Pith Number

pith:GRRGPHVL

pith:2018:GRRGPHVLU4WXDPV7DON7JXBB2F

not attested not anchored not stored refs pending

Heat kernel for Liouville Brownian motion and Liouville graph distance

Fuxi Zhang, Jian Ding, Ofer Zeitouni

arxiv:1807.00422 v1 · 2018-07-02 · 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{GRRGPHVLU4WXDPV7DON7JXBB2F}

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	2026-05-17T23:44:13.354745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3462679eaba72d71bebf1b9bf4dc21d16039e6fc07903eeaaa61486dd1c105a6

Aliases

arxiv: 1807.00422 · arxiv_version: 1807.00422v1 · doi: 10.48550/arxiv.1807.00422 · pith_short_12: GRRGPHVLU4WX · pith_short_16: GRRGPHVLU4WXDPV7 · pith_short_8: GRRGPHVL

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/GRRGPHVLU4WXDPV7DON7JXBB2F \
  | 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: 3462679eaba72d71bebf1b9bf4dc21d16039e6fc07903eeaaa61486dd1c105a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4839aa7cbc9874a01a708285b38df667906bf484cf0a3b0ccc5dacc8e1891c71",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-07-02T00:26:16Z",
    "title_canon_sha256": "5d801c8e29912be903b004a8035c10a6a6676d064b5d362bc3e4731d8a288b6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.00422",
    "kind": "arxiv",
    "version": 1
  }
}