Pith Number

pith:7H43H76W

pith:2013:7H43H76WCGJTS7XN2GSLZ7VJVV

not attested not anchored not stored refs pending

Ideal Whitehead Graphs in Out(F_r) II: The Complete Graph in Each Rank

Catherine Pfaff

arxiv:1301.6645 v2 · 2013-01-28 · 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{7H43H76WCGJTS7XN2GSLZ7VJVV}

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	2026-05-18T02:43:24.478553Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9f9b3ffd61193397eedd1a4bcfea9ad5a7a27736112c114e19d73db4df11f12

Aliases

arxiv: 1301.6645 · arxiv_version: 1301.6645v2 · doi: 10.48550/arxiv.1301.6645 · pith_short_12: 7H43H76WCGJT · pith_short_16: 7H43H76WCGJTS7XN · pith_short_8: 7H43H76W

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/7H43H76WCGJTS7XN2GSLZ7VJVV \
  | 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: f9f9b3ffd61193397eedd1a4bcfea9ad5a7a27736112c114e19d73db4df11f12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06512e59750496d01a245ed1e5804463e4487fef619ccc773c7732233e167dcd",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-28T19:06:38Z",
    "title_canon_sha256": "bd96167f1a6b55fa8f55f7c061b2a9ea9243093ec421719608332d302408e237"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.6645",
    "kind": "arxiv",
    "version": 2
  }
}