Pith Number

pith:ZLGKYTC5

pith:2010:ZLGKYTC5IG76C54UP6XNAMJOKF

not attested not anchored not stored refs pending

A non-trivial example of a free-by-free group with the Haagerup property

Fran\c{c}ois Gautero

arxiv:1008.3766 v2 · 2010-08-23 · 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{ZLGKYTC5IG76C54UP6XNAMJOKF}

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	2026-05-18T04:22:02.332573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caccac4c5d41bfe177947faed0312e515e36d4ef06743fc963819d6994324397

Aliases

arxiv: 1008.3766 · arxiv_version: 1008.3766v2 · doi: 10.48550/arxiv.1008.3766 · pith_short_12: ZLGKYTC5IG76 · pith_short_16: ZLGKYTC5IG76C54U · pith_short_8: ZLGKYTC5

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/ZLGKYTC5IG76C54UP6XNAMJOKF \
  | 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: caccac4c5d41bfe177947faed0312e515e36d4ef06743fc963819d6994324397

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5fe4b0d8f4618c02b50407bf2a50a607b4ac0b2ed2c6cd7ed6543cd29b70ea27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-08-23T07:48:04Z",
    "title_canon_sha256": "7e7f6b42566a71fb8db4ab2f11ee7b43f568658d09e2615e049e8804b800c868"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.3766",
    "kind": "arxiv",
    "version": 2
  }
}