Pith Number

pith:4ZQIDLVZ

pith:2009:4ZQIDLVZSU4SFZDVK47SJHQTIO

not attested not anchored not stored refs pending

Poisson boundary of groups acting on real trees

Fran\c{c}ois Gautero, Fr\'ed\'eric Math\'eus

arxiv:0911.0616 v3 · 2009-11-03 · math.PR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ZQIDLVZSU4SFZDVK47SJHQTIO}

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	2026-05-18T04:32:00.064161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e66081aeb9953922e475573f249e1343928e159e7720dd8d32ec45c1965956ec

Aliases

arxiv: 0911.0616 · arxiv_version: 0911.0616v3 · doi: 10.48550/arxiv.0911.0616 · pith_short_12: 4ZQIDLVZSU4S · pith_short_16: 4ZQIDLVZSU4SFZDV · pith_short_8: 4ZQIDLVZ

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/4ZQIDLVZSU4SFZDVK47SJHQTIO \
  | 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: e66081aeb9953922e475573f249e1343928e159e7720dd8d32ec45c1965956ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26df335acbba047ca6513b11f7a6bd515d583245fae790352b534b1140ec0eaf",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-11-03T17:00:52Z",
    "title_canon_sha256": "7ed6f3688f11e459b8e92ec352530ca60dc720b421b786646b07f0ff3cd2a057"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.0616",
    "kind": "arxiv",
    "version": 3
  }
}