Pith Number

pith:4VOO7FOA

pith:2009:4VOO7FOAMTDMHMDL4345L4CREV

not attested not anchored not stored refs pending

The Free Group of Rank 2 is a Limit of Thompson's Group F

Matthew G. Brin

arxiv:0904.2626 v2 · 2009-04-17 · 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{4VOO7FOAMTDMHMDL4345L4CREV}

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	2026-05-18T03:14:27.128518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e55cef95c064c6c3b06be6f9d5f0512560382db8511714fe5ddd74fd92e7b62e

Aliases

arxiv: 0904.2626 · arxiv_version: 0904.2626v2 · doi: 10.48550/arxiv.0904.2626 · pith_short_12: 4VOO7FOAMTDM · pith_short_16: 4VOO7FOAMTDMHMDL · pith_short_8: 4VOO7FOA

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/4VOO7FOAMTDMHMDL4345L4CREV \
  | 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: e55cef95c064c6c3b06be6f9d5f0512560382db8511714fe5ddd74fd92e7b62e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3acacbc5f64408b380b857992a4fe2ca35270a663c19b51c1af67bebdb10f588",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-04-17T04:05:10Z",
    "title_canon_sha256": "cbd20be9fadfb77c811926fe70b35516b2d19d40706cfdc2a726951c7358ab72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.2626",
    "kind": "arxiv",
    "version": 2
  }
}