Pith Number

pith:T62D77U3

pith:2012:T62D77U3U7FVLD77Q3BYGYVL5L

not attested not anchored not stored refs pending

A finitely generated branch group of exponential growth without free subgroups

Elisabeth Fink

arxiv:1207.6548 v2 · 2012-07-27 · 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{T62D77U3U7FVLD77Q3BYGYVL5L}

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	2026-05-18T03:45:00.088435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fb43ffe9ba7cb558fff86c38362abeae4cdc1524c97f566942f007f86d7411f

Aliases

arxiv: 1207.6548 · arxiv_version: 1207.6548v2 · doi: 10.48550/arxiv.1207.6548 · pith_short_12: T62D77U3U7FV · pith_short_16: T62D77U3U7FVLD77 · pith_short_8: T62D77U3

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/T62D77U3U7FVLD77Q3BYGYVL5L \
  | 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: 9fb43ffe9ba7cb558fff86c38362abeae4cdc1524c97f566942f007f86d7411f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7888bf6329976cfcd6e57afa838efca3351142466239c4dda3818374f41f34fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-27T14:03:37Z",
    "title_canon_sha256": "fc667028162008ed1dc0c0542981cbf235491e49ad033b5bfd85f9d1bd0084be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6548",
    "kind": "arxiv",
    "version": 2
  }
}