Pith Number

pith:4OYGRAUG

pith:2011:4OYGRAUGNYPEA6VI64XI3XWPJA

not attested not anchored not stored refs pending

Brownian motion and Harmonic functions on Sol(p,q)

Maura Salvatori, Sara Brofferio, Wolfgang Woess

arxiv:1105.4430 v1 · 2011-05-23 · math.PR · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4OYGRAUGNYPEA6VI64XI3XWPJA}

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	2026-05-18T03:27:23.317911Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3b06882866e1e407aa8f72e8ddecf481e7e68bfcbdc06c9e1446d120763f439

Aliases

arxiv: 1105.4430 · arxiv_version: 1105.4430v1 · doi: 10.48550/arxiv.1105.4430 · pith_short_12: 4OYGRAUGNYPE · pith_short_16: 4OYGRAUGNYPEA6VI · pith_short_8: 4OYGRAUG

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/4OYGRAUGNYPEA6VI64XI3XWPJA \
  | 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: e3b06882866e1e407aa8f72e8ddecf481e7e68bfcbdc06c9e1446d120763f439

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bb953ddcfbbf4359170c9b4d4a247870a805b049e1ef9313ae309ad6f1a9594",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-05-23T08:29:25Z",
    "title_canon_sha256": "f736e39b3b1c9689187cc2d6c0026a2b74a3f350346de8ad18933144da6a17a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.4430",
    "kind": "arxiv",
    "version": 1
  }
}