Pith Number

pith:VHDPM4CV

pith:2012:VHDPM4CV2PUPT6CKGPJNZFDB73

not attested not anchored not stored refs pending

Ideal Whitehead Graphs in Out(F_r) I: Some Unachieved Graphs

Catherine Pfaff

arxiv:1210.5762 v1 · 2012-10-21 · 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{VHDPM4CV2PUPT6CKGPJNZFDB73}

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	2026-05-18T03:42:43.142939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9c6f67055d3e8f9f84a33d2dc9461fedddee610656415f5dd1b3bcd0e69d338

Aliases

arxiv: 1210.5762 · arxiv_version: 1210.5762v1 · doi: 10.48550/arxiv.1210.5762 · pith_short_12: VHDPM4CV2PUP · pith_short_16: VHDPM4CV2PUPT6CK · pith_short_8: VHDPM4CV

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/VHDPM4CV2PUPT6CKGPJNZFDB73 \
  | 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: a9c6f67055d3e8f9f84a33d2dc9461fedddee610656415f5dd1b3bcd0e69d338

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7674decc958f9f45710b7754e7a3b4f171b98cd22829da9db4c0250d8c0c84af",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-21T20:50:24Z",
    "title_canon_sha256": "4b08eef12a53b7343e0e29c1aed29a8c569c435ae1d3c6e0d197a81032ea926e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5762",
    "kind": "arxiv",
    "version": 1
  }
}