Pith Number

pith:GZXWGUJP

pith:2014:GZXWGUJPXFE2MG4VOEHY7MQVFC

not attested not anchored not stored refs pending

Brownian motion on treebolic space: positive harmonic functions

Alexander Bendikov, Laurent Saloff-Coste, Maura Salvatori, Wolfgang Woess

arxiv:1412.2218 v2 · 2014-12-06 · math.PR · math.DG · 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{GZXWGUJPXFE2MG4VOEHY7MQVFC}

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	2026-05-18T00:57:32.148282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

366f63512fb949a61b95710f8fb21528bf40ebdf4f5ee0fbd771b680b10a2bd2

Aliases

arxiv: 1412.2218 · arxiv_version: 1412.2218v2 · doi: 10.48550/arxiv.1412.2218 · pith_short_12: GZXWGUJPXFE2 · pith_short_16: GZXWGUJPXFE2MG4V · pith_short_8: GZXWGUJP

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/GZXWGUJPXFE2MG4VOEHY7MQVFC \
  | 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: 366f63512fb949a61b95710f8fb21528bf40ebdf4f5ee0fbd771b680b10a2bd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "647ab2e8fb5d9896aa7746171e17ce2dfb1434ac51aa1a79c1d62edb64075156",
    "cross_cats_sorted": [
      "math.DG",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-12-06T10:32:00Z",
    "title_canon_sha256": "6d688a504095a51ba92d259a78c581bd1378a844c2bc43a7fd5862af5a65ad9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2218",
    "kind": "arxiv",
    "version": 2
  }
}