Pith Number

pith:QDDRKQBL

pith:2008:QDDRKQBLIGSDDEQZCW2USEJ7JB

not attested not anchored not stored refs pending

The automorphism group of the free group of rank two is a CAT(0) group

Adam Piggott, Genevieve S. Walsh, Kim Ruane

arxiv:0809.2034 v3 · 2008-09-11 · 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{QDDRKQBLIGSDDEQZCW2USEJ7JB}

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	2026-05-17T23:54:42.161649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80c715402b41a431921915b549113f4862f12161efda8d6d763c7530f5f25b49

Aliases

arxiv: 0809.2034 · arxiv_version: 0809.2034v3 · doi: 10.48550/arxiv.0809.2034 · pith_short_12: QDDRKQBLIGSD · pith_short_16: QDDRKQBLIGSDDEQZ · pith_short_8: QDDRKQBL

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/QDDRKQBLIGSDDEQZCW2USEJ7JB \
  | 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: 80c715402b41a431921915b549113f4862f12161efda8d6d763c7530f5f25b49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a085511070b77e160cf96de313e98b6f58ace86d3f359486957acba260f11cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-09-11T19:12:04Z",
    "title_canon_sha256": "8c1fa1bd5c86c7e636abdb2d7ccb3a7616f416b3c473aea6dbd2db78e67bffc7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.2034",
    "kind": "arxiv",
    "version": 3
  }
}