Pith Number

pith:TZJUPPHK

pith:2011:TZJUPPHKONY7PMHLJQGPOZQMDC

not attested not anchored not stored refs pending

Invariant percolation and measured theory of nonamenable groups

Cyril Houdayer

arxiv:1106.5337 v1 · 2011-06-27 · math.GR · math.DS · math.OA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TZJUPPHKONY7PMHLJQGPOZQMDC}

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	2026-05-18T03:35:28.393278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e5347bcea7371f7b0eb4c0cf7660c1898cffb8a1efddfc66a5781e95218c573

Aliases

arxiv: 1106.5337 · arxiv_version: 1106.5337v1 · doi: 10.48550/arxiv.1106.5337 · pith_short_12: TZJUPPHKONY7 · pith_short_16: TZJUPPHKONY7PMHL · pith_short_8: TZJUPPHK

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/TZJUPPHKONY7PMHLJQGPOZQMDC \
  | 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: 9e5347bcea7371f7b0eb4c0cf7660c1898cffb8a1efddfc66a5781e95218c573

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "363db5497fbd2d8c6eb7a78ab88af7ed6779da3dae1cc8d09b712df9e8dad44f",
    "cross_cats_sorted": [
      "math.DS",
      "math.OA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-27T09:34:54Z",
    "title_canon_sha256": "598a8a71f03a724a4bad5c5fafe3aff78d29e118b85ad4d605a20d9b3475581a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5337",
    "kind": "arxiv",
    "version": 1
  }
}