Pith Number

pith:WPPZE2BF

pith:2019:WPPZE2BFLYHV7S4AK3Y2WGRQRH

not attested not anchored not stored refs pending

Brownian Loops, Layering Fields and Imaginary Gaussian Multiplicative Chaos

Alberto Gandolfi, Federico Camia, Giovanni Peccati, Tulasi Ram Reddy

arxiv:1908.05881 v2 · 2019-08-16 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPPZE2BFLYHV7S4AK3Y2WGRQRH}

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	2026-07-05T02:02:50.863392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3df9268255e0f5fcb8056f1ab1a3089e10640d2fe9b50e3f21171e583dd9f08

Aliases

arxiv: 1908.05881 · arxiv_version: 1908.05881v2 · doi: 10.48550/arxiv.1908.05881 · pith_short_12: WPPZE2BFLYHV · pith_short_16: WPPZE2BFLYHV7S4A · pith_short_8: WPPZE2BF

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/WPPZE2BFLYHV7S4AK3Y2WGRQRH \
  | 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: b3df9268255e0f5fcb8056f1ab1a3089e10640d2fe9b50e3f21171e583dd9f08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d549cbf40a50832508c0a8b162203e838cab93d47ac5a9d1a4bbd624588252a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-08-16T08:12:22Z",
    "title_canon_sha256": "560fb212904eb647f27119f2d21cb0299c2e0ba134dfbde11d522a09a17255f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.05881",
    "kind": "arxiv",
    "version": 2
  }
}