Pith Number

pith:ACLOPJNV

pith:2019:ACLOPJNVT3DZCQUF4UR4ANDYUC

not attested not anchored not stored refs pending

Random subgroups, automorphisms, splittings

Gilbert Levitt, Vincent Guirardel

arxiv:1906.09654 v1 · 2019-06-23 · math.GR · math.GN · 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{ACLOPJNVT3DZCQUF4UR4ANDYUC}

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	2026-05-17T23:42:18.347802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0096e7a5b59ec7914285e523c03478a0a4944821123247a88f599b816a12a211

Aliases

arxiv: 1906.09654 · arxiv_version: 1906.09654v1 · doi: 10.48550/arxiv.1906.09654 · pith_short_12: ACLOPJNVT3DZ · pith_short_16: ACLOPJNVT3DZCQUF · pith_short_8: ACLOPJNV

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/ACLOPJNVT3DZCQUF4UR4ANDYUC \
  | 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: 0096e7a5b59ec7914285e523c03478a0a4944821123247a88f599b816a12a211

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f17b272ee36c965a9055433590a96a8759f0b0985775cede998a48fe191bdc84",
    "cross_cats_sorted": [
      "math.GN",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-06-23T21:39:57Z",
    "title_canon_sha256": "17ccdd5c36811f8a54cc961685ea6b7a7cce7d69ae47e3bc0ae701e41b464cd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.09654",
    "kind": "arxiv",
    "version": 1
  }
}