Pith Number

pith:VIOHNK5Q

pith:2012:VIOHNK5Q2MZIRWTLKYCSMTXYNT

not attested not anchored not stored refs pending

Kesten's theorem for Invariant Random Subgroups

Balint Virag, Miklos Abert, Yair Glasner

arxiv:1201.3399 v1 · 2012-01-17 · 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{VIOHNK5Q2MZIRWTLKYCSMTXYNT}

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	2026-05-18T02:29:32.660658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa1c76abb0d33288da6b5605264ef86ce65587a5e8f151d5f0ea4174d9a2d3d2

Aliases

arxiv: 1201.3399 · arxiv_version: 1201.3399v1 · doi: 10.48550/arxiv.1201.3399 · pith_short_12: VIOHNK5Q2MZI · pith_short_16: VIOHNK5Q2MZIRWTL · pith_short_8: VIOHNK5Q

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/VIOHNK5Q2MZIRWTLKYCSMTXYNT \
  | 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: aa1c76abb0d33288da6b5605264ef86ce65587a5e8f151d5f0ea4174d9a2d3d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d8ebd75dce20343cb939192ced0e6d4329d69e0ee4bd3cb964709c0ced766bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-01-17T00:10:39Z",
    "title_canon_sha256": "9b82cec1ddcc6cc6982984b435bd54780ad6192a9e4c9cc7fd86152e805daa42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3399",
    "kind": "arxiv",
    "version": 1
  }
}