Pith Number

pith:ZZLLWVBB

pith:2013:ZZLLWVBBR6RBJ3CPWOCD6YP6XI

not attested not anchored not stored refs pending

Ideal Whitehead Graphs in Out(F_r) III: Achieved Graphs in Rank 3

Catherine Pfaff

arxiv:1301.7080 v2 · 2013-01-29 · 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{ZZLLWVBBR6RBJ3CPWOCD6YP6XI}

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	2026-05-18T02:43:24.471658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce56bb54218fa214ec4fb3843f61feba3042b9e07e64c018e70d14732b0c0385

Aliases

arxiv: 1301.7080 · arxiv_version: 1301.7080v2 · doi: 10.48550/arxiv.1301.7080 · pith_short_12: ZZLLWVBBR6RB · pith_short_16: ZZLLWVBBR6RBJ3CP · pith_short_8: ZZLLWVBB

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/ZZLLWVBBR6RBJ3CPWOCD6YP6XI \
  | 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: ce56bb54218fa214ec4fb3843f61feba3042b9e07e64c018e70d14732b0c0385

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "096a6d8d3e3d4dfa022b7f9e5ae2bca7332ea57afca214a64bc0588e83da1e72",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-29T21:26:40Z",
    "title_canon_sha256": "9d9a043487b73a8912c369ee15c1fa097e7ec463fe68a11b95a46cffeb078714"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.7080",
    "kind": "arxiv",
    "version": 2
  }
}