Pith Number

pith:BMUYLXLG

pith:2021:BMUYLXLGQOOWC7NGEADDRBYDKR

not attested not anchored not stored refs pending

Near critical scaling relations for planar Bernoulli percolation without differential inequalities

Hugo Duminil-Copin, Ioan Manolescu, Vincent Tassion

arxiv:2111.14414 v1 · 2021-11-29 · 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{BMUYLXLGQOOWC7NGEADDRBYDKR}

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

1 paper in Pith

Critical long-range percolation II: Low effective dimension

Receipt and verification

First computed	2026-07-05T03:35:51.579098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b2985dd66839d617da620063887035459024402220c0354d4f2cbe102db631b

Aliases

arxiv: 2111.14414 · arxiv_version: 2111.14414v1 · doi: 10.48550/arxiv.2111.14414 · pith_short_12: BMUYLXLGQOOW · pith_short_16: BMUYLXLGQOOWC7NG · pith_short_8: BMUYLXLG

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/BMUYLXLGQOOWC7NGEADDRBYDKR \
  | 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: 0b2985dd66839d617da620063887035459024402220c0354d4f2cbe102db631b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10b1e3d44b0a39940912518d723b2ba613584c7eb914ca2b0c996697b7dee80b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-11-29T09:52:29Z",
    "title_canon_sha256": "e087ae6b836c26820143b8e319b96ad356fb55e2a76a3caa9186fcbe287e5d51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.14414",
    "kind": "arxiv",
    "version": 1
  }
}