Pith Number

pith:MBDYG7Q3

pith:2015:MBDYG7Q3F6OTQE3YAYTCI7DWVX

not attested not anchored not stored refs pending

Universal groups of intermediate growth and their invariant random subgroups

Mustafa Gokhan Benli, Rostislav Grigorchuk, Tatiana Nagnibeda

arxiv:1503.01705 v4 · 2015-03-05 · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MBDYG7Q3F6OTQE3YAYTCI7DWVX}

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	2026-05-18T01:37:47.243109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6047837e1b2f9d3813780626247c76adcf2229ba25c730b07bbbe0c24a945596

Aliases

arxiv: 1503.01705 · arxiv_version: 1503.01705v4 · doi: 10.48550/arxiv.1503.01705 · pith_short_12: MBDYG7Q3F6OT · pith_short_16: MBDYG7Q3F6OTQE3Y · pith_short_8: MBDYG7Q3

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/MBDYG7Q3F6OTQE3YAYTCI7DWVX \
  | 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: 6047837e1b2f9d3813780626247c76adcf2229ba25c730b07bbbe0c24a945596

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdd733376f12116d89a525b171dd9661ed032aa824bc2d767bf1987eaacc80c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-03-05T17:41:28Z",
    "title_canon_sha256": "dae0dfca67cf8b7921e92523ced09e8f5d5192f97a8a3435745fbce6de891ed3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.01705",
    "kind": "arxiv",
    "version": 4
  }
}