Pith Number

pith:4TP6X4JK

pith:2003:4TP6X4JKFOEDNNLGCEVAYY5G3J

not attested not anchored not stored refs pending

The Brownian loop soup

Gregory F. Lawler, Wendelin Werner

arxiv:math/0304419 v1 · 2003-04-26 · 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{4TP6X4JKFOEDNNLGCEVAYY5G3J}

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	2026-05-18T00:40:08.946231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4dfebf12a2b8836b566112a0c63a6da7b297390339461ef7141289801dfe279

Aliases

arxiv: math/0304419 · arxiv_version: math/0304419v1 · doi: 10.48550/arxiv.math/0304419 · pith_short_12: 4TP6X4JKFOED · pith_short_16: 4TP6X4JKFOEDNNLG · pith_short_8: 4TP6X4JK

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/4TP6X4JKFOEDNNLGCEVAYY5G3J \
  | 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: e4dfebf12a2b8836b566112a0c63a6da7b297390339461ef7141289801dfe279

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0558f736fd169f2c14310b0ae5b5d5358da76609a44ac8532df54f870f90123b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2003-04-26T08:37:24Z",
    "title_canon_sha256": "12512fa6249531c731d235258bb71b8cf9428bd46fe7cccd0ee83197b6a281e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0304419",
    "kind": "arxiv",
    "version": 1
  }
}