Pith Number

pith:VY6AUQRB

pith:2022:VY6AUQRBPCOCFOHI6TVDL4DVIT

not attested not anchored not stored refs pending

Sharpness of Bernoulli percolation via couplings

Hugo Vanneuville

arxiv:2201.08223 v2 · 2022-01-20 · 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{VY6AUQRBPCOCFOHI6TVDL4DVIT}

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.

Cited by

2 papers in Pith

A random walk approach to high-dimensional critical phenomena

Receipt and verification

First computed	2026-07-05T06:03:44.694410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae3c0a4221789c22b8e8f4ea35f07544e44c4dc5c6f0257d375cf9a136cd62c9

Aliases

arxiv: 2201.08223 · arxiv_version: 2201.08223v2 · doi: 10.48550/arxiv.2201.08223 · pith_short_12: VY6AUQRBPCOC · pith_short_16: VY6AUQRBPCOCFOHI · pith_short_8: VY6AUQRB

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/VY6AUQRBPCOCFOHI6TVDL4DVIT \
  | 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: ae3c0a4221789c22b8e8f4ea35f07544e44c4dc5c6f0257d375cf9a136cd62c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78787fda9c11ed883b2e520c6a014b63d4410ecb26a2a9ca0dc187ddb9f1c87f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-01-20T15:27:54Z",
    "title_canon_sha256": "860d57e01069bb90f246d4925aa3f1c279cd36ffd0a0a7c7968a3f8c0a412f07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2201.08223",
    "kind": "arxiv",
    "version": 2
  }
}