Pith Number

pith:A2TIMVPF

pith:2014:A2TIMVPFVPLB7JGACFVWFHUDWR

not attested not anchored not stored refs pending

A train track directed random walk on $Out(F_r)$

Catherine Pfaff, Ilya Kapovich

arxiv:1409.8044 v4 · 2014-09-29 · 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{A2TIMVPFVPLB7JGACFVWFHUDWR}

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	2026-05-18T01:59:58.370562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06a68655e5abd61fa4c0116b629e83b47bca93ce625a0702dfc45ae07f53fb2a

Aliases

arxiv: 1409.8044 · arxiv_version: 1409.8044v4 · doi: 10.48550/arxiv.1409.8044 · pith_short_12: A2TIMVPFVPLB · pith_short_16: A2TIMVPFVPLB7JGA · pith_short_8: A2TIMVPF

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/A2TIMVPFVPLB7JGACFVWFHUDWR \
  | 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: 06a68655e5abd61fa4c0116b629e83b47bca93ce625a0702dfc45ae07f53fb2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d65fd568eb1d607b624e59938389ceacb9100c515d28d2934e7da729b2699bf9",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-09-29T09:32:46Z",
    "title_canon_sha256": "1c1e76c594dafb053576b18934dd51f9ceb15ba46aecc306165b6d51ca0bc119"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.8044",
    "kind": "arxiv",
    "version": 4
  }
}