Pith Number

pith:MHMMSFFT

pith:2018:MHMMSFFTSI3NJDZLMBFDXPYMVV

not attested not anchored not stored refs pending

Subcritical phase of $d$-dimensional Poisson-Boolean percolation and its vacant set

Aran Raoufi, Hugo Duminil-Copin, Vincent Tassion

arxiv:1805.00695 v2 · 2018-05-02 · math.PR · math-ph · math.CO · 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{MHMMSFFTSI3NJDZLMBFDXPYMVV}

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	2026-05-18T00:01:38.457145Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61d8c914b39236d48f2b604a3bbf0cad5bddccab63bd55294609b05021a35263

Aliases

arxiv: 1805.00695 · arxiv_version: 1805.00695v2 · doi: 10.48550/arxiv.1805.00695 · pith_short_12: MHMMSFFTSI3N · pith_short_16: MHMMSFFTSI3NJDZL · pith_short_8: MHMMSFFT

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/MHMMSFFTSI3NJDZLMBFDXPYMVV \
  | 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: 61d8c914b39236d48f2b604a3bbf0cad5bddccab63bd55294609b05021a35263

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9906b29737ddd4734fc0a741fba39efbac5f8ab70dbba8780346d8073701172b",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-05-02T09:42:46Z",
    "title_canon_sha256": "34d63315bb6a1d8a7ea382317a88b23cbd5cc16b4a3cad46fedebfbc4cd0ba4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.00695",
    "kind": "arxiv",
    "version": 2
  }
}