Pith Number

pith:VUY4JEMN

pith:2023:VUY4JEMNTJRHVPLW4FTHMKPJLQ

not attested not anchored not stored refs pending

Scaling limits and universality: Critical percolation on weighted graphs converging to an $L^3$ graphon

Jnaneshwar Baslingker, Nicolas Broutin, Sanchayan Sen, Shankar Bhamidi, Xuan Wang

arxiv:2303.10082 v3 · 2023-03-17 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VUY4JEMNTJRHVPLW4FTHMKPJLQ}

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	2026-07-05T08:34:46.475431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad31c4918d9a627abd76e1667629e95c0ea720c849f62ead26622049ab5576e8

Aliases

arxiv: 2303.10082 · arxiv_version: 2303.10082v3 · doi: 10.48550/arxiv.2303.10082 · pith_short_12: VUY4JEMNTJRH · pith_short_16: VUY4JEMNTJRHVPLW · pith_short_8: VUY4JEMN

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/VUY4JEMNTJRHVPLW4FTHMKPJLQ \
  | 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: ad31c4918d9a627abd76e1667629e95c0ea720c849f62ead26622049ab5576e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "759800d62dd4ea26923e31dfd26acd62c48ed709c33d1704c780c1a3f365f332",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-03-17T16:08:55Z",
    "title_canon_sha256": "acef9d5c9ae3312fce39e035ffd479fa8d4ae80008ff6d62153cfba1ad103bd3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.10082",
    "kind": "arxiv",
    "version": 3
  }
}