d2f0a73bad892b0dc72653a0f0b5863"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0512",
    "kind": "arxiv",
    "version": 4
  }
}