Pith Number

pith:ZZ4UXKGK

pith:2007:ZZ4UXKGKR5ERIOOC22KNN4AVCJ

not attested not anchored not stored refs pending

The Dehn function of Stallings' group

Murray Elder, Robert Young, Tim Riley, Will Dison

arxiv:0712.3877 v2 · 2007-12-22 · 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{ZZ4UXKGKR5ERIOOC22KNN4AVCJ}

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	2026-05-18T03:55:37.815672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce794ba8ca8f491439c2d694d6f01512402c4f8bacb364792f4088d94f7855b8

Aliases

arxiv: 0712.3877 · arxiv_version: 0712.3877v2 · doi: 10.48550/arxiv.0712.3877 · pith_short_12: ZZ4UXKGKR5ER · pith_short_16: ZZ4UXKGKR5ERIOOC · pith_short_8: ZZ4UXKGK

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/ZZ4UXKGKR5ERIOOC22KNN4AVCJ \
  | 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: ce794ba8ca8f491439c2d694d6f01512402c4f8bacb364792f4088d94f7855b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa1bab879d430df8f5d1694d3814cf3f810138fe8af4865f6e6417a7d56ae25c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2007-12-22T20:17:52Z",
    "title_canon_sha256": "02e1e3cc71179f68030820daede227e4ef24e41dc184217f40524794ea11d6ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3877",
    "kind": "arxiv",
    "version": 2
  }
}