Pith Number

pith:KKH3GFVT

pith:2014:KKH3GFVTDLJJ3744IZPNKG53LU

not attested not anchored not stored refs pending

Invariable Generation of Infinite Groups

Alexander Lubotzky, Aner Shalev, William M. Kantor

arxiv:1407.4631 v1 · 2014-07-17 · 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{KKH3GFVTDLJJ3744IZPNKG53LU}

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	2026-05-18T02:47:23.645769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

528fb316b31ad29dff9c465ed51bbb5d3bb2ec623afce3182440ffbea7425e54

Aliases

arxiv: 1407.4631 · arxiv_version: 1407.4631v1 · doi: 10.48550/arxiv.1407.4631 · pith_short_12: KKH3GFVTDLJJ · pith_short_16: KKH3GFVTDLJJ3744 · pith_short_8: KKH3GFVT

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/KKH3GFVTDLJJ3744IZPNKG53LU \
  | 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: 528fb316b31ad29dff9c465ed51bbb5d3bb2ec623afce3182440ffbea7425e54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1ebe819adfde9ec8f8be3699afe9475994ba6ef86bf8f55537514c834427ca3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-07-17T11:09:15Z",
    "title_canon_sha256": "93f3b650691ad30b6734aa5254b6977cf4aa900c6f174528c937d248a1cbae19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.4631",
    "kind": "arxiv",
    "version": 1
  }
}