Pith Number

pith:M62FL754

pith:2013:M62FL754QLNO6JFYAN323PVQ3O

not attested not anchored not stored refs pending

Random groups contain surface subgroups

Alden Walker, Danny Calegari

arxiv:1304.2188 v2 · 2013-04-08 · math.GR · math.DS · 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{M62FL754QLNO6JFYAN323PVQ3O}

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	2026-05-18T02:29:08.499820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67b455ffbc82daef24b80377adbeb0db8d1b0871846623747234c9c8d333f3b8

Aliases

arxiv: 1304.2188 · arxiv_version: 1304.2188v2 · doi: 10.48550/arxiv.1304.2188 · pith_short_12: M62FL754QLNO · pith_short_16: M62FL754QLNO6JFY · pith_short_8: M62FL754

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/M62FL754QLNO6JFYAN323PVQ3O \
  | 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: 67b455ffbc82daef24b80377adbeb0db8d1b0871846623747234c9c8d333f3b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b087673c81998ce9dda8e8b39ff822796b6b13dfc092fd052ac3194ea4666f13",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-04-08T12:39:56Z",
    "title_canon_sha256": "54382b9a79a987662b87256f87a149d3a9a02245c27a2abc9c6c465808feb536"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.2188",
    "kind": "arxiv",
    "version": 2
  }
}