Pith Number

pith:NHZCHW3R

pith:2024:NHZCHW3RMJJTTBU5UCHF4S7B3Z

not attested not anchored not stored refs pending

An alternative approach for the mean-field behaviour of spread-out Bernoulli percolation in dimensions $d>6$

Hugo Duminil-Copin, Romain Panis

arxiv:2410.03647 v2 · 2024-10-04 · 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{NHZCHW3RMJJTTBU5UCHF4S7B3Z}

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 III: The upper critical dimension

Receipt and verification

First computed	2026-07-05T11:43:07.617007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69f223db71625339869da08e5e4be1de64911557308e64a1279990a29f148c3d

Aliases

arxiv: 2410.03647 · arxiv_version: 2410.03647v2 · doi: 10.48550/arxiv.2410.03647 · pith_short_12: NHZCHW3RMJJT · pith_short_16: NHZCHW3RMJJTTBU5 · pith_short_8: NHZCHW3R

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/NHZCHW3RMJJTTBU5UCHF4S7B3Z \
  | 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: 69f223db71625339869da08e5e4be1de64911557308e64a1279990a29f148c3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "804776eaae1ec61c20e6ef1b080494ecd81d1edf6e49277842635ed45a0da056",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-10-04T17:52:59Z",
    "title_canon_sha256": "7cb8f54b5ceedb8b0a7a42ce730b32d3201b372381aff35fb57df8ff945f0e84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.03647",
    "kind": "arxiv",
    "version": 2
  }
}