Pith Number

pith:JOT765P4

pith:2014:JOT765P4MVGIFNJPZLFVQAONYF

not attested not anchored not stored refs pending

Exponential decay of loop lengths in the loop $O(n)$ model with large $n$

Hugo Duminil-Copin, Ron Peled, Wojciech Samotij, Yinon Spinka

arxiv:1412.8326 v3 · 2014-12-29 · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JOT765P4MVGIFNJPZLFVQAONYF}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:01:08.957938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ba7ff75fc654c82b52fcacb5801cdc149d91f2f8d6ecfc3ff625255adcc1bbc

Aliases

arxiv: 1412.8326 · arxiv_version: 1412.8326v3 · doi: 10.48550/arxiv.1412.8326 · pith_short_12: JOT765P4MVGI · pith_short_16: JOT765P4MVGIFNJP · pith_short_8: JOT765P4

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/JOT765P4MVGIFNJPZLFVQAONYF \
  | 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: 4ba7ff75fc654c82b52fcacb5801cdc149d91f2f8d6ecfc3ff625255adcc1bbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37ffcf0646f1ffd9a5fc68f1d40b381669a3b883856fedf034b97827ab9cafe3",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2014-12-29T12:55:40Z",
    "title_canon_sha256": "ca85b2a971f9abe03588ec26bb9b122c9a7a90cb27408595760db6d50172b065"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8326",
    "kind": "arxiv",
    "version": 3
  }
}