Pith Number

pith:XKLLQ7M3

pith:2008:XKLLQ7M34UO3JXZF4MZON7W6SR

not attested not anchored not stored refs pending

Actions of automorphism groups of free groups on homology spheres and acyclic manifolds

Karen Vogtmann, Martin R. Bridson

arxiv:0803.2062 v3 · 2008-03-13 · math.GR · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XKLLQ7M34UO3JXZF4MZON7W6SR}

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	2026-05-18T04:34:09.126742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba96b87d9be51db4df25e332e6fede9445baa7b3231773484d5de750e8943e99

Aliases

arxiv: 0803.2062 · arxiv_version: 0803.2062v3 · doi: 10.48550/arxiv.0803.2062 · pith_short_12: XKLLQ7M34UO3 · pith_short_16: XKLLQ7M34UO3JXZF · pith_short_8: XKLLQ7M3

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/XKLLQ7M34UO3JXZF4MZON7W6SR \
  | 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: ba96b87d9be51db4df25e332e6fede9445baa7b3231773484d5de750e8943e99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "723b52ad14c5889bbbada949f862e4d0e0dcd921af14ffba79700cde7f255862",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2008-03-13T22:29:55Z",
    "title_canon_sha256": "835089f0c34dac0567c0332b1e4dae7cf3b81ab9eda65c78be7272bd107ab295"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0803.2062",
    "kind": "arxiv",
    "version": 3
  }
}