Pith Number

pith:45M4M3OC

pith:2013:45M4M3OC3OAREZY73C6TFL4E6I

not attested not anchored not stored refs pending

Basic properties of critical lognormal multiplicative chaos

Antti Kupiainen, Christian Webb, Eero Saksman, Julien Barral, Miika Nikula

arxiv:1303.4548 v4 · 2013-03-19 · 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{45M4M3OC3OAREZY73C6TFL4E6I}

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	2026-05-18T01:29:13.574992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e759c66dc2db8112671fd8bd32af84f2132b83f353967e2ee4cec02a27ecbfe6

Aliases

arxiv: 1303.4548 · arxiv_version: 1303.4548v4 · doi: 10.48550/arxiv.1303.4548 · pith_short_12: 45M4M3OC3OAR · pith_short_16: 45M4M3OC3OAREZY7 · pith_short_8: 45M4M3OC

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/45M4M3OC3OAREZY73C6TFL4E6I \
  | 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: e759c66dc2db8112671fd8bd32af84f2132b83f353967e2ee4cec02a27ecbfe6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a29c6a02b0d6f022d72d91124cd41f0e23d348503e11ecb86ddc2621b928e71e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-03-19T11:04:31Z",
    "title_canon_sha256": "682ba79e15c9fd2d40a3e7ee9a53ed9d0e1810fd169f0e7cb7b5c41a4a8bf577"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.4548",
    "kind": "arxiv",
    "version": 4
  }
}