Pith Number

pith:QZWHTDZL

pith:2011:QZWHTDZL7SFXFXBD6HG36XCFF6

not attested not anchored not stored refs pending

Bernoulli actions are weakly contained in any free action

Benjamin Weiss, Mikl\'os Ab\'ert

arxiv:1103.1063 v2 · 2011-03-05 · math.DS · 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{QZWHTDZL7SFXFXBD6HG36XCFF6}

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	2026-05-18T04:12:11.893441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

866c798f2bfc8b72dc23f1cdbf5c452fb2aac659dfeac2a7f01b739235447746

Aliases

arxiv: 1103.1063 · arxiv_version: 1103.1063v2 · doi: 10.48550/arxiv.1103.1063 · pith_short_12: QZWHTDZL7SFX · pith_short_16: QZWHTDZL7SFXFXBD · pith_short_8: QZWHTDZL

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/QZWHTDZL7SFXFXBD6HG36XCFF6 \
  | 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: 866c798f2bfc8b72dc23f1cdbf5c452fb2aac659dfeac2a7f01b739235447746

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0a58630a3a4fb04d119c8627b0adecf54e65526001ded2257ebfd3e2b7fb16d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-03-05T15:46:10Z",
    "title_canon_sha256": "db17f34f1242f6514b4586ab09c343cfa40d3d1ecc24f3ca05238ee66821e404"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1063",
    "kind": "arxiv",
    "version": 2
  }
}